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<a href="qureg__expectval_8cpp.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno"> 1</span> <span class="comment">//------------------------------------------------------------------------------</span></div><div class="line"><a name="l00002"></a><span class="lineno"> 2</span> <span class="comment">// Copyright 2017 Intel Corporation</span></div><div class="line"><a name="l00003"></a><span class="lineno"> 3</span> <span class="comment">//</span></div><div class="line"><a name="l00004"></a><span class="lineno"> 4</span> <span class="comment">// Licensed under the Apache License, Version 2.0 (the "License");</span></div><div class="line"><a name="l00005"></a><span class="lineno"> 5</span> <span class="comment">// you may not use this file except in compliance with the License.</span></div><div class="line"><a name="l00006"></a><span class="lineno"> 6</span> <span class="comment">// You may obtain a copy of the License at</span></div><div class="line"><a name="l00007"></a><span class="lineno"> 7</span> <span class="comment">//</span></div><div class="line"><a name="l00008"></a><span class="lineno"> 8</span> <span class="comment">// http://www.apache.org/licenses/LICENSE-2.0</span></div><div class="line"><a name="l00009"></a><span class="lineno"> 9</span> <span class="comment">//</span></div><div class="line"><a name="l00010"></a><span class="lineno"> 10</span> <span class="comment">// Unless required by applicable law or agreed to in writing, software</span></div><div class="line"><a name="l00011"></a><span class="lineno"> 11</span> <span class="comment">// distributed under the License is distributed on an "AS IS" BASIS,</span></div><div class="line"><a name="l00012"></a><span class="lineno"> 12</span> <span class="comment">// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.</span></div><div class="line"><a name="l00013"></a><span class="lineno"> 13</span> <span class="comment">// See the License for the specific language governing permissions and</span></div><div class="line"><a name="l00014"></a><span class="lineno"> 14</span> <span class="comment">// limitations under the License.</span></div><div class="line"><a name="l00015"></a><span class="lineno"> 15</span> <span class="comment">//------------------------------------------------------------------------------</span></div><div class="line"><a name="l00016"></a><span class="lineno"> 16</span> </div><div class="line"><a name="l00017"></a><span class="lineno"><a class="line" href="qureg__expectval_8cpp.html#a2f7a179061239718962640b89e378dbe"> 17</a></span> <span class="preprocessor">#define __ONLY_NORMALIZED_STATES__</span></div><div class="line"><a name="l00018"></a><span class="lineno"> 18</span> </div><div class="line"><a name="l00019"></a><span class="lineno"> 19</span> <span class="preprocessor">#include "<a class="code" href="qureg_8hpp.html">qureg.hpp</a>"</span></div><div class="line"><a name="l00020"></a><span class="lineno"> 20</span> </div><div class="line"><a name="l00023"></a><span class="lineno"> 23</span> </div><div class="line"><a name="l00026"></a><span class="lineno"> 26</span> </div><div class="line"><a name="l00034"></a><span class="lineno"> 34</span> <span class="comment">//------------------------------------------------------------------------------</span></div><div class="line"><a name="l00035"></a><span class="lineno"> 35</span> <span class="keyword">template</span> <<span class="keyword">class</span> Type></div><div class="line"><a name="l00036"></a><span class="lineno"><a class="line" href="group__qureg.html#ga0ae1cb5b712e6ab145581a76b1fae63c"> 36</a></span> <span class="keywordtype">void</span> <a class="code" href="group__qureg.html#ga0ae1cb5b712e6ab145581a76b1fae63c">QbitRegister<Type>::expectationValueX</a>(<span class="keywordtype">unsigned</span> qubit, <a class="code" href="classQbitRegister.html#ae523cb97079963ca2ba8edaf947b1ca7">BaseType</a> &sum, <a class="code" href="classQbitRegister.html#ae523cb97079963ca2ba8edaf947b1ca7">BaseType</a> coeff)</div><div class="line"><a name="l00037"></a><span class="lineno"> 37</span> {</div><div class="line"><a name="l00038"></a><span class="lineno"> 38</span> <span class="comment">// compute the iexpectation value <psi|X|psi> = <psi|H.Z.H|psi></span></div><div class="line"><a name="l00039"></a><span class="lineno"> 39</span>  applyHadamard(qubit);</div><div class="line"><a name="l00040"></a><span class="lineno"> 40</span>  sum += coeff*(1. - 2.*getProbability(qubit));</div><div class="line"><a name="l00041"></a><span class="lineno"> 41</span> <span class="comment">// recover the initial state |psi></span></div><div class="line"><a name="l00042"></a><span class="lineno"> 42</span>  applyHadamard(qubit);</div><div class="line"><a name="l00043"></a><span class="lineno"> 43</span> }</div><div class="line"><a name="l00044"></a><span class="lineno"> 44</span> </div><div class="line"><a name="l00045"></a><span class="lineno"> 45</span> </div><div class="line"><a name="l00046"></a><span class="lineno"> 46</span> <span class="preprocessor">#if 0</span></div><div class="line"><a name="l00047"></a><span class="lineno"> 47</span> <span class="comment">//------------------------------------------------------------------------------</span></div><div class="line"><a name="l00048"></a><span class="lineno"> 48</span> <span class="keyword">template</span> <<span class="keyword">class</span> Type></div><div class="line"><a name="l00049"></a><span class="lineno"> 49</span> <span class="keywordtype">void</span> <a class="code" href="group__qureg.html#ga0ae1cb5b712e6ab145581a76b1fae63c">QbitRegister<Type>::expectationValueX</a>(<span class="keywordtype">unsigned</span> qubit, <a class="code" href="classQbitRegister.html#ae523cb97079963ca2ba8edaf947b1ca7">BaseType</a> &sum)</div><div class="line"><a name="l00050"></a><span class="lineno"> 50</span> {</div><div class="line"><a name="l00051"></a><span class="lineno"> 51</span> <span class="preprocessor">#ifdef __ONLY_NORMALIZED_STATES__</span></div><div class="line"><a name="l00052"></a><span class="lineno"> 52</span>  <a class="code" href="classQbitRegister.html#ae523cb97079963ca2ba8edaf947b1ca7">BaseType</a> initial_norm = 1.;</div><div class="line"><a name="l00053"></a><span class="lineno"> 53</span> <span class="preprocessor">#else</span></div><div class="line"><a name="l00054"></a><span class="lineno"> 54</span>  <a class="code" href="classQbitRegister.html#ae523cb97079963ca2ba8edaf947b1ca7">BaseType</a> initial_norm = computenorm();</div><div class="line"><a name="l00055"></a><span class="lineno"> 55</span> <span class="preprocessor">#endif</span></div><div class="line"><a name="l00056"></a><span class="lineno"> 56</span> </div><div class="line"><a name="l00057"></a><span class="lineno"> 57</span> <span class="comment">// given initial qureg state in |psi></span></div><div class="line"><a name="l00058"></a><span class="lineno"> 58</span> <span class="comment">// compute the non-normalized vector corresponding to (2+X)|psi></span></div><div class="line"><a name="l00059"></a><span class="lineno"> 59</span>  <a class="code" href="classopenqu_1_1TinyMatrix.html">openqu::TinyMatrix<Type, 2, 2, 32></a> x_plus_2id;</div><div class="line"><a name="l00060"></a><span class="lineno"> 60</span>  x_plus_2id(0, 1) = x_plus_2id(1, 0) = <a class="code" href="interface__api__memory_8cpp.html#a8a7796dc492015686a15b44dfa64e347">Type</a>(1., 0.);</div><div class="line"><a name="l00061"></a><span class="lineno"> 61</span>  x_plus_2id(0, 0) = x_plus_2id(1, 1) = <a class="code" href="interface__api__memory_8cpp.html#a8a7796dc492015686a15b44dfa64e347">Type</a>(2., 0.);</div><div class="line"><a name="l00062"></a><span class="lineno"> 62</span>  apply1QubitGate(qubit, x_plus_2id);</div><div class="line"><a name="l00063"></a><span class="lineno"> 63</span> </div><div class="line"><a name="l00064"></a><span class="lineno"> 64</span> <span class="comment">// update sum adding <psi|X|psi></span></div><div class="line"><a name="l00065"></a><span class="lineno"> 65</span>  <a class="code" href="classQbitRegister.html#ae523cb97079963ca2ba8edaf947b1ca7">BaseType</a> final_norm = computenorm();</div><div class="line"><a name="l00066"></a><span class="lineno"> 66</span>  sum += (final_norm*final_norm - 5.*initial_norm*initial_norm)/4.;</div><div class="line"><a name="l00067"></a><span class="lineno"> 67</span> </div><div class="line"><a name="l00068"></a><span class="lineno"> 68</span> <span class="comment">// undo the computation to recover the initial state |psi></span></div><div class="line"><a name="l00069"></a><span class="lineno"> 69</span>  <a class="code" href="classopenqu_1_1TinyMatrix.html">openqu::TinyMatrix<Type, 2, 2, 32></a> inverse;</div><div class="line"><a name="l00070"></a><span class="lineno"> 70</span>  inverse(0, 1) = inverse(1, 0) = <a class="code" href="interface__api__memory_8cpp.html#a8a7796dc492015686a15b44dfa64e347">Type</a>(-1./3., 0.);</div><div class="line"><a name="l00071"></a><span class="lineno"> 71</span>  inverse(0, 0) = inverse(1, 1) = <a class="code" href="interface__api__memory_8cpp.html#a8a7796dc492015686a15b44dfa64e347">Type</a>( 2./3., 0.);</div><div class="line"><a name="l00072"></a><span class="lineno"> 72</span>  apply1QubitGate(qubit, inverse);</div><div class="line"><a name="l00073"></a><span class="lineno"> 73</span> }</div><div class="line"><a name="l00074"></a><span class="lineno"> 74</span> <span class="preprocessor">#endif</span></div><div class="line"><a name="l00075"></a><span class="lineno"> 75</span> </div><div class="line"><a name="l00076"></a><span class="lineno"> 76</span> </div><div class="line"><a name="l00084"></a><span class="lineno"> 84</span> <span class="comment">//------------------------------------------------------------------------------</span></div><div class="line"><a name="l00085"></a><span class="lineno"> 85</span> <span class="keyword">template</span> <<span class="keyword">class</span> Type></div><div class="line"><a name="l00086"></a><span class="lineno"><a class="line" href="group__qureg.html#ga24e31d763d955038cc666d3f187b4b8c"> 86</a></span> <span class="keywordtype">void</span> <a class="code" href="group__qureg.html#ga24e31d763d955038cc666d3f187b4b8c">QbitRegister<Type>::expectationValueY</a>(<span class="keywordtype">unsigned</span> qubit, <a class="code" href="classQbitRegister.html#ae523cb97079963ca2ba8edaf947b1ca7">BaseType</a> &sum, <a class="code" href="classQbitRegister.html#ae523cb97079963ca2ba8edaf947b1ca7">BaseType</a> coeff)</div><div class="line"><a name="l00087"></a><span class="lineno"> 87</span> {</div><div class="line"><a name="l00088"></a><span class="lineno"> 88</span> <span class="comment">// G is matrix from change of basis Y --> Z , such that G^dagger.Z.G=Y</span></div><div class="line"><a name="l00089"></a><span class="lineno"> 89</span>  <a class="code" href="classopenqu_1_1TinyMatrix.html">openqu::TinyMatrix<Type, 2, 2, 32></a> G;</div><div class="line"><a name="l00090"></a><span class="lineno"> 90</span>  <a class="code" href="classQbitRegister.html#ae523cb97079963ca2ba8edaf947b1ca7">BaseType</a> f = 1. / std::sqrt(2.);</div><div class="line"><a name="l00091"></a><span class="lineno"> 91</span>  G(0, 0) = G(1, 0) = <a class="code" href="interface__api__memory_8cpp.html#a8a7796dc492015686a15b44dfa64e347">Type</a>(f, 0.);</div><div class="line"><a name="l00092"></a><span class="lineno"> 92</span>  G(0, 1) = <a class="code" href="interface__api__memory_8cpp.html#a8a7796dc492015686a15b44dfa64e347">Type</a>(0.,-f);</div><div class="line"><a name="l00093"></a><span class="lineno"> 93</span>  G(1, 1) = <a class="code" href="interface__api__memory_8cpp.html#a8a7796dc492015686a15b44dfa64e347">Type</a>(0., f);</div><div class="line"><a name="l00094"></a><span class="lineno"> 94</span> <span class="comment">// compute the iexpectation value <psi|Y|psi> = <psi|G^dagger.Z.G|psi></span></div><div class="line"><a name="l00095"></a><span class="lineno"> 95</span>  apply1QubitGate(qubit,G);</div><div class="line"><a name="l00096"></a><span class="lineno"> 96</span>  sum += coeff*(1. - 2.*getProbability(qubit));</div><div class="line"><a name="l00097"></a><span class="lineno"> 97</span> <span class="comment">// recover the initial state |psi> by applying G^dagger</span></div><div class="line"><a name="l00098"></a><span class="lineno"> 98</span>  G(0, 0) = G(0, 1) = <a class="code" href="interface__api__memory_8cpp.html#a8a7796dc492015686a15b44dfa64e347">Type</a>(f, 0.);</div><div class="line"><a name="l00099"></a><span class="lineno"> 99</span>  G(1, 0) = <a class="code" href="interface__api__memory_8cpp.html#a8a7796dc492015686a15b44dfa64e347">Type</a>(0., f);</div><div class="line"><a name="l00100"></a><span class="lineno"> 100</span>  G(1, 1) = <a class="code" href="interface__api__memory_8cpp.html#a8a7796dc492015686a15b44dfa64e347">Type</a>(0.,-f);</div><div class="line"><a name="l00101"></a><span class="lineno"> 101</span>  apply1QubitGate(qubit,G);</div><div class="line"><a name="l00102"></a><span class="lineno"> 102</span> }</div><div class="line"><a name="l00103"></a><span class="lineno"> 103</span> </div><div class="line"><a name="l00104"></a><span class="lineno"> 104</span> </div><div class="line"><a name="l00112"></a><span class="lineno"> 112</span> <span class="comment">//------------------------------------------------------------------------------</span></div><div class="line"><a name="l00113"></a><span class="lineno"> 113</span> <span class="keyword">template</span> <<span class="keyword">class</span> Type></div><div class="line"><a name="l00114"></a><span class="lineno"><a class="line" href="group__qureg.html#ga6e6e962a8da5782537f14c55850f46c7"> 114</a></span> <span class="keywordtype">void</span> <a class="code" href="group__qureg.html#ga6e6e962a8da5782537f14c55850f46c7">QbitRegister<Type>::expectationValueZ</a>(<span class="keywordtype">unsigned</span> qubit, <a class="code" href="classQbitRegister.html#ae523cb97079963ca2ba8edaf947b1ca7">BaseType</a> &sum, <a class="code" href="classQbitRegister.html#ae523cb97079963ca2ba8edaf947b1ca7">BaseType</a> coeff)</div><div class="line"><a name="l00115"></a><span class="lineno"> 115</span> {</div><div class="line"><a name="l00116"></a><span class="lineno"> 116</span>  sum += coeff*(1. - 2.*getProbability(qubit));</div><div class="line"><a name="l00117"></a><span class="lineno"> 117</span> }</div><div class="line"><a name="l00118"></a><span class="lineno"> 118</span> </div><div class="line"><a name="l00119"></a><span class="lineno"> 119</span> </div><div class="line"><a name="l00128"></a><span class="lineno"> 128</span> <span class="comment">//------------------------------------------------------------------------------</span></div><div class="line"><a name="l00129"></a><span class="lineno"> 129</span> <span class="keyword">template</span> <<span class="keyword">class</span> Type></div><div class="line"><a name="l00130"></a><span class="lineno"><a class="line" href="group__qureg.html#gafccc7f7f54d595c7582f19b7ea0f8aac"> 130</a></span> <span class="keywordtype">void</span> <a class="code" href="group__qureg.html#gafccc7f7f54d595c7582f19b7ea0f8aac">QbitRegister<Type>::expectationValueXX</a>(<span class="keywordtype">unsigned</span> qubit, <span class="keywordtype">unsigned</span> qubit2, <a class="code" href="classQbitRegister.html#ae523cb97079963ca2ba8edaf947b1ca7">BaseType</a> &sum, <a class="code" href="classQbitRegister.html#ae523cb97079963ca2ba8edaf947b1ca7">BaseType</a> coeff)</div><div class="line"><a name="l00131"></a><span class="lineno"> 131</span> {</div><div class="line"><a name="l00132"></a><span class="lineno"> 132</span> <span class="preprocessor">#ifdef __ONLY_NORMALIZED_STATES__</span></div><div class="line"><a name="l00133"></a><span class="lineno"> 133</span>  <a class="code" href="classQbitRegister.html#ae523cb97079963ca2ba8edaf947b1ca7">BaseType</a> initial_norm = 1.;</div><div class="line"><a name="l00134"></a><span class="lineno"> 134</span> <span class="preprocessor">#else</span></div><div class="line"><a name="l00135"></a><span class="lineno"> 135</span>  <a class="code" href="classQbitRegister.html#ae523cb97079963ca2ba8edaf947b1ca7">BaseType</a> initial_norm = computenorm();</div><div class="line"><a name="l00136"></a><span class="lineno"> 136</span> <span class="preprocessor">#endif</span></div><div class="line"><a name="l00137"></a><span class="lineno"> 137</span> </div><div class="line"><a name="l00138"></a><span class="lineno"> 138</span> <span class="comment">// given initial qureg state in |psi></span></div><div class="line"><a name="l00139"></a><span class="lineno"> 139</span> <span class="comment">// compute the non-normalized vector corresponding to (2+XX)|psi></span></div><div class="line"><a name="l00140"></a><span class="lineno"> 140</span>  <a class="code" href="classopenqu_1_1TinyMatrix.html">openqu::TinyMatrix<Type, 4, 4, 32></a> xx_plus_2id;</div><div class="line"><a name="l00141"></a><span class="lineno"> 141</span>  xx_plus_2id(0, 1) = xx_plus_2id(0, 2) = xx_plus_2id(1, 0) = xx_plus_2id(1, 3) = <a class="code" href="interface__api__memory_8cpp.html#a8a7796dc492015686a15b44dfa64e347">Type</a>(0., 0.);</div><div class="line"><a name="l00142"></a><span class="lineno"> 142</span>  xx_plus_2id(2, 0) = xx_plus_2id(2, 3) = xx_plus_2id(3, 1) = xx_plus_2id(3, 2) = <a class="code" href="interface__api__memory_8cpp.html#a8a7796dc492015686a15b44dfa64e347">Type</a>(0., 0.);</div><div class="line"><a name="l00143"></a><span class="lineno"> 143</span>  xx_plus_2id(0, 3) = xx_plus_2id(1, 2) = xx_plus_2id(2, 1) = xx_plus_2id(3, 0) = <a class="code" href="interface__api__memory_8cpp.html#a8a7796dc492015686a15b44dfa64e347">Type</a>(1., 0.);</div><div class="line"><a name="l00144"></a><span class="lineno"> 144</span>  xx_plus_2id(0, 0) = xx_plus_2id(1, 1) = xx_plus_2id(2, 2) = xx_plus_2id(3, 3) = <a class="code" href="interface__api__memory_8cpp.html#a8a7796dc492015686a15b44dfa64e347">Type</a>(2., 0.);</div><div class="line"><a name="l00145"></a><span class="lineno"> 145</span>  apply2QubitGate(qubit, qubit2, xx_plus_2id);</div><div class="line"><a name="l00146"></a><span class="lineno"> 146</span> </div><div class="line"><a name="l00147"></a><span class="lineno"> 147</span> <span class="comment">// update sum adding <psi|XX|psi></span></div><div class="line"><a name="l00148"></a><span class="lineno"> 148</span>  <a class="code" href="classQbitRegister.html#ae523cb97079963ca2ba8edaf947b1ca7">BaseType</a> final_norm = computenorm();</div><div class="line"><a name="l00149"></a><span class="lineno"> 149</span>  sum += coeff*(final_norm*final_norm - 5.*initial_norm*initial_norm)/4.;</div><div class="line"><a name="l00150"></a><span class="lineno"> 150</span> </div><div class="line"><a name="l00151"></a><span class="lineno"> 151</span> <span class="comment">// undo the computation to recover the initial state |psi></span></div><div class="line"><a name="l00152"></a><span class="lineno"> 152</span>  <a class="code" href="classopenqu_1_1TinyMatrix.html">openqu::TinyMatrix<Type, 4, 4, 32></a> inverse;</div><div class="line"><a name="l00153"></a><span class="lineno"> 153</span>  inverse(0, 1) = inverse(0, 2) = inverse(1, 0) = inverse(1, 3) = <a class="code" href="interface__api__memory_8cpp.html#a8a7796dc492015686a15b44dfa64e347">Type</a>(0., 0.);</div><div class="line"><a name="l00154"></a><span class="lineno"> 154</span>  inverse(2, 0) = inverse(2, 3) = inverse(3, 1) = inverse(3, 2) = <a class="code" href="interface__api__memory_8cpp.html#a8a7796dc492015686a15b44dfa64e347">Type</a>(0., 0.);</div><div class="line"><a name="l00155"></a><span class="lineno"> 155</span>  inverse(0, 3) = inverse(1, 2) = inverse(2, 1) = inverse(3, 0) = <a class="code" href="interface__api__memory_8cpp.html#a8a7796dc492015686a15b44dfa64e347">Type</a>(-1./3., 0.);</div><div class="line"><a name="l00156"></a><span class="lineno"> 156</span>  inverse(0, 0) = inverse(1, 1) = inverse(2, 2) = inverse(3, 3) = <a class="code" href="interface__api__memory_8cpp.html#a8a7796dc492015686a15b44dfa64e347">Type</a>( 2./3., 0.);</div><div class="line"><a name="l00157"></a><span class="lineno"> 157</span>  apply2QubitGate(qubit, qubit2, inverse);</div><div class="line"><a name="l00158"></a><span class="lineno"> 158</span> }</div><div class="line"><a name="l00159"></a><span class="lineno"> 159</span> </div><div class="line"><a name="l00160"></a><span class="lineno"> 160</span> </div><div class="line"><a name="l00169"></a><span class="lineno"> 169</span> <span class="comment">//------------------------------------------------------------------------------</span></div><div class="line"><a name="l00170"></a><span class="lineno"> 170</span> <span class="comment">// TODO : check how the basis is it is: 00-01-10-11 or 00-10-01-11 !!!!</span></div><div class="line"><a name="l00171"></a><span class="lineno"> 171</span> <span class="comment">// this code uses the standard 00-01-10-11 despite this being opposite to backend storage convention</span></div><div class="line"><a name="l00172"></a><span class="lineno"> 172</span> <span class="keyword">template</span> <<span class="keyword">class</span> Type></div><div class="line"><a name="l00173"></a><span class="lineno"><a class="line" href="group__qureg.html#ga6efb952da150825c4168b99095b89303"> 173</a></span> <span class="keywordtype">void</span> <a class="code" href="group__qureg.html#ga6efb952da150825c4168b99095b89303">QbitRegister<Type>::expectationValueYX</a>(<span class="keywordtype">unsigned</span> qubit, <span class="keywordtype">unsigned</span> qubit2, <a class="code" href="classQbitRegister.html#ae523cb97079963ca2ba8edaf947b1ca7">BaseType</a> &sum, <a class="code" href="classQbitRegister.html#ae523cb97079963ca2ba8edaf947b1ca7">BaseType</a> coeff)</div><div class="line"><a name="l00174"></a><span class="lineno"> 174</span> {</div><div class="line"><a name="l00175"></a><span class="lineno"> 175</span> <span class="preprocessor">#ifdef __ONLY_NORMALIZED_STATES__</span></div><div class="line"><a name="l00176"></a><span class="lineno"> 176</span>  <a class="code" href="classQbitRegister.html#ae523cb97079963ca2ba8edaf947b1ca7">BaseType</a> initial_norm = 1.;</div><div class="line"><a name="l00177"></a><span class="lineno"> 177</span> <span class="preprocessor">#else</span></div><div class="line"><a name="l00178"></a><span class="lineno"> 178</span>  <a class="code" href="classQbitRegister.html#ae523cb97079963ca2ba8edaf947b1ca7">BaseType</a> initial_norm = computenorm();</div><div class="line"><a name="l00179"></a><span class="lineno"> 179</span> <span class="preprocessor">#endif</span></div><div class="line"><a name="l00180"></a><span class="lineno"> 180</span> </div><div class="line"><a name="l00181"></a><span class="lineno"> 181</span> <span class="comment">// given initial qureg state in |psi></span></div><div class="line"><a name="l00182"></a><span class="lineno"> 182</span> <span class="comment">// compute the non-normalized vector corresponding to (2+XY)|psi></span></div><div class="line"><a name="l00183"></a><span class="lineno"> 183</span>  <a class="code" href="classopenqu_1_1TinyMatrix.html">openqu::TinyMatrix<Type, 4, 4, 32></a> xy_plus_2id;</div><div class="line"><a name="l00184"></a><span class="lineno"> 184</span>  xy_plus_2id(0, 1) = xy_plus_2id(0, 2) = xy_plus_2id(1, 0) = xy_plus_2id(1, 3) = <a class="code" href="interface__api__memory_8cpp.html#a8a7796dc492015686a15b44dfa64e347">Type</a>(0., 0.);</div><div class="line"><a name="l00185"></a><span class="lineno"> 185</span>  xy_plus_2id(2, 0) = xy_plus_2id(2, 3) = xy_plus_2id(3, 1) = xy_plus_2id(3, 2) = <a class="code" href="interface__api__memory_8cpp.html#a8a7796dc492015686a15b44dfa64e347">Type</a>(0., 0.);</div><div class="line"><a name="l00186"></a><span class="lineno"> 186</span>  xy_plus_2id(0, 3) = xy_plus_2id(1, 2) = <a class="code" href="interface__api__memory_8cpp.html#a8a7796dc492015686a15b44dfa64e347">Type</a>(0.,-1.);</div><div class="line"><a name="l00187"></a><span class="lineno"> 187</span>  xy_plus_2id(2, 1) = xy_plus_2id(3, 0) = <a class="code" href="interface__api__memory_8cpp.html#a8a7796dc492015686a15b44dfa64e347">Type</a>(0., 1.);</div><div class="line"><a name="l00188"></a><span class="lineno"> 188</span>  xy_plus_2id(0, 0) = xy_plus_2id(1, 1) = xy_plus_2id(2, 2) = xy_plus_2id(3, 3) = <a class="code" href="interface__api__memory_8cpp.html#a8a7796dc492015686a15b44dfa64e347">Type</a>(2., 0.);</div><div class="line"><a name="l00189"></a><span class="lineno"> 189</span>  apply2QubitGate(qubit, qubit2, xy_plus_2id);</div><div class="line"><a name="l00190"></a><span class="lineno"> 190</span> </div><div class="line"><a name="l00191"></a><span class="lineno"> 191</span> <span class="comment">// update sum adding <psi|XY|psi></span></div><div class="line"><a name="l00192"></a><span class="lineno"> 192</span>  <a class="code" href="classQbitRegister.html#ae523cb97079963ca2ba8edaf947b1ca7">BaseType</a> final_norm = computenorm();</div><div class="line"><a name="l00193"></a><span class="lineno"> 193</span>  sum += coeff*(final_norm*final_norm - 5.*initial_norm*initial_norm)/4.;</div><div class="line"><a name="l00194"></a><span class="lineno"> 194</span> </div><div class="line"><a name="l00195"></a><span class="lineno"> 195</span> <span class="comment">// undo the computation to recover the initial state |psi></span></div><div class="line"><a name="l00196"></a><span class="lineno"> 196</span>  <a class="code" href="classopenqu_1_1TinyMatrix.html">openqu::TinyMatrix<Type, 4, 4, 32></a> inverse;</div><div class="line"><a name="l00197"></a><span class="lineno"> 197</span>  inverse(0, 1) = inverse(0, 2) = inverse(1, 0) = inverse(1, 3) = <a class="code" href="interface__api__memory_8cpp.html#a8a7796dc492015686a15b44dfa64e347">Type</a>(0., 0.);</div><div class="line"><a name="l00198"></a><span class="lineno"> 198</span>  inverse(2, 0) = inverse(2, 3) = inverse(3, 1) = inverse(3, 2) = <a class="code" href="interface__api__memory_8cpp.html#a8a7796dc492015686a15b44dfa64e347">Type</a>(0., 0.);</div><div class="line"><a name="l00199"></a><span class="lineno"> 199</span>  inverse(0, 3) = inverse(1, 2) = <a class="code" href="interface__api__memory_8cpp.html#a8a7796dc492015686a15b44dfa64e347">Type</a>(0., 1./3.);</div><div class="line"><a name="l00200"></a><span class="lineno"> 200</span>  inverse(2, 1) = inverse(3, 0) = <a class="code" href="interface__api__memory_8cpp.html#a8a7796dc492015686a15b44dfa64e347">Type</a>(0.,-1./3.);</div><div class="line"><a name="l00201"></a><span class="lineno"> 201</span>  inverse(0, 0) = inverse(1, 1) = inverse(2, 2) = inverse(3, 3) = <a class="code" href="interface__api__memory_8cpp.html#a8a7796dc492015686a15b44dfa64e347">Type</a>( 2./3., 0.);</div><div class="line"><a name="l00202"></a><span class="lineno"> 202</span>  apply2QubitGate(qubit, qubit2, inverse);</div><div class="line"><a name="l00203"></a><span class="lineno"> 203</span> }</div><div class="line"><a name="l00204"></a><span class="lineno"> 204</span> </div><div class="line"><a name="l00205"></a><span class="lineno"> 205</span> </div><div class="line"><a name="l00214"></a><span class="lineno"> 214</span> <span class="comment">//------------------------------------------------------------------------------</span></div><div class="line"><a name="l00215"></a><span class="lineno"> 215</span> <span class="comment">// TODO : check how the basis is it is: 00-01-10-11 or 00-10-01-11 !!!!</span></div><div class="line"><a name="l00216"></a><span class="lineno"> 216</span> <span class="comment">// this code uses the standard 00-01-10-11 despite this being opposite to backend storage convention</span></div><div class="line"><a name="l00217"></a><span class="lineno"> 217</span> <span class="keyword">template</span> <<span class="keyword">class</span> Type></div><div class="line"><a name="l00218"></a><span class="lineno"><a class="line" href="group__qureg.html#ga6a8dcf0d8e8fc2f84166944d7c7a62f2"> 218</a></span> <span class="keywordtype">void</span> <a class="code" href="group__qureg.html#ga6a8dcf0d8e8fc2f84166944d7c7a62f2">QbitRegister<Type>::expectationValueZX</a>(<span class="keywordtype">unsigned</span> qubit, <span class="keywordtype">unsigned</span> qubit2, <a class="code" href="classQbitRegister.html#ae523cb97079963ca2ba8edaf947b1ca7">BaseType</a> &sum, <a class="code" href="classQbitRegister.html#ae523cb97079963ca2ba8edaf947b1ca7">BaseType</a> coeff)</div><div class="line"><a name="l00219"></a><span class="lineno"> 219</span> {</div><div class="line"><a name="l00220"></a><span class="lineno"> 220</span> <span class="preprocessor">#ifdef __ONLY_NORMALIZED_STATES__</span></div><div class="line"><a name="l00221"></a><span class="lineno"> 221</span>  <a class="code" href="classQbitRegister.html#ae523cb97079963ca2ba8edaf947b1ca7">BaseType</a> initial_norm = 1.;</div><div class="line"><a name="l00222"></a><span class="lineno"> 222</span> <span class="preprocessor">#else</span></div><div class="line"><a name="l00223"></a><span class="lineno"> 223</span>  <a class="code" href="classQbitRegister.html#ae523cb97079963ca2ba8edaf947b1ca7">BaseType</a> initial_norm = computenorm();</div><div class="line"><a name="l00224"></a><span class="lineno"> 224</span> <span class="preprocessor">#endif</span></div><div class="line"><a name="l00225"></a><span class="lineno"> 225</span> </div><div class="line"><a name="l00226"></a><span class="lineno"> 226</span> <span class="comment">// given initial qureg state in |psi></span></div><div class="line"><a name="l00227"></a><span class="lineno"> 227</span> <span class="comment">// compute the non-normalized vector corresponding to (2+XZ)|psi></span></div><div class="line"><a name="l00228"></a><span class="lineno"> 228</span>  <a class="code" href="classopenqu_1_1TinyMatrix.html">openqu::TinyMatrix<Type, 4, 4, 32></a> xz_plus_2id;</div><div class="line"><a name="l00229"></a><span class="lineno"> 229</span>  xz_plus_2id(0, 2) = xz_plus_2id(0, 3) = xz_plus_2id(1, 2) = xz_plus_2id(1, 3) = <a class="code" href="interface__api__memory_8cpp.html#a8a7796dc492015686a15b44dfa64e347">Type</a>(0., 0.);</div><div class="line"><a name="l00230"></a><span class="lineno"> 230</span>  xz_plus_2id(2, 0) = xz_plus_2id(2, 1) = xz_plus_2id(3, 0) = xz_plus_2id(3, 1) = <a class="code" href="interface__api__memory_8cpp.html#a8a7796dc492015686a15b44dfa64e347">Type</a>(0., 0.);</div><div class="line"><a name="l00231"></a><span class="lineno"> 231</span>  xz_plus_2id(0, 1) = xz_plus_2id(1, 0) = <a class="code" href="interface__api__memory_8cpp.html#a8a7796dc492015686a15b44dfa64e347">Type</a>( 1., 0.);</div><div class="line"><a name="l00232"></a><span class="lineno"> 232</span>  xz_plus_2id(2, 3) = xz_plus_2id(3, 2) = <a class="code" href="interface__api__memory_8cpp.html#a8a7796dc492015686a15b44dfa64e347">Type</a>(-1., 0.);</div><div class="line"><a name="l00233"></a><span class="lineno"> 233</span>  xz_plus_2id(0, 0) = xz_plus_2id(1, 1) = xz_plus_2id(2, 2) = xz_plus_2id(3, 3) = <a class="code" href="interface__api__memory_8cpp.html#a8a7796dc492015686a15b44dfa64e347">Type</a>(2., 0.);</div><div class="line"><a name="l00234"></a><span class="lineno"> 234</span>  apply2QubitGate(qubit, qubit2, xz_plus_2id);</div><div class="line"><a name="l00235"></a><span class="lineno"> 235</span> </div><div class="line"><a name="l00236"></a><span class="lineno"> 236</span> <span class="comment">// update sum adding <psi|XZ|psi></span></div><div class="line"><a name="l00237"></a><span class="lineno"> 237</span>  <a class="code" href="classQbitRegister.html#ae523cb97079963ca2ba8edaf947b1ca7">BaseType</a> final_norm = computenorm();</div><div class="line"><a name="l00238"></a><span class="lineno"> 238</span>  sum += coeff*(final_norm*final_norm - 5.*initial_norm*initial_norm)/4.;</div><div class="line"><a name="l00239"></a><span class="lineno"> 239</span> </div><div class="line"><a name="l00240"></a><span class="lineno"> 240</span> <span class="comment">// undo the computation to recover the initial state |psi></span></div><div class="line"><a name="l00241"></a><span class="lineno"> 241</span>  <a class="code" href="classopenqu_1_1TinyMatrix.html">openqu::TinyMatrix<Type, 4, 4, 32></a> inverse;</div><div class="line"><a name="l00242"></a><span class="lineno"> 242</span>  inverse(0, 2) = inverse(0, 3) = inverse(1, 2) = inverse(1, 3) = <a class="code" href="interface__api__memory_8cpp.html#a8a7796dc492015686a15b44dfa64e347">Type</a>(0., 0.);</div><div class="line"><a name="l00243"></a><span class="lineno"> 243</span>  inverse(2, 0) = inverse(2, 1) = inverse(3, 0) = inverse(3, 1) = <a class="code" href="interface__api__memory_8cpp.html#a8a7796dc492015686a15b44dfa64e347">Type</a>(0., 0.);</div><div class="line"><a name="l00244"></a><span class="lineno"> 244</span>  inverse(0, 1) = inverse(1, 0) = <a class="code" href="interface__api__memory_8cpp.html#a8a7796dc492015686a15b44dfa64e347">Type</a>(-1./3., 0.);</div><div class="line"><a name="l00245"></a><span class="lineno"> 245</span>  inverse(2, 3) = inverse(3, 2) = <a class="code" href="interface__api__memory_8cpp.html#a8a7796dc492015686a15b44dfa64e347">Type</a>( 1./3., 0.);</div><div class="line"><a name="l00246"></a><span class="lineno"> 246</span>  inverse(0, 0) = inverse(1, 1) = inverse(2, 2) = inverse(3, 3) = <a class="code" href="interface__api__memory_8cpp.html#a8a7796dc492015686a15b44dfa64e347">Type</a>( 2./3., 0.);</div><div class="line"><a name="l00247"></a><span class="lineno"> 247</span>  apply2QubitGate(qubit, qubit2, inverse);</div><div class="line"><a name="l00248"></a><span class="lineno"> 248</span> }</div><div class="line"><a name="l00249"></a><span class="lineno"> 249</span> </div><div class="line"><a name="l00250"></a><span class="lineno"> 250</span> </div><div class="line"><a name="l00259"></a><span class="lineno"> 259</span> <span class="comment">//------------------------------------------------------------------------------</span></div><div class="line"><a name="l00260"></a><span class="lineno"> 260</span> <span class="comment">// TODO : check how the basis is it is: 00-01-10-11 or 00-10-01-11 !!!!</span></div><div class="line"><a name="l00261"></a><span class="lineno"> 261</span> <span class="comment">// this code uses the standard 00-01-10-11 despite this being opposite to backend storage convention</span></div><div class="line"><a name="l00262"></a><span class="lineno"> 262</span> <span class="keyword">template</span> <<span class="keyword">class</span> Type></div><div class="line"><a name="l00263"></a><span class="lineno"><a class="line" href="group__qureg.html#ga941531519080f64e12d5760ef90a4846"> 263</a></span> <span class="keywordtype">void</span> <a class="code" href="group__qureg.html#ga941531519080f64e12d5760ef90a4846">QbitRegister<Type>::expectationValueXY</a>(<span class="keywordtype">unsigned</span> qubit, <span class="keywordtype">unsigned</span> qubit2, <a class="code" href="classQbitRegister.html#ae523cb97079963ca2ba8edaf947b1ca7">BaseType</a> &sum, <a class="code" href="classQbitRegister.html#ae523cb97079963ca2ba8edaf947b1ca7">BaseType</a> coeff)</div><div class="line"><a name="l00264"></a><span class="lineno"> 264</span> {</div><div class="line"><a name="l00265"></a><span class="lineno"> 265</span>  expectationValueYX(qubit2, qubit, sum, coeff);</div><div class="line"><a name="l00266"></a><span class="lineno"> 266</span> }</div><div class="line"><a name="l00267"></a><span class="lineno"> 267</span> </div><div class="line"><a name="l00268"></a><span class="lineno"> 268</span> </div><div class="line"><a name="l00277"></a><span class="lineno"> 277</span> <span class="comment">//------------------------------------------------------------------------------</span></div><div class="line"><a name="l00278"></a><span class="lineno"> 278</span> <span class="keyword">template</span> <<span class="keyword">class</span> Type></div><div class="line"><a name="l00279"></a><span class="lineno"><a class="line" href="group__qureg.html#gaadaa702593635dd3bc4bcb4db9d2d361"> 279</a></span> <span class="keywordtype">void</span> <a class="code" href="group__qureg.html#gaadaa702593635dd3bc4bcb4db9d2d361">QbitRegister<Type>::expectationValueYY</a>(<span class="keywordtype">unsigned</span> qubit, <span class="keywordtype">unsigned</span> qubit2, <a class="code" href="classQbitRegister.html#ae523cb97079963ca2ba8edaf947b1ca7">BaseType</a> &sum, <a class="code" href="classQbitRegister.html#ae523cb97079963ca2ba8edaf947b1ca7">BaseType</a> coeff)</div><div class="line"><a name="l00280"></a><span class="lineno"> 280</span> {</div><div class="line"><a name="l00281"></a><span class="lineno"> 281</span> <span class="preprocessor">#ifdef __ONLY_NORMALIZED_STATES__</span></div><div class="line"><a name="l00282"></a><span class="lineno"> 282</span>  <a class="code" href="classQbitRegister.html#ae523cb97079963ca2ba8edaf947b1ca7">BaseType</a> initial_norm = 1.;</div><div class="line"><a name="l00283"></a><span class="lineno"> 283</span> <span class="preprocessor">#else</span></div><div class="line"><a name="l00284"></a><span class="lineno"> 284</span>  <a class="code" href="classQbitRegister.html#ae523cb97079963ca2ba8edaf947b1ca7">BaseType</a> initial_norm = computenorm();</div><div class="line"><a name="l00285"></a><span class="lineno"> 285</span> <span class="preprocessor">#endif</span></div><div class="line"><a name="l00286"></a><span class="lineno"> 286</span> </div><div class="line"><a name="l00287"></a><span class="lineno"> 287</span> <span class="comment">// given initial qureg state in |psi></span></div><div class="line"><a name="l00288"></a><span class="lineno"> 288</span> <span class="comment">// compute the non-normalized vector corresponding to (2+YY)|psi></span></div><div class="line"><a name="l00289"></a><span class="lineno"> 289</span>  <a class="code" href="classopenqu_1_1TinyMatrix.html">openqu::TinyMatrix<Type, 4, 4, 32></a> yy_plus_2id;</div><div class="line"><a name="l00290"></a><span class="lineno"> 290</span>  yy_plus_2id(0, 1) = yy_plus_2id(0, 2) = yy_plus_2id(1, 0) = yy_plus_2id(1, 3) = <a class="code" href="interface__api__memory_8cpp.html#a8a7796dc492015686a15b44dfa64e347">Type</a>(0., 0.);</div><div class="line"><a name="l00291"></a><span class="lineno"> 291</span>  yy_plus_2id(2, 0) = yy_plus_2id(2, 3) = yy_plus_2id(3, 1) = yy_plus_2id(3, 2) = <a class="code" href="interface__api__memory_8cpp.html#a8a7796dc492015686a15b44dfa64e347">Type</a>(0., 0.);</div><div class="line"><a name="l00292"></a><span class="lineno"> 292</span>  yy_plus_2id(0, 3) = yy_plus_2id(3, 0) = <a class="code" href="interface__api__memory_8cpp.html#a8a7796dc492015686a15b44dfa64e347">Type</a>(-1., 0.);</div><div class="line"><a name="l00293"></a><span class="lineno"> 293</span>  yy_plus_2id(1, 2) = yy_plus_2id(2, 1) = <a class="code" href="interface__api__memory_8cpp.html#a8a7796dc492015686a15b44dfa64e347">Type</a>( 1., 0.);</div><div class="line"><a name="l00294"></a><span class="lineno"> 294</span>  yy_plus_2id(0, 0) = yy_plus_2id(1, 1) = yy_plus_2id(2, 2) = yy_plus_2id(3, 3) = <a class="code" href="interface__api__memory_8cpp.html#a8a7796dc492015686a15b44dfa64e347">Type</a>(2., 0.);</div><div class="line"><a name="l00295"></a><span class="lineno"> 295</span>  apply2QubitGate(qubit, qubit2, yy_plus_2id);</div><div class="line"><a name="l00296"></a><span class="lineno"> 296</span> </div><div class="line"><a name="l00297"></a><span class="lineno"> 297</span> <span class="comment">// update sum adding <psi|YY|psi></span></div><div class="line"><a name="l00298"></a><span class="lineno"> 298</span>  <a class="code" href="classQbitRegister.html#ae523cb97079963ca2ba8edaf947b1ca7">BaseType</a> final_norm = computenorm();</div><div class="line"><a name="l00299"></a><span class="lineno"> 299</span>  sum += coeff*(final_norm*final_norm - 5.*initial_norm*initial_norm)/4.;</div><div class="line"><a name="l00300"></a><span class="lineno"> 300</span> </div><div class="line"><a name="l00301"></a><span class="lineno"> 301</span> <span class="comment">// undo the computation to recover the initial state |psi></span></div><div class="line"><a name="l00302"></a><span class="lineno"> 302</span>  <a class="code" href="classopenqu_1_1TinyMatrix.html">openqu::TinyMatrix<Type, 4, 4, 32></a> inverse;</div><div class="line"><a name="l00303"></a><span class="lineno"> 303</span>  inverse(0, 1) = inverse(0, 2) = inverse(1, 0) = inverse(1, 3) = <a class="code" href="interface__api__memory_8cpp.html#a8a7796dc492015686a15b44dfa64e347">Type</a>(0., 0.);</div><div class="line"><a name="l00304"></a><span class="lineno"> 304</span>  inverse(2, 0) = inverse(2, 3) = inverse(3, 1) = inverse(3, 2) = <a class="code" href="interface__api__memory_8cpp.html#a8a7796dc492015686a15b44dfa64e347">Type</a>(0., 0.);</div><div class="line"><a name="l00305"></a><span class="lineno"> 305</span>  inverse(0, 3) = inverse(3, 0) = <a class="code" href="interface__api__memory_8cpp.html#a8a7796dc492015686a15b44dfa64e347">Type</a>( 1./3., 0.);</div><div class="line"><a name="l00306"></a><span class="lineno"> 306</span>  inverse(1, 2) = inverse(2, 1) = <a class="code" href="interface__api__memory_8cpp.html#a8a7796dc492015686a15b44dfa64e347">Type</a>(-1./3., 0.);</div><div class="line"><a name="l00307"></a><span class="lineno"> 307</span>  inverse(0, 0) = inverse(1, 1) = inverse(2, 2) = inverse(3, 3) = <a class="code" href="interface__api__memory_8cpp.html#a8a7796dc492015686a15b44dfa64e347">Type</a>( 2./3., 0.);</div><div class="line"><a name="l00308"></a><span class="lineno"> 308</span>  apply2QubitGate(qubit, qubit2, inverse);</div><div class="line"><a name="l00309"></a><span class="lineno"> 309</span> }</div><div class="line"><a name="l00310"></a><span class="lineno"> 310</span> </div><div class="line"><a name="l00311"></a><span class="lineno"> 311</span> </div><div class="line"><a name="l00320"></a><span class="lineno"> 320</span> <span class="comment">//------------------------------------------------------------------------------</span></div><div class="line"><a name="l00321"></a><span class="lineno"> 321</span> <span class="comment">// TODO : check how the basis is it is: 00-01-10-11 or 00-10-01-11 !!!!</span></div><div class="line"><a name="l00322"></a><span class="lineno"> 322</span> <span class="comment">// this code uses the standard 00-01-10-11 despite this being opposite to backend storage convention</span></div><div class="line"><a name="l00323"></a><span class="lineno"> 323</span> <span class="keyword">template</span> <<span class="keyword">class</span> Type></div><div class="line"><a name="l00324"></a><span class="lineno"><a class="line" href="group__qureg.html#gac16f25cc0af677cebfe0fcdbc048fd23"> 324</a></span> <span class="keywordtype">void</span> <a class="code" href="group__qureg.html#gac16f25cc0af677cebfe0fcdbc048fd23">QbitRegister<Type>::expectationValueZY</a>(<span class="keywordtype">unsigned</span> qubit, <span class="keywordtype">unsigned</span> qubit2, <a class="code" href="classQbitRegister.html#ae523cb97079963ca2ba8edaf947b1ca7">BaseType</a> &sum, <a class="code" href="classQbitRegister.html#ae523cb97079963ca2ba8edaf947b1ca7">BaseType</a> coeff)</div><div class="line"><a name="l00325"></a><span class="lineno"> 325</span> {</div><div class="line"><a name="l00326"></a><span class="lineno"> 326</span> <span class="preprocessor">#ifdef __ONLY_NORMALIZED_STATES__</span></div><div class="line"><a name="l00327"></a><span class="lineno"> 327</span>  <a class="code" href="classQbitRegister.html#ae523cb97079963ca2ba8edaf947b1ca7">BaseType</a> initial_norm = 1.;</div><div class="line"><a name="l00328"></a><span class="lineno"> 328</span> <span class="preprocessor">#else</span></div><div class="line"><a name="l00329"></a><span class="lineno"> 329</span>  <a class="code" href="classQbitRegister.html#ae523cb97079963ca2ba8edaf947b1ca7">BaseType</a> initial_norm = computenorm();</div><div class="line"><a name="l00330"></a><span class="lineno"> 330</span> <span class="preprocessor">#endif</span></div><div class="line"><a name="l00331"></a><span class="lineno"> 331</span> </div><div class="line"><a name="l00332"></a><span class="lineno"> 332</span> <span class="comment">// given initial qureg state in |psi></span></div><div class="line"><a name="l00333"></a><span class="lineno"> 333</span> <span class="comment">// compute the non-normalized vector corresponding to (2+YZ)|psi></span></div><div class="line"><a name="l00334"></a><span class="lineno"> 334</span>  <a class="code" href="classopenqu_1_1TinyMatrix.html">openqu::TinyMatrix<Type, 4, 4, 32></a> yz_plus_2id;</div><div class="line"><a name="l00335"></a><span class="lineno"> 335</span>  yz_plus_2id(0, 2) = yz_plus_2id(0, 3) = yz_plus_2id(1, 2) = yz_plus_2id(1, 3) = <a class="code" href="interface__api__memory_8cpp.html#a8a7796dc492015686a15b44dfa64e347">Type</a>(0., 0.);</div><div class="line"><a name="l00336"></a><span class="lineno"> 336</span>  yz_plus_2id(2, 0) = yz_plus_2id(2, 1) = yz_plus_2id(3, 0) = yz_plus_2id(3, 1) = <a class="code" href="interface__api__memory_8cpp.html#a8a7796dc492015686a15b44dfa64e347">Type</a>(0., 0.);</div><div class="line"><a name="l00337"></a><span class="lineno"> 337</span>  yz_plus_2id(0, 1) = yz_plus_2id(3, 2) = <a class="code" href="interface__api__memory_8cpp.html#a8a7796dc492015686a15b44dfa64e347">Type</a>( 0.,-1.);</div><div class="line"><a name="l00338"></a><span class="lineno"> 338</span>  yz_plus_2id(1, 0) = yz_plus_2id(2, 3) = <a class="code" href="interface__api__memory_8cpp.html#a8a7796dc492015686a15b44dfa64e347">Type</a>( 0., 1.);</div><div class="line"><a name="l00339"></a><span class="lineno"> 339</span>  yz_plus_2id(0, 0) = yz_plus_2id(1, 1) = yz_plus_2id(2, 2) = yz_plus_2id(3, 3) = <a class="code" href="interface__api__memory_8cpp.html#a8a7796dc492015686a15b44dfa64e347">Type</a>(2., 0.);</div><div class="line"><a name="l00340"></a><span class="lineno"> 340</span>  apply2QubitGate(qubit, qubit2, yz_plus_2id);</div><div class="line"><a name="l00341"></a><span class="lineno"> 341</span> </div><div class="line"><a name="l00342"></a><span class="lineno"> 342</span> <span class="comment">// update sum adding <psi|YZ|psi></span></div><div class="line"><a name="l00343"></a><span class="lineno"> 343</span>  <a class="code" href="classQbitRegister.html#ae523cb97079963ca2ba8edaf947b1ca7">BaseType</a> final_norm = computenorm();</div><div class="line"><a name="l00344"></a><span class="lineno"> 344</span>  sum += coeff*(final_norm*final_norm - 5.*initial_norm*initial_norm)/4.;</div><div class="line"><a name="l00345"></a><span class="lineno"> 345</span> </div><div class="line"><a name="l00346"></a><span class="lineno"> 346</span> <span class="comment">// undo the computation to recover the initial state |psi></span></div><div class="line"><a name="l00347"></a><span class="lineno"> 347</span>  <a class="code" href="classopenqu_1_1TinyMatrix.html">openqu::TinyMatrix<Type, 4, 4, 32></a> inverse;</div><div class="line"><a name="l00348"></a><span class="lineno"> 348</span>  inverse(0, 2) = inverse(0, 3) = inverse(1, 2) = inverse(1, 3) = <a class="code" href="interface__api__memory_8cpp.html#a8a7796dc492015686a15b44dfa64e347">Type</a>(0., 0.);</div><div class="line"><a name="l00349"></a><span class="lineno"> 349</span>  inverse(2, 0) = inverse(2, 1) = inverse(3, 0) = inverse(3, 1) = <a class="code" href="interface__api__memory_8cpp.html#a8a7796dc492015686a15b44dfa64e347">Type</a>(0., 0.);</div><div class="line"><a name="l00350"></a><span class="lineno"> 350</span>  inverse(0, 1) = inverse(3, 2) = <a class="code" href="interface__api__memory_8cpp.html#a8a7796dc492015686a15b44dfa64e347">Type</a>(0., 1./3.);</div><div class="line"><a name="l00351"></a><span class="lineno"> 351</span>  inverse(1, 0) = inverse(2, 3) = <a class="code" href="interface__api__memory_8cpp.html#a8a7796dc492015686a15b44dfa64e347">Type</a>(0.,-1./3.);</div><div class="line"><a name="l00352"></a><span class="lineno"> 352</span>  inverse(0, 0) = inverse(1, 1) = inverse(2, 2) = inverse(3, 3) = <a class="code" href="interface__api__memory_8cpp.html#a8a7796dc492015686a15b44dfa64e347">Type</a>( 2./3., 0.);</div><div class="line"><a name="l00353"></a><span class="lineno"> 353</span>  apply2QubitGate(qubit, qubit2, inverse);</div><div class="line"><a name="l00354"></a><span class="lineno"> 354</span> }</div><div class="line"><a name="l00355"></a><span class="lineno"> 355</span> </div><div class="line"><a name="l00356"></a><span class="lineno"> 356</span> </div><div class="line"><a name="l00365"></a><span class="lineno"> 365</span> <span class="comment">//------------------------------------------------------------------------------</span></div><div class="line"><a name="l00366"></a><span class="lineno"> 366</span> <span class="comment">// TODO : check how the basis is it is: 00-01-10-11 or 00-10-01-11 !!!!</span></div><div class="line"><a name="l00367"></a><span class="lineno"> 367</span> <span class="comment">// this code uses the standard 00-01-10-11 despite this being opposite to backend storage convention</span></div><div class="line"><a name="l00368"></a><span class="lineno"> 368</span> <span class="keyword">template</span> <<span class="keyword">class</span> Type></div><div class="line"><a name="l00369"></a><span class="lineno"><a class="line" href="group__qureg.html#ga1c80a0d017488b172cf2710f8bdf4ae2"> 369</a></span> <span class="keywordtype">void</span> <a class="code" href="group__qureg.html#ga1c80a0d017488b172cf2710f8bdf4ae2">QbitRegister<Type>::expectationValueXZ</a>(<span class="keywordtype">unsigned</span> qubit, <span class="keywordtype">unsigned</span> qubit2, <a class="code" href="classQbitRegister.html#ae523cb97079963ca2ba8edaf947b1ca7">BaseType</a> &sum, <a class="code" href="classQbitRegister.html#ae523cb97079963ca2ba8edaf947b1ca7">BaseType</a> coeff)</div><div class="line"><a name="l00370"></a><span class="lineno"> 370</span> {</div><div class="line"><a name="l00371"></a><span class="lineno"> 371</span>  expectationValueZX(qubit2, qubit, sum, coeff);</div><div class="line"><a name="l00372"></a><span class="lineno"> 372</span> }</div><div class="line"><a name="l00373"></a><span class="lineno"> 373</span> </div><div class="line"><a name="l00374"></a><span class="lineno"> 374</span> </div><div class="line"><a name="l00383"></a><span class="lineno"> 383</span> <span class="comment">//------------------------------------------------------------------------------</span></div><div class="line"><a name="l00384"></a><span class="lineno"> 384</span> <span class="comment">// TODO : check how the basis is it is: 00-01-10-11 or 00-10-01-11 !!!!</span></div><div class="line"><a name="l00385"></a><span class="lineno"> 385</span> <span class="comment">// this code uses the standard 00-01-10-11 despite this being opposite to backend storage convention</span></div><div class="line"><a name="l00386"></a><span class="lineno"> 386</span> <span class="keyword">template</span> <<span class="keyword">class</span> Type></div><div class="line"><a name="l00387"></a><span class="lineno"><a class="line" href="group__qureg.html#gadd95cc822c2017a62698be2cc58641fb"> 387</a></span> <span class="keywordtype">void</span> <a class="code" href="group__qureg.html#gadd95cc822c2017a62698be2cc58641fb">QbitRegister<Type>::expectationValueYZ</a>(<span class="keywordtype">unsigned</span> qubit, <span class="keywordtype">unsigned</span> qubit2, <a class="code" href="classQbitRegister.html#ae523cb97079963ca2ba8edaf947b1ca7">BaseType</a> &sum, <a class="code" href="classQbitRegister.html#ae523cb97079963ca2ba8edaf947b1ca7">BaseType</a> coeff)</div><div class="line"><a name="l00388"></a><span class="lineno"> 388</span> {</div><div class="line"><a name="l00389"></a><span class="lineno"> 389</span>  expectationValueZY(qubit2, qubit, sum, coeff);</div><div class="line"><a name="l00390"></a><span class="lineno"> 390</span> }</div><div class="line"><a name="l00391"></a><span class="lineno"> 391</span> </div><div class="line"><a name="l00392"></a><span class="lineno"> 392</span> </div><div class="line"><a name="l00401"></a><span class="lineno"> 401</span> <span class="comment">//------------------------------------------------------------------------------</span></div><div class="line"><a name="l00402"></a><span class="lineno"> 402</span> <span class="keyword">template</span> <<span class="keyword">class</span> Type></div><div class="line"><a name="l00403"></a><span class="lineno"><a class="line" href="group__qureg.html#ga4a404ae169a0bb0985bb7edbedbd8e7b"> 403</a></span> <span class="keywordtype">void</span> <a class="code" href="group__qureg.html#ga4a404ae169a0bb0985bb7edbedbd8e7b">QbitRegister<Type>::expectationValueZZ</a>(<span class="keywordtype">unsigned</span> qubit, <span class="keywordtype">unsigned</span> qubit2, <a class="code" href="classQbitRegister.html#ae523cb97079963ca2ba8edaf947b1ca7">BaseType</a> &sum, <a class="code" href="classQbitRegister.html#ae523cb97079963ca2ba8edaf947b1ca7">BaseType</a> coeff)</div><div class="line"><a name="l00404"></a><span class="lineno"> 404</span> {</div><div class="line"><a name="l00405"></a><span class="lineno"> 405</span> <span class="preprocessor">#ifdef __ONLY_NORMALIZED_STATES__</span></div><div class="line"><a name="l00406"></a><span class="lineno"> 406</span>  <a class="code" href="classQbitRegister.html#ae523cb97079963ca2ba8edaf947b1ca7">BaseType</a> initial_norm = 1.;</div><div class="line"><a name="l00407"></a><span class="lineno"> 407</span> <span class="preprocessor">#else</span></div><div class="line"><a name="l00408"></a><span class="lineno"> 408</span>  <a class="code" href="classQbitRegister.html#ae523cb97079963ca2ba8edaf947b1ca7">BaseType</a> initial_norm = computenorm();</div><div class="line"><a name="l00409"></a><span class="lineno"> 409</span> <span class="preprocessor">#endif</span></div><div class="line"><a name="l00410"></a><span class="lineno"> 410</span> </div><div class="line"><a name="l00411"></a><span class="lineno"> 411</span> <span class="comment">// given initial qureg state in |psi></span></div><div class="line"><a name="l00412"></a><span class="lineno"> 412</span> <span class="comment">// compute the non-normalized vector corresponding to (2+ZZ)|psi></span></div><div class="line"><a name="l00413"></a><span class="lineno"> 413</span>  <a class="code" href="classopenqu_1_1TinyMatrix.html">openqu::TinyMatrix<Type, 4, 4, 32></a> zz_plus_2id;</div><div class="line"><a name="l00414"></a><span class="lineno"> 414</span>  zz_plus_2id(0, 1) = zz_plus_2id(0, 2) = zz_plus_2id(0, 3) = <a class="code" href="interface__api__memory_8cpp.html#a8a7796dc492015686a15b44dfa64e347">Type</a>(0., 0.);</div><div class="line"><a name="l00415"></a><span class="lineno"> 415</span>  zz_plus_2id(1, 0) = zz_plus_2id(1, 2) = zz_plus_2id(1, 3) = <a class="code" href="interface__api__memory_8cpp.html#a8a7796dc492015686a15b44dfa64e347">Type</a>(0., 0.);</div><div class="line"><a name="l00416"></a><span class="lineno"> 416</span>  zz_plus_2id(2, 0) = zz_plus_2id(2, 1) = zz_plus_2id(2, 3) = <a class="code" href="interface__api__memory_8cpp.html#a8a7796dc492015686a15b44dfa64e347">Type</a>(0., 0.);</div><div class="line"><a name="l00417"></a><span class="lineno"> 417</span>  zz_plus_2id(3, 0) = zz_plus_2id(3, 1) = zz_plus_2id(3, 2) = <a class="code" href="interface__api__memory_8cpp.html#a8a7796dc492015686a15b44dfa64e347">Type</a>(0., 0.);</div><div class="line"><a name="l00418"></a><span class="lineno"> 418</span>  zz_plus_2id(0, 0) = zz_plus_2id(3, 3) = <a class="code" href="interface__api__memory_8cpp.html#a8a7796dc492015686a15b44dfa64e347">Type</a>(3., 0.); </div><div class="line"><a name="l00419"></a><span class="lineno"> 419</span>  zz_plus_2id(1, 1) = zz_plus_2id(2, 2) = <a class="code" href="interface__api__memory_8cpp.html#a8a7796dc492015686a15b44dfa64e347">Type</a>(1., 0.);</div><div class="line"><a name="l00420"></a><span class="lineno"> 420</span>  apply2QubitGate(qubit, qubit2, zz_plus_2id);</div><div class="line"><a name="l00421"></a><span class="lineno"> 421</span> </div><div class="line"><a name="l00422"></a><span class="lineno"> 422</span> <span class="comment">// update sum adding <psi|ZZ|psi></span></div><div class="line"><a name="l00423"></a><span class="lineno"> 423</span>  <a class="code" href="classQbitRegister.html#ae523cb97079963ca2ba8edaf947b1ca7">BaseType</a> final_norm = computenorm();</div><div class="line"><a name="l00424"></a><span class="lineno"> 424</span>  sum += coeff*(final_norm*final_norm - 5.*initial_norm*initial_norm)/4.;</div><div class="line"><a name="l00425"></a><span class="lineno"> 425</span> </div><div class="line"><a name="l00426"></a><span class="lineno"> 426</span> <span class="comment">// undo the computation to recover the initial state |psi></span></div><div class="line"><a name="l00427"></a><span class="lineno"> 427</span>  <a class="code" href="classopenqu_1_1TinyMatrix.html">openqu::TinyMatrix<Type, 4, 4, 32></a> inverse;</div><div class="line"><a name="l00428"></a><span class="lineno"> 428</span>  inverse(0, 1) = inverse(0, 2) = inverse(0, 3) = <a class="code" href="interface__api__memory_8cpp.html#a8a7796dc492015686a15b44dfa64e347">Type</a>(0., 0.);</div><div class="line"><a name="l00429"></a><span class="lineno"> 429</span>  inverse(1, 0) = inverse(1, 2) = inverse(1, 3) = <a class="code" href="interface__api__memory_8cpp.html#a8a7796dc492015686a15b44dfa64e347">Type</a>(0., 0.);</div><div class="line"><a name="l00430"></a><span class="lineno"> 430</span>  inverse(2, 0) = inverse(2, 1) = inverse(2, 3) = <a class="code" href="interface__api__memory_8cpp.html#a8a7796dc492015686a15b44dfa64e347">Type</a>(0., 0.);</div><div class="line"><a name="l00431"></a><span class="lineno"> 431</span>  inverse(3, 0) = inverse(3, 1) = inverse(3, 2) = <a class="code" href="interface__api__memory_8cpp.html#a8a7796dc492015686a15b44dfa64e347">Type</a>(0., 0.);</div><div class="line"><a name="l00432"></a><span class="lineno"> 432</span>  inverse(0, 0) = inverse(3, 3) = <a class="code" href="interface__api__memory_8cpp.html#a8a7796dc492015686a15b44dfa64e347">Type</a>( 1./3., 0.);</div><div class="line"><a name="l00433"></a><span class="lineno"> 433</span>  inverse(1, 1) = inverse(2, 2) = <a class="code" href="interface__api__memory_8cpp.html#a8a7796dc492015686a15b44dfa64e347">Type</a>( 1. , 0.);</div><div class="line"><a name="l00434"></a><span class="lineno"> 434</span>  apply2QubitGate(qubit, qubit2, inverse);</div><div class="line"><a name="l00435"></a><span class="lineno"> 435</span> }</div><div class="line"><a name="l00436"></a><span class="lineno"> 436</span> </div><div class="line"><a name="l00437"></a><span class="lineno"> 437</span> </div><div class="line"><a name="l00439"></a><span class="lineno"> 439</span> <span class="comment">//------------------------------------------------------------------------------</span></div><div class="line"><a name="l00440"></a><span class="lineno"> 440</span> <span class="comment">// Hamming weight function</span></div><div class="line"><a name="l00441"></a><span class="lineno"><a class="line" href="group__qureg.html#gad3f05291c152d09919807c21aecf8959"> 441</a></span> std::size_t <a class="code" href="group__qureg.html#gad3f05291c152d09919807c21aecf8959">Hamming_weight</a>(std::size_t x)</div><div class="line"><a name="l00442"></a><span class="lineno"> 442</span> {</div><div class="line"><a name="l00443"></a><span class="lineno"> 443</span>  std::size_t count=0;</div><div class="line"><a name="l00444"></a><span class="lineno"> 444</span>  <span class="keywordflow">for</span> (count=0; x; count++)</div><div class="line"><a name="l00445"></a><span class="lineno"> 445</span>  x &= x-1;</div><div class="line"><a name="l00446"></a><span class="lineno"> 446</span>  <span class="keywordflow">return</span> count;</div><div class="line"><a name="l00447"></a><span class="lineno"> 447</span> }</div><div class="line"><a name="l00448"></a><span class="lineno"> 448</span> </div><div class="line"><a name="l00449"></a><span class="lineno"> 449</span> </div><div class="line"><a name="l00462"></a><span class="lineno"> 462</span> <span class="comment">//------------------------------------------------------------------------------</span></div><div class="line"><a name="l00463"></a><span class="lineno"> 463</span> <span class="comment">// observable: 1==PauliX , 2==PauliY , 3==PauliZ</span></div><div class="line"><a name="l00464"></a><span class="lineno"> 464</span> <span class="keyword">template</span> <<span class="keyword">class</span> Type></div><div class="line"><a name="l00465"></a><span class="lineno"><a class="line" href="group__qureg.html#gaff59d4b5e5e6c68516723fcbad2d9eea"> 465</a></span> <span class="keywordtype">void</span> <a class="code" href="group__qureg.html#gaff59d4b5e5e6c68516723fcbad2d9eea">QbitRegister<Type>::expectationValue</a>(std::vector<unsigned> &qubits, std::vector<unsigned> &observables, <a class="code" href="classQbitRegister.html#ae523cb97079963ca2ba8edaf947b1ca7">BaseType</a> &sum, <a class="code" href="classQbitRegister.html#ae523cb97079963ca2ba8edaf947b1ca7">BaseType</a> coeff)</div><div class="line"><a name="l00466"></a><span class="lineno"> 466</span> {</div><div class="line"><a name="l00467"></a><span class="lineno"> 467</span>  <a class="code" href="highperfkernels_8cpp.html#a3c5c1de356c65cc2bfca5046ecd71e6d">assert</a>( qubits.size() == observables.size() );</div><div class="line"><a name="l00468"></a><span class="lineno"> 468</span> </div><div class="line"><a name="l00469"></a><span class="lineno"> 469</span> <span class="comment">// G is matrix from change of basis Y --> Z, such that Ginv.Z.G = Y </span></div><div class="line"><a name="l00470"></a><span class="lineno"> 470</span>  <a class="code" href="classopenqu_1_1TinyMatrix.html">openqu::TinyMatrix<Type, 2, 2, 32></a> G;</div><div class="line"><a name="l00471"></a><span class="lineno"> 471</span>  <a class="code" href="classQbitRegister.html#ae523cb97079963ca2ba8edaf947b1ca7">BaseType</a> f = 1. / std::sqrt(2.);</div><div class="line"><a name="l00472"></a><span class="lineno"> 472</span>  G(0, 0) = G(1, 0) = <a class="code" href="interface__api__memory_8cpp.html#a8a7796dc492015686a15b44dfa64e347">Type</a>(f , 0.);</div><div class="line"><a name="l00473"></a><span class="lineno"> 473</span>  G(0, 1) = <a class="code" href="interface__api__memory_8cpp.html#a8a7796dc492015686a15b44dfa64e347">Type</a>(0.,-f);</div><div class="line"><a name="l00474"></a><span class="lineno"> 474</span>  G(1, 1) = <a class="code" href="interface__api__memory_8cpp.html#a8a7796dc492015686a15b44dfa64e347">Type</a>(0., f);</div><div class="line"><a name="l00475"></a><span class="lineno"> 475</span> <span class="comment">// G^dagger = G^-1</span></div><div class="line"><a name="l00476"></a><span class="lineno"> 476</span>  <a class="code" href="classopenqu_1_1TinyMatrix.html">openqu::TinyMatrix<Type, 2, 2, 32></a> Ginv;</div><div class="line"><a name="l00477"></a><span class="lineno"> 477</span>  Ginv(0, 0) = Ginv(0, 1) = <a class="code" href="interface__api__memory_8cpp.html#a8a7796dc492015686a15b44dfa64e347">Type</a>(f , 0.);</div><div class="line"><a name="l00478"></a><span class="lineno"> 478</span>  Ginv(1, 0) = <a class="code" href="interface__api__memory_8cpp.html#a8a7796dc492015686a15b44dfa64e347">Type</a>(0., f);</div><div class="line"><a name="l00479"></a><span class="lineno"> 479</span>  Ginv(1, 1) = <a class="code" href="interface__api__memory_8cpp.html#a8a7796dc492015686a15b44dfa64e347">Type</a>(0.,-f);</div><div class="line"><a name="l00480"></a><span class="lineno"> 480</span> </div><div class="line"><a name="l00481"></a><span class="lineno"> 481</span>  <span class="keywordflow">for</span> (std::size_t i=0; i<qubits.size(); i++)</div><div class="line"><a name="l00482"></a><span class="lineno"> 482</span>  {</div><div class="line"><a name="l00483"></a><span class="lineno"> 483</span>  <span class="keywordflow">if</span> (observables[i]==1)</div><div class="line"><a name="l00484"></a><span class="lineno"> 484</span>  applyHadamard(qubits[i]);</div><div class="line"><a name="l00485"></a><span class="lineno"> 485</span>  <span class="keywordflow">else</span> <span class="keywordflow">if</span> (observables[i]==2)</div><div class="line"><a name="l00486"></a><span class="lineno"> 486</span>  apply1QubitGate(qubits[i],G);</div><div class="line"><a name="l00487"></a><span class="lineno"> 487</span>  <span class="keywordflow">else</span> <span class="keywordflow">if</span> (observables[i]==3)</div><div class="line"><a name="l00488"></a><span class="lineno"> 488</span>  <span class="keywordflow">continue</span>;</div><div class="line"><a name="l00489"></a><span class="lineno"> 489</span>  <span class="keywordflow">else</span></div><div class="line"><a name="l00490"></a><span class="lineno"> 490</span>  <a class="code" href="highperfkernels_8cpp.html#a3c5c1de356c65cc2bfca5046ecd71e6d">assert</a>(0); <span class="comment">// should never be called</span></div><div class="line"><a name="l00491"></a><span class="lineno"> 491</span>  } </div><div class="line"><a name="l00492"></a><span class="lineno"> 492</span> </div><div class="line"><a name="l00493"></a><span class="lineno"> 493</span> <span class="comment">// compute the expectation value</span></div><div class="line"><a name="l00494"></a><span class="lineno"> 494</span>  MPI_Comm comm = openqu::mpi::Environment::comm();</div><div class="line"><a name="l00495"></a><span class="lineno"> 495</span>  std::size_t myrank = <a class="code" href="classopenqu_1_1mpi_1_1Environment.html#a1c0c48f8af817320768ef3a1c9b98854">openqu::mpi::Environment::rank</a>();</div><div class="line"><a name="l00496"></a><span class="lineno"> 496</span>  <a class="code" href="classQbitRegister.html#ae523cb97079963ca2ba8edaf947b1ca7">BaseType</a> local_value = 0;</div><div class="line"><a name="l00497"></a><span class="lineno"> 497</span>  std::size_t glb_start = <a class="code" href="utils_8hpp.html#a2d1ace2be4b6d58d3260b1b5fd1d63e0">UL</a>(myrank) * localSize();</div><div class="line"><a name="l00498"></a><span class="lineno"> 498</span> <span class="comment">// integer in binary notation with 1 located at the position of the qubits</span></div><div class="line"><a name="l00499"></a><span class="lineno"> 499</span>  std::size_t y=0;</div><div class="line"><a name="l00500"></a><span class="lineno"> 500</span>  <span class="keywordflow">for</span> (std::size_t i=0; i<qubits.size(); i++)</div><div class="line"><a name="l00501"></a><span class="lineno"> 501</span>  y += 1 << qubits[i];</div><div class="line"><a name="l00502"></a><span class="lineno"> 502</span> </div><div class="line"><a name="l00503"></a><span class="lineno"> 503</span> <span class="preprocessor">#pragma omp parallel</span></div><div class="line"><a name="l00504"></a><span class="lineno"> 504</span> {</div><div class="line"><a name="l00505"></a><span class="lineno"> 505</span>  std::size_t x;</div><div class="line"><a name="l00506"></a><span class="lineno"> 506</span> <span class="preprocessor"> #pragma omp for reduction(+ : local_value)</span></div><div class="line"><a name="l00507"></a><span class="lineno"> 507</span>  <span class="keywordflow">for</span>(std::size_t i = 0; i < localSize(); i++)</div><div class="line"><a name="l00508"></a><span class="lineno"> 508</span>  {</div><div class="line"><a name="l00509"></a><span class="lineno"> 509</span>  x = glb_start + i;</div><div class="line"><a name="l00510"></a><span class="lineno"> 510</span>  <span class="keywordflow">if</span> ( <a class="code" href="group__qureg.html#gad3f05291c152d09919807c21aecf8959">Hamming_weight</a>( x & y ) & 1 ) <span class="comment">// odd number of 1 in the qubits involved</span></div><div class="line"><a name="l00511"></a><span class="lineno"> 511</span>  local_value -= std::abs(state[i]) * std::abs(state[i]);</div><div class="line"><a name="l00512"></a><span class="lineno"> 512</span>  <span class="keywordflow">else</span></div><div class="line"><a name="l00513"></a><span class="lineno"> 513</span>  local_value += std::abs(state[i]) * std::abs(state[i]);</div><div class="line"><a name="l00514"></a><span class="lineno"> 514</span>  }</div><div class="line"><a name="l00515"></a><span class="lineno"> 515</span> }</div><div class="line"><a name="l00516"></a><span class="lineno"> 516</span>  <a class="code" href="classQbitRegister.html#ae523cb97079963ca2ba8edaf947b1ca7">BaseType</a> global_value;</div><div class="line"><a name="l00517"></a><span class="lineno"> 517</span>  <span class="comment">// MPI_Allreduce(&local_value, &global_value, 1, MPI_DOUBLE, MPI_SUM, comm);</span></div><div class="line"><a name="l00518"></a><span class="lineno"> 518</span>  MPI_Allreduce_x(&local_value, &global_value, MPI_SUM, comm);</div><div class="line"><a name="l00519"></a><span class="lineno"> 519</span> </div><div class="line"><a name="l00520"></a><span class="lineno"> 520</span> <span class="comment">// update sum</span></div><div class="line"><a name="l00521"></a><span class="lineno"> 521</span>  sum += coeff * global_value;</div><div class="line"><a name="l00522"></a><span class="lineno"> 522</span> </div><div class="line"><a name="l00523"></a><span class="lineno"> 523</span> <span class="comment">// undo the quantum gates to recover the initial state |psi></span></div><div class="line"><a name="l00524"></a><span class="lineno"> 524</span>  <span class="keywordflow">for</span> (std::size_t i=0; i<qubits.size(); i++)</div><div class="line"><a name="l00525"></a><span class="lineno"> 525</span>  {</div><div class="line"><a name="l00526"></a><span class="lineno"> 526</span>  <span class="keywordflow">if</span> (observables[i]==1)</div><div class="line"><a name="l00527"></a><span class="lineno"> 527</span>  applyHadamard(qubits[i]);</div><div class="line"><a name="l00528"></a><span class="lineno"> 528</span>  <span class="keywordflow">else</span> <span class="keywordflow">if</span> (observables[i]==2)</div><div class="line"><a name="l00529"></a><span class="lineno"> 529</span>  apply1QubitGate(qubits[i],Ginv);</div><div class="line"><a name="l00530"></a><span class="lineno"> 530</span>  <span class="keywordflow">else</span> <span class="keywordflow">if</span> (observables[i]==3)</div><div class="line"><a name="l00531"></a><span class="lineno"> 531</span>  <span class="keywordflow">continue</span>;</div><div class="line"><a name="l00532"></a><span class="lineno"> 532</span>  <span class="keywordflow">else</span></div><div class="line"><a name="l00533"></a><span class="lineno"> 533</span>  <a class="code" href="highperfkernels_8cpp.html#a3c5c1de356c65cc2bfca5046ecd71e6d">assert</a>(0); <span class="comment">// should never be called</span></div><div class="line"><a name="l00534"></a><span class="lineno"> 534</span>  } </div><div class="line"><a name="l00535"></a><span class="lineno"> 535</span> }</div><div class="line"><a name="l00536"></a><span class="lineno"> 536</span> </div><div class="line"><a name="l00537"></a><span class="lineno"> 537</span> <span class="keyword">template</span> <span class="keyword">class </span><a class="code" href="classQbitRegister.html">QbitRegister<ComplexSP></a>;</div><div class="line"><a name="l00538"></a><span class="lineno"> 538</span> <span class="keyword">template</span> <span class="keyword">class </span><a class="code" href="classQbitRegister.html">QbitRegister<ComplexDP></a>;</div><div class="line"><a name="l00539"></a><span class="lineno"> 539</span> </div><div class="ttc" id="classopenqu_1_1mpi_1_1Environment_html_a1c0c48f8af817320768ef3a1c9b98854"><div class="ttname"><a href="classopenqu_1_1mpi_1_1Environment.html#a1c0c48f8af817320768ef3a1c9b98854">openqu::mpi::Environment::rank</a></div><div class="ttdeci">static int rank()</div><div class="ttdef"><b>Definition:</b> <a href="mpi_8cpp_source.html#l00180">mpi.cpp:180</a></div></div>
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<div class="ttc" id="group__qureg_html_gadd95cc822c2017a62698be2cc58641fb"><div class="ttname"><a href="group__qureg.html#gadd95cc822c2017a62698be2cc58641fb">QbitRegister::expectationValueYZ</a></div><div class="ttdeci">void expectationValueYZ(unsigned const qubit, unsigned const qubit2, BaseType &sum, BaseType coeff=1.)</div><div class="ttdoc">Compute expectation value of Pauli Y.Z for two qubits over the full-register state. </div><div class="ttdef"><b>Definition:</b> <a href="qureg__expectval_8cpp_source.html#l00387">qureg_expectval.cpp:387</a></div></div>
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<div class="ttc" id="group__qureg_html_gaadaa702593635dd3bc4bcb4db9d2d361"><div class="ttname"><a href="group__qureg.html#gaadaa702593635dd3bc4bcb4db9d2d361">QbitRegister::expectationValueYY</a></div><div class="ttdeci">void expectationValueYY(unsigned const qubit, unsigned const qubit2, BaseType &sum, BaseType coeff=1.)</div><div class="ttdoc">Compute expectation value of Pauli Y.Y for two qubits over the full-register state. </div><div class="ttdef"><b>Definition:</b> <a href="qureg__expectval_8cpp_source.html#l00279">qureg_expectval.cpp:279</a></div></div>
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<div class="ttc" id="group__qureg_html_ga941531519080f64e12d5760ef90a4846"><div class="ttname"><a href="group__qureg.html#ga941531519080f64e12d5760ef90a4846">QbitRegister::expectationValueXY</a></div><div class="ttdeci">void expectationValueXY(unsigned const qubit, unsigned const qubit2, BaseType &sum, BaseType coeff=1.)</div><div class="ttdoc">Compute expectation value of Pauli Y.X for two qubits over the full-register state. </div><div class="ttdef"><b>Definition:</b> <a href="qureg__expectval_8cpp_source.html#l00263">qureg_expectval.cpp:263</a></div></div>
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<div class="ttc" id="group__qureg_html_ga6e6e962a8da5782537f14c55850f46c7"><div class="ttname"><a href="group__qureg.html#ga6e6e962a8da5782537f14c55850f46c7">QbitRegister::expectationValueZ</a></div><div class="ttdeci">void expectationValueZ(unsigned const qubit, BaseType &sum, BaseType coeff=1.)</div><div class="ttdoc">Compute expectation value of Pauli Z for qubit over the full-register state. </div><div class="ttdef"><b>Definition:</b> <a href="qureg__expectval_8cpp_source.html#l00114">qureg_expectval.cpp:114</a></div></div>
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<div class="ttc" id="group__qureg_html_ga4a404ae169a0bb0985bb7edbedbd8e7b"><div class="ttname"><a href="group__qureg.html#ga4a404ae169a0bb0985bb7edbedbd8e7b">QbitRegister::expectationValueZZ</a></div><div class="ttdeci">void expectationValueZZ(unsigned const qubit, unsigned const qubit2, BaseType &sum, BaseType coeff=1.)</div><div class="ttdoc">Compute expectation value of Pauli Z.Z for two qubits over the full-register state. </div><div class="ttdef"><b>Definition:</b> <a href="qureg__expectval_8cpp_source.html#l00403">qureg_expectval.cpp:403</a></div></div>
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<div class="ttc" id="interface__api__memory_8cpp_html_a8a7796dc492015686a15b44dfa64e347"><div class="ttname"><a href="interface__api__memory_8cpp.html#a8a7796dc492015686a15b44dfa64e347">Type</a></div><div class="ttdeci">ComplexDP Type</div><div class="ttdef"><b>Definition:</b> <a href="interface__api__memory_8cpp_source.html#l00025">interface_api_memory.cpp:25</a></div></div>
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<div class="ttc" id="classopenqu_1_1TinyMatrix_html"><div class="ttname"><a href="classopenqu_1_1TinyMatrix.html">openqu::TinyMatrix</a></div><div class="ttdoc">A small matrix with dimensions fixed at compile time. </div><div class="ttdef"><b>Definition:</b> <a href="tinymatrix_8hpp_source.html#l00044">tinymatrix.hpp:44</a></div></div>
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<div class="ttc" id="group__qureg_html_ga1c80a0d017488b172cf2710f8bdf4ae2"><div class="ttname"><a href="group__qureg.html#ga1c80a0d017488b172cf2710f8bdf4ae2">QbitRegister::expectationValueXZ</a></div><div class="ttdeci">void expectationValueXZ(unsigned const qubit, unsigned const qubit2, BaseType &sum, BaseType coeff=1.)</div><div class="ttdoc">Compute expectation value of Pauli X.Z for two qubits over the full-register state. </div><div class="ttdef"><b>Definition:</b> <a href="qureg__expectval_8cpp_source.html#l00369">qureg_expectval.cpp:369</a></div></div>
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<div class="ttc" id="group__qureg_html_gaff59d4b5e5e6c68516723fcbad2d9eea"><div class="ttname"><a href="group__qureg.html#gaff59d4b5e5e6c68516723fcbad2d9eea">QbitRegister::expectationValue</a></div><div class="ttdeci">void expectationValue(std::vector< unsigned > &qubits, std::vector< unsigned > &observables, BaseType &sum, BaseType coeff=1.)</div><div class="ttdoc">Compute expectation value of a Pauli string for multiple qubits over the full-register state...</div><div class="ttdef"><b>Definition:</b> <a href="qureg__expectval_8cpp_source.html#l00465">qureg_expectval.cpp:465</a></div></div>
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<div class="ttc" id="highperfkernels_8cpp_html_a3c5c1de356c65cc2bfca5046ecd71e6d"><div class="ttname"><a href="highperfkernels_8cpp.html#a3c5c1de356c65cc2bfca5046ecd71e6d">assert</a></div><div class="ttdeci">assert(((c22-c21)%c23)==0)</div></div>
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<div class="ttc" id="group__qureg_html_ga6efb952da150825c4168b99095b89303"><div class="ttname"><a href="group__qureg.html#ga6efb952da150825c4168b99095b89303">QbitRegister::expectationValueYX</a></div><div class="ttdeci">void expectationValueYX(unsigned const qubit, unsigned const qubit2, BaseType &sum, BaseType coeff=1.)</div><div class="ttdoc">Compute expectation value of Pauli Y.X for two qubits over the full-register state. </div><div class="ttdef"><b>Definition:</b> <a href="qureg__expectval_8cpp_source.html#l00173">qureg_expectval.cpp:173</a></div></div>
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<div class="ttc" id="group__qureg_html_gad3f05291c152d09919807c21aecf8959"><div class="ttname"><a href="group__qureg.html#gad3f05291c152d09919807c21aecf8959">Hamming_weight</a></div><div class="ttdeci">std::size_t Hamming_weight(std::size_t x)</div><div class="ttdoc">Utility function that computes the Hamming weight of a bitstring given as integer. </div><div class="ttdef"><b>Definition:</b> <a href="qureg__expectval_8cpp_source.html#l00441">qureg_expectval.cpp:441</a></div></div>
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<div class="ttc" id="qureg_8hpp_html"><div class="ttname"><a href="qureg_8hpp.html">qureg.hpp</a></div></div>
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<div class="ttc" id="group__qureg_html_gac16f25cc0af677cebfe0fcdbc048fd23"><div class="ttname"><a href="group__qureg.html#gac16f25cc0af677cebfe0fcdbc048fd23">QbitRegister::expectationValueZY</a></div><div class="ttdeci">void expectationValueZY(unsigned const qubit, unsigned const qubit2, BaseType &sum, BaseType coeff=1.)</div><div class="ttdoc">Compute expectation value of Pauli Z.Y for two qubits over the full-register state. </div><div class="ttdef"><b>Definition:</b> <a href="qureg__expectval_8cpp_source.html#l00324">qureg_expectval.cpp:324</a></div></div>
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<div class="ttc" id="group__qureg_html_gafccc7f7f54d595c7582f19b7ea0f8aac"><div class="ttname"><a href="group__qureg.html#gafccc7f7f54d595c7582f19b7ea0f8aac">QbitRegister::expectationValueXX</a></div><div class="ttdeci">void expectationValueXX(unsigned const qubit, unsigned const qubit2, BaseType &sum, BaseType coeff=1.)</div><div class="ttdoc">Compute expectation value of Pauli X.X for two qubits over the full-register state. </div><div class="ttdef"><b>Definition:</b> <a href="qureg__expectval_8cpp_source.html#l00130">qureg_expectval.cpp:130</a></div></div>
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<div class="ttc" id="group__qureg_html_ga0ae1cb5b712e6ab145581a76b1fae63c"><div class="ttname"><a href="group__qureg.html#ga0ae1cb5b712e6ab145581a76b1fae63c">QbitRegister::expectationValueX</a></div><div class="ttdeci">void expectationValueX(unsigned const qubit, BaseType &sum, BaseType coeff=1.)</div><div class="ttdoc">Compute expectation value of Pauli X for qubit over the full-register state. </div><div class="ttdef"><b>Definition:</b> <a href="qureg__expectval_8cpp_source.html#l00036">qureg_expectval.cpp:36</a></div></div>
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<div class="ttc" id="utils_8hpp_html_a2d1ace2be4b6d58d3260b1b5fd1d63e0"><div class="ttname"><a href="utils_8hpp.html#a2d1ace2be4b6d58d3260b1b5fd1d63e0">UL</a></div><div class="ttdeci">#define UL(x)</div><div class="ttdef"><b>Definition:</b> <a href="utils_8hpp_source.html#l00034">utils.hpp:34</a></div></div>
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<div class="ttc" id="group__qureg_html_ga24e31d763d955038cc666d3f187b4b8c"><div class="ttname"><a href="group__qureg.html#ga24e31d763d955038cc666d3f187b4b8c">QbitRegister::expectationValueY</a></div><div class="ttdeci">void expectationValueY(unsigned const qubit, BaseType &sum, BaseType coeff=1.)</div><div class="ttdoc">Compute expectation value of Pauli Y for qubit over the full-register state. </div><div class="ttdef"><b>Definition:</b> <a href="qureg__expectval_8cpp_source.html#l00086">qureg_expectval.cpp:86</a></div></div>
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<div class="ttc" id="group__qureg_html_ga6a8dcf0d8e8fc2f84166944d7c7a62f2"><div class="ttname"><a href="group__qureg.html#ga6a8dcf0d8e8fc2f84166944d7c7a62f2">QbitRegister::expectationValueZX</a></div><div class="ttdeci">void expectationValueZX(unsigned const qubit, unsigned const qubit2, BaseType &sum, BaseType coeff=1.)</div><div class="ttdoc">Compute expectation value of Pauli Z.X for two qubits over the full-register state. </div><div class="ttdef"><b>Definition:</b> <a href="qureg__expectval_8cpp_source.html#l00218">qureg_expectval.cpp:218</a></div></div>
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<div class="ttc" id="classQbitRegister_html"><div class="ttname"><a href="classQbitRegister.html">QbitRegister</a></div><div class="ttdef"><b>Definition:</b> <a href="qureg_8hpp_source.html#l00068">qureg.hpp:68</a></div></div>
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<div class="ttc" id="classQbitRegister_html_ae523cb97079963ca2ba8edaf947b1ca7"><div class="ttname"><a href="classQbitRegister.html#ae523cb97079963ca2ba8edaf947b1ca7">QbitRegister::BaseType</a></div><div class="ttdeci">extract_value_type< Type >::value_type BaseType</div><div class="ttdef"><b>Definition:</b> <a href="qureg_8hpp_source.html#l00072">qureg.hpp:72</a></div></div>
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