2020 lines
234 KiB
Plaintext
2020 lines
234 KiB
Plaintext
{
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"cells": [
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{
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"cell_type": "markdown",
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"id": "b8f25160-5130-4913-9330-648444d5c77f",
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"metadata": {},
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"source": [
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"# Getting started with Sample-based quantum diagonalization (SQD)\n",
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"\n",
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"This guide demonstrates a simple working example to get started with the `qiskit-addons-sqd` package. In this example, you can use SQD to obtain an approximation of the ground state of the $N_2$ molecule at equilibrium.\n",
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"\n",
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"To begin, recall that the generic interacting-electron Hamiltonian has the form:\n",
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"\n",
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"$$ \\hat{H} = \\sum_{\\substack{pr\\\\ \\sigma}}h_{pr} \\hat{a}_{p\\sigma}^\\dagger \\hat{a}_{r\\sigma} + \\sum_{\\substack{prqs\\\\ \\sigma\\tau}} \\frac{1}{2}\\left(pr|qs\\right)\\hat{a}_{p\\sigma}^\\dagger \\hat{a}_{q\\tau}^\\dagger \\hat{a}_{s\\tau}\\hat{a}_{r\\sigma} $$\n",
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"\n",
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"where $\\hat{a}_{p\\sigma}^\\dagger$ and $\\hat{a}_{p\\sigma}$ are the Fermionic creation and annihilation operators associated with the $p$-th orbital with spin $\\sigma$ and $h_{pr}$ and $\\left(pr|qs\\right)$ are the one and two-body electronic integrals."
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]
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},
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{
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"cell_type": "markdown",
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"id": "db4db859-4190-42a5-b512-1128eeaf82db",
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"metadata": {},
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"source": [
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"<Admonition type = \"note\">\n",
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"This example ingests pre-generated data in a file called `n2_fci.txt`, which contains one- and two-body electronic integrals. To run the code cells below on a local machine, copy and paste the data into a file with the same name. This example also requires the `pyscf` package to be installed.\n",
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"</Admonition>\n",
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"\n",
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"<details>\n",
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"<summary>\n",
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"Click here to examine the orbital information used to generate the ansatz.\n",
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"\n",
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"</summary>\n",
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"\n",
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"```\n",
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"&FCI NORB= 16,NELEC=10,MS2=0,\n",
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" ORBSYM=1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1\n",
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" ISYM=1,\n",
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" &END\n",
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" 0.535263084520174 2 2 2 2\n",
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" 0.05793493716089329 3 1 3 1\n",
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" 0.08632998383785331 3 2 2 1\n",
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" 0.2097929322213681 3 2 3 2\n",
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" 0.4988558024531632 16 16 16 16\n",
|
|
" -6.683210272480665 1 1 0 0\n",
|
|
" -5.05801991735896 2 2 0 0\n",
|
|
" 0.5093740535790473 3 1 0 0\n",
|
|
" -5.060718004401872 3 3 0 0\n",
|
|
" -5.241594321289754 4 4 0 0\n",
|
|
" -5.241594321289755 5 5 0 0\n",
|
|
" -4.495352077885957 6 6 0 0\n",
|
|
" 1.031276567087045e-15 7 1 0 0\n",
|
|
" -4.495352077885959 7 7 0 0\n",
|
|
" -1.852207064622862e-15 8 1 0 0\n",
|
|
" 0.5862891072481656 8 2 0 0\n",
|
|
" 5.217912372939835e-15 8 3 0 0\n",
|
|
" -4.174967908523783e-15 8 4 0 0\n",
|
|
" -3.004188106134393 8 8 0 0\n",
|
|
" 0.353765259990788 9 1 0 0\n",
|
|
" -0.6083289518389058 9 3 0 0\n",
|
|
" 2.666971454264797e-15 9 8 0 0\n",
|
|
" -3.157845111668903 9 9 0 0\n",
|
|
" -0.9400165388605516 10 4 0 0\n",
|
|
" 1.175322440382098e-15 10 8 0 0\n",
|
|
" -3.516783993981039 10 10 0 0\n",
|
|
" -0.9400165388605513 11 5 0 0\n",
|
|
" -3.51678399398104 11 11 0 0\n",
|
|
" 0.4229990555408695 12 1 0 0\n",
|
|
" -1.905974893100913e-15 12 2 0 0\n",
|
|
" 0.626081952156225 12 3 0 0\n",
|
|
" 5.823279594237991e-15 12 8 0 0\n",
|
|
" -0.2288000350163298 12 9 0 0\n",
|
|
" -3.333008040651025 12 12 0 0\n",
|
|
" -1.174115690312534 13 6 0 0\n",
|
|
" 1.462965175656052e-15 13 11 0 0\n",
|
|
" -3.451001907784892 13 13 0 0\n",
|
|
" -1.174115690312534 14 7 0 0\n",
|
|
" 2.097688254432345e-15 14 10 0 0\n",
|
|
" -3.451001907784885 14 14 0 0\n",
|
|
" 1.510890214156748e-15 15 1 0 0\n",
|
|
" 0.4323970482854796 15 2 0 0\n",
|
|
" -1.262860516547564e-15 15 3 0 0\n",
|
|
" 1.982594591989286e-15 15 4 0 0\n",
|
|
" 0.4973837150599378 15 8 0 0\n",
|
|
" -4.330965086964359e-15 15 9 0 0\n",
|
|
" -3.214794676707322e-15 15 12 0 0\n",
|
|
" -3.961405744595176 15 15 0 0\n",
|
|
" -0.4289222488017268 16 2 0 0\n",
|
|
" 5.039051098775309e-15 16 3 0 0\n",
|
|
" -3.293855240294314e-15 16 4 0 0\n",
|
|
" 0.8512656679561205 16 8 0 0\n",
|
|
" 5.29294696293402e-15 16 9 0 0\n",
|
|
" 1.301363795748629e-15 16 10 0 0\n",
|
|
" 2.727924913158556e-15 16 12 0 0\n",
|
|
" -0.838369929881854 16 15 0 0\n",
|
|
" -3.317587539899629 16 16 0 0\n",
|
|
" -77.40622425962903 0 0 0 0\n",
|
|
" ```\n",
|
|
" </details>"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "bf007314-cc6b-4dcf-8678-5fd73df44b34",
|
|
"metadata": {},
|
|
"source": [
|
|
"## Prepare molecule information\n",
|
|
"\n",
|
|
"To begin, specify the molecule and its properties using `pyscf` and the electronic integrals stored in `n2_fci.txt`."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 1,
|
|
"id": "94d3f09d-324c-4eb3-a82a-3c88b9a11752",
|
|
"metadata": {
|
|
"tags": [
|
|
"remove-cell"
|
|
]
|
|
},
|
|
"outputs": [],
|
|
"source": [
|
|
"orbital_string = \"&FCI NORB= 16,NELEC=10,MS2=0,\\n ORBSYM=1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1\\n ISYM=1,\\n &END\\n 0.8227153295684669 1 1 1 1\\n 0.05187587577524144 2 1 2 1\\n 0.5219201962559413 2 2 1 1\\n 0.535263084520174 2 2 2 2\\n -0.1347836972470542 3 1 1 1\\n -0.008657841512417053 3 1 2 2\\n 0.05793493716089329 3 1 3 1\\n 0.08632998383785331 3 2 2 1\\n 0.2097929322213681 3 2 3 2\\n 0.5579235002150018 3 3 1 1\\n 0.5400470008931167 3 3 2 2\\n -0.03025371939317356 3 3 3 1\\n 0.5605460154373538 3 3 3 3\\n 0.09174878837664172 4 1 4 1\\n 0.04723726824560959 4 2 4 2\\n 0.01793854091372141 4 3 4 1\\n 0.02777111434804593 4 3 4 3\\n 0.6167116434966806 4 4 1 1\\n 0.4950011142931046 4 4 2 2\\n -0.05120347206217244 4 4 3 1\\n 0.4994721784892377 4 4 3 3\\n 0.5574513568785978 4 4 4 4\\n 0.09174878837664172 5 1 5 1\\n 0.04723726824560959 5 2 5 2\\n 0.01793854091372141 5 3 5 1\\n 0.02777111434804593 5 3 5 3\\n 0.02173144186568365 5 4 5 4\\n 0.6167116434966806 5 5 1 1\\n 0.4950011142931046 5 5 2 2\\n -0.05120347206217243 5 5 3 1\\n 0.4994721784892377 5 5 3 3\\n 0.5139884731472305 5 5 4 4\\n 0.5574513568785978 5 5 5 5\\n -0.03561566048469387 6 1 5 2\\n 0.03274533140789082 6 1 6 1\\n -0.06326282529165393 6 2 5 1\\n -0.03802750942520941 6 2 5 3\\n 0.07187262411478063 6 2 6 2\\n -0.03634033716578009 6 3 5 2\\n 0.02129640076005778 6 3 6 1\\n 0.03508481685867926 6 3 6 3\\n 0.01461681127204733 6 4 6 4\\n -0.08239995604786524 6 5 2 1\\n -0.1408740357900443 6 5 3 2\\n 0.1491913500304486 6 5 6 5\\n 0.5357098613594921 6 6 1 1\\n 0.4797794886355124 6 6 2 2\\n -0.02657196082195435 6 6 3 1\\n 0.4797443654275239 6 6 3 3\\n 0.4715924627481501 6 6 4 4\\n 0.5081607966085441 6 6 5 5\\n 0.4820906746005189 6 6 6 6\\n -0.0356156604846939 7 1 4 2\\n 0.03274533140789088 7 1 7 1\\n -0.06326282529165396 7 2 4 1\\n -0.03802750942520942 7 2 4 3\\n 0.07187262411478068 7 2 7 2\\n -0.0363403371657801 7 3 4 2\\n 0.02129640076005779 7 3 7 1\\n 0.03508481685867928 7 3 7 3\\n -0.08239995604786529 7 4 2 1\\n -0.1408740357900444 7 4 3 2\\n 0.1199577274863541 7 4 6 5\\n 0.1491913500304488 7 4 7 4\\n 0.01461681127204733 7 5 6 4\\n 0.01461681127204734 7 5 7 5\\n 0.01828416693019705 7 6 5 4\\n 0.01825888562015071 7 6 7 6\\n 0.5357098613594925 7 7 1 1\\n 0.4797794886355127 7 7 2 2\\n -0.02657196082195444 7 7 3 1\\n 0.4797443654275243 7 7 3 3\\n 0.5081607966085445 7 7 4 4\\n 0.4715924627481504 7 7 5 5\\n 0.4455729033602178 7 7 6 6\\n 0.4820906746005196 7 7 7 7\\n -0.03524297684128183 8 1 2 1\\n -0.04074732313525206 8 1 3 2\\n 0.05461805447735864 8 1 6 5\\n 0.0546180544773587 8 1 7 4\\n 0.03139253594027781 8 1 8 1\\n -0.09902456594727965 8 2 1 1\\n -0.04661452206194711 8 2 2 2\\n 0.01745134735859632 8 2 3 1\\n -0.0434285157352537 8 2 3 3\\n -0.07441150662198262 8 2 4 4\\n -0.07441150662198263 8 2 5 5\\n -0.05756619827574588 8 2 6 6\\n -0.05756619827574614 8 2 7 7\\n 0.03454616823267013 8 2 8 2\\n 0.01020038606708412 8 3 2 1\\n 0.03390671413208901 8 3 3 2\\n -0.01685771610674289 8 3 6 5\\n -0.01685771610674282 8 3 7 4\\n -0.001758941272080179 8 3 8 1\\n -1.454253424481812e-15 8 3 8 2\\n 0.02574499145622101 8 3 8 3\\n -0.02077063701641325 8 4 4 2\\n 0.02061769217890737 8 4 7 1\\n 0.009719515085149335 8 4 7 3\\n 0.01542975405064832 8 4 8 4\\n -0.02077063701641325 8 5 5 2\\n 0.02061769217890735 8 5 6 1\\n 0.009719515085149337 8 5 6 3\\n 0.01542975405064834 8 5 8 5\\n 0.03382971287644416 8 6 5 1\\n 0.006981782449266088 8 6 5 3\\n -0.02290667301698743 8 6 6 2\\n 0.01920341543530237 8 6 8 6\\n 0.0338297128764442 8 7 4 1\\n 0.006981782449266106 8 7 4 3\\n -0.02290667301698751 8 7 7 2\\n 0.0192034154353025 8 7 8 7\\n 0.3849906228031625 8 8 1 1\\n 1.532139515234422e-15 8 8 2 1\\n 0.3739434384087874 8 8 2 2\\n -0.01189244298406278 8 8 3 1\\n -1.70487262919109e-15 8 8 3 2\\n 0.3806281806388789 8 8 3 3\\n 0.3592472833223549 8 8 4 4\\n 0.3592472833223548 8 8 5 5\\n 0.3518218572933207 8 8 6 6\\n 0.3518218572933239 8 8 7 7\\n -9.213014454321943e-15 8 8 8 1\\n -0.002559575988447579 8 8 8 2\\n 2.582877514276093e-15 8 8 8 3\\n 0.3533280612079513 8 8 8 8\\n -0.08437056478993962 9 1 1 1\\n -0.02483152558294141 9 1 2 2\\n 0.03508237116075699 9 1 3 1\\n -0.04238233132830437 9 1 3 3\\n -0.03130903659562344 9 1 4 4\\n -0.03130903659562344 9 1 5 5\\n -0.0247567692246128 9 1 6 6\\n -0.0247567692246129 9 1 7 7\\n 0.006664526188246471 9 1 8 2\\n -0.0187004290474871 9 1 8 8\\n 0.03411063970385471 9 1 9 1\\n -0.000324543222555269 9 2 2 1\\n -0.009544290122943031 9 2 3 2\\n 0.0005846207771048886 9 2 6 5\\n 0.0005846207771048843 9 2 7 4\\n -0.004225446575758229 9 2 8 1\\n -0.0160233903830305 9 2 8 3\\n -1.296223756241197e-15 9 2 8 8\\n 0.01252498165364666 9 2 9 2\\n 0.1150822839777867 9 3 1 1\\n 0.04437457961389323 9 3 2 2\\n -0.03205451729612252 9 3 3 1\\n 0.05345664062548897 9 3 3 3\\n 0.07018063195288905 9 3 4 4\\n 0.07018063195288905 9 3 5 5\\n 0.05161063877667307 9 3 6 6\\n 0.05161063877667314 9 3 7 7\\n -0.03084929147706867 9 3 8 2\\n 0.003453484898978239 9 3 8 8\\n -0.01908776834443358 9 3 9 1\\n 0.0376521330958023 9 3 9 3\\n 0.02105492525439208 9 4 4 1\\n 0.009612956934137195 9 4 4 3\\n -0.0170208385670036 9 4 7 2\\n 0.0101644211871623 9 4 8 7\\n 0.01781400513488478 9 4 9 4\\n 0.02105492525439208 9 5 5 1\\n 0.009612956934137199 9 5 5 3\\n -0.0170208385670036 9 5 6 2\\n 0.01016442118716232 9 5 8 6\\n 0.01781400513488478 9 5 9 5\\n -0.002498627753198275 9 6 5 2\\n 0.00165309872168953 9 6 6 1\\n 0.0008160296419366277 9 6 6 3\\n 0.004146388883456698 9 6 8 5\\n 0.006081954311234169 9 6 9 6\\n -0.002498627753198287 9 7 4 2\\n 0.001653098721689535 9 7 7 1\\n 0.0008160296419366425 9 7 7 3\\n 0.004146388883456699 9 7 8 4\\n 0.006081954311234147 9 7 9 7\\n -0.02886065392650743 9 8 2 1\\n -0.08059579771897678 9 8 3 2\\n 0.05013528703473159 9 8 6 5\\n 0.05013528703473144 9 8 7 4\\n 0.00512605536727401 9 8 8 1\\n -0.03791888034075609 9 8 8 3\\n 1.79921551363938e-15 9 8 8 8\\n 0.0223703801094375 9 8 9 2\\n 0.07999279914080047 9 8 9 8\\n 0.4512983231568335 9 9 1 1\\n 0.3840689338373527 9 9 2 2\\n -0.03229840501917277 9 9 3 1\\n 0.3951272309006291 9 9 3 3\\n 0.4007276788093279 9 9 4 4\\n 0.4007276788093278 9 9 5 5\\n 0.3756829401859137 9 9 6 6\\n 0.3756829401859138 9 9 7 7\\n -0.02463475509719546 9 9 8 2\\n 0.3350906948054849 9 9 8 8\\n -0.01899282782297876 9 9 9 1\\n 0.0301941885483401 9 9 9 3\\n 0.357505673937019 9 9 9 9\\n 0.03002688675915308 10 1 4 1\\n 0.0005995709470891994 10 1 4 3\\n -0.0172438543749579 10 1 7 2\\n 0.01291169677940597 10 1 8 7\\n -0.003259507299477913 10 1 9 4\\n 0.02102579188104308 10 1 10 1\\n 0.01645536769518047 10 2 4 2\\n -0.01311940331444267 10 2 7 1\\n -0.009565545339108458 10 2 7 3\\n -0.01007660992560598 10 2 8 4\\n -0.001949322189805196 10 2 9 7\\n 0.0150687251098785 10 2 10 2\\n -0.00782040018913332 10 3 4 1\\n 0.005781477858077181 10 3 4 3\\n -0.001699410038954856 10 3 7 2\\n 0.001405760196545938 10 3 8 7\\n -0.001632221494911969 10 3 9 4\\n 0.001484050816561781 10 3 10 1\\n 0.011469849615765 10 3 10 3\\n 0.1449696637125928 10 4 1 1\\n 0.09695275968073921 10 4 2 2\\n -0.02683904819641667 10 4 3 1\\n 0.1040182545591939 10 4 3 3\\n 0.1054748177652819 10 4 4 4\\n 0.09906461632725239 10 4 5 5\\n 0.08547188003399001 10 4 6 6\\n 0.09092939778596297 10 4 7 7\\n -0.02924953767671292 10 4 8 2\\n 0.04394828485485928 10 4 8 8\\n -0.02947686995983997 10 4 9 1\\n 0.03114857713688626 10 4 9 3\\n 0.04298462169731809 10 4 9 9\\n 0.07359191071476424 10 4 10 4\\n 0.003205100719014754 10 5 5 4\\n 0.002728758875986386 10 5 7 6\\n 0.008191070656016116 10 5 10 5\\n 0.003740916537628832 10 6 6 4\\n 0.003740916537628842 10 6 7 5\\n 0.006733892595476496 10 6 10 6\\n -0.03175412552065111 10 7 2 1\\n -0.04419991710849876 10 7 3 2\\n 0.04413705154502855 10 7 6 5\\n 0.05161888462028632 10 7 7 4\\n 0.02799596056973121 10 7 8 1\\n 0.003753276611977636 10 7 8 3\\n 1.440315974143754e-15 10 7 8 8\\n -0.007265518703405046 10 7 9 2\\n -0.006288168906483342 10 7 9 8\\n 0.0512691171069093 10 7 10 7\\n -0.01432355064897697 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0.0005995709470891968 11 1 5 3\\n -0.01724385437495788 11 1 6 2\\n 0.01291169677940596 11 1 8 6\\n -0.003259507299477917 11 1 9 5\\n 0.02102579188104309 11 1 11 1\\n 0.01645536769518047 11 2 5 2\\n -0.01311940331444265 11 2 6 1\\n -0.009565545339108448 11 2 6 3\\n -0.01007660992560598 11 2 8 5\\n -0.001949322189805188 11 2 9 6\\n 0.0150687251098785 11 2 11 2\\n -0.007820400189133322 11 3 5 1\\n 0.00578147785807718 11 3 5 3\\n -0.001699410038954843 11 3 6 2\\n 0.001405760196545969 11 3 8 6\\n -0.001632221494911968 11 3 9 5\\n 0.00148405081656178 11 3 11 1\\n 0.011469849615765 11 3 11 3\\n 0.003205100719014754 11 4 5 4\\n 0.002728758875986387 11 4 7 6\\n 0.008191070656016116 11 4 10 5\\n 0.008191070656016116 11 4 11 4\\n 0.1449696637125928 11 5 1 1\\n 0.09695275968073919 11 5 2 2\\n -0.02683904819641666 11 5 3 1\\n 0.1040182545591939 11 5 3 3\\n 0.09906461632725239 11 5 4 4\\n 0.1054748177652819 11 5 5 5\\n 0.09092939778596278 11 5 6 6\\n 0.08547188003399016 11 5 7 7\\n 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16 8 3 3\\n -0.0929971341104211 16 8 4 4\\n -0.09299713411042132 16 8 5 5\\n -0.07447215480573277 16 8 6 6\\n 1.418913112035805e-15 16 8 7 4\\n -0.0744721548057293 16 8 7 7\\n -1.235496650450857e-14 16 8 8 1\\n 0.03058385024012861 16 8 8 2\\n -2.807618449520703e-15 16 8 8 3\\n -0.02162514696570199 16 8 8 8\\n 0.02292707768165599 16 8 9 1\\n -3.251211823944972e-15 16 8 9 2\\n -0.03305362734233186 16 8 9 3\\n 1.198113803374731e-14 16 8 9 8\\n -0.04047120735154422 16 8 9 9\\n -0.0436136845792128 16 8 10 4\\n -0.06660155569040506 16 8 10 10\\n -0.04361368457921235 16 8 11 5\\n 1.463491660010121e-15 16 8 11 6\\n -0.06660155569040617 16 8 11 11\\n 0.02249343448980179 16 8 12 1\\n 0.02283701299315213 16 8 12 3\\n -2.51805614312191e-15 16 8 12 8\\n -0.0141620101163715 16 8 12 9\\n -0.05196836611442802 16 8 12 12\\n -0.05003984710396388 16 8 13 6\\n -2.531158421807263e-15 16 8 13 11\\n -0.07057045222541083 16 8 13 13\\n -0.05003984710396864 16 8 14 7\\n -1.216273631049413e-15 16 8 14 10\\n -0.07057045222540506 16 8 14 14\\n 3.79844221080359e-15 16 8 15 1\\n 0.01216215746575668 16 8 15 2\\n 3.067028103237474e-15 16 8 15 3\\n 0.02553272980478118 16 8 15 8\\n -1.184736758566405e-14 16 8 15 9\\n -0.08945000627081254 16 8 15 15\\n -1.885148753175887e-14 16 8 16 1\\n -0.02268601333133103 16 8 16 2\\n -6.982787611444669e-15 16 8 16 3\\n 0.04364362361703802 16 8 16 8\\n -0.02328740596505909 16 9 2 1\\n -0.0341445044705503 16 9 3 2\\n 0.03789323894263637 16 9 6 5\\n 0.03789323894263621 16 9 7 4\\n 0.01990141487515895 16 9 8 1\\n -1.769783988096733e-15 16 9 8 2\\n -0.01237780914110229 16 9 8 3\\n 2.487937102691625e-14 16 9 8 8\\n 0.003232605014997546 16 9 9 2\\n 0.0201751912812144 16 9 9 8\\n 0.0137717600085071 16 9 10 7\\n 0.01377176000850698 16 9 11 6\\n 0.01296667359171537 16 9 12 2\\n -0.01915028448904604 16 9 12 8\\n -1.59564548212461e-15 16 9 12 9\\n 0.0208729992628594 16 9 13 5\\n 0.03662416839527009 16 9 13 11\\n 0.02087299926285967 16 9 14 4\\n 0.03662416839527043 16 9 14 10\\n -0.02635727351133685 16 9 15 1\\n 1.153001801588478e-15 16 9 15 2\\n 0.02772220207190784 16 9 15 3\\n -1.343675923343791e-14 16 9 15 8\\n 0.02008476535573606 16 9 15 9\\n -0.02498675818995541 16 9 15 12\\n 6.286637876939949e-15 16 9 15 15\\n -0.0346223583056286 16 9 16 1\\n -2.808777214152596e-15 16 9 16 2\\n 0.0170445544789866 16 9 16 3\\n 4.15319597915637e-14 16 9 16 8\\n 0.02380874268885576 16 9 16 9\\n 0.02769440758746226 16 10 4 2\\n -0.02673016631071906 16 10 7 1\\n -0.0161557132592215 16 10 7 3\\n -0.01638813739815387 16 10 8 4\\n -0.0007699984003947267 16 10 9 7\\n 0.007442968458760703 16 10 10 2\\n -0.009889489083785945 16 10 10 8\\n 0.001554393503338174 16 10 12 7\\n -0.01735043648355827 16 10 14 1\\n 0.002753286902048062 16 10 14 3\\n 0.001494807418268969 16 10 14 9\\n 0.02335754497241757 16 10 14 12\\n 0.01404471420438996 16 10 15 4\\n -0.006396325132918946 16 10 15 10\\n 0.01091245741709193 16 10 16 4\\n 0.0277313078959266 16 10 16 10\\n 0.02769440758746226 16 11 5 2\\n -0.02673016631071906 16 11 6 1\\n -0.01615571325922149 16 11 6 3\\n -0.01638813739815391 16 11 8 5\\n -0.0007699984003947657 16 11 9 6\\n 0.007442968458760724 16 11 11 2\\n -0.009889489083785927 16 11 11 8\\n 0.00155439350333822 16 11 12 6\\n -0.01735043648355834 16 11 13 1\\n 0.002753286902048006 16 11 13 3\\n 0.001494807418269107 16 11 13 9\\n 0.02335754497241761 16 11 13 12\\n 0.01404471420438998 16 11 15 5\\n -0.006396325132918912 16 11 15 11\\n 0.01091245741709197 16 11 16 5\\n 0.02773130789592675 16 11 16 11\\n -0.03222053773764886 16 12 2 1\\n -0.04825017259262916 16 12 3 2\\n 0.0533838638975611 16 12 6 5\\n 0.05338386389756125 16 12 7 4\\n 0.02303025246046144 16 12 8 1\\n -4.509262430078913e-15 16 12 8 2\\n -0.003494809294692472 16 12 8 3\\n 3.84297303606773e-14 16 12 8 8\\n -0.001519629208699993 16 12 9 2\\n 0.01384026476000111 16 12 9 8\\n 1.776653005017684e-15 16 12 9 9\\n 0.01460262989473362 16 12 10 7\\n 0.01460262989473362 16 12 11 6\\n 0.01891237059503479 16 12 12 2\\n -0.01498043615347002 16 12 12 8\\n -1.457920716678454e-15 16 12 12 9\\n -3.051532156117631e-15 16 12 12 12\\n 0.02386454932121355 16 12 13 5\\n 0.04683595810183153 16 12 13 11\\n 1.383016952962567e-15 16 12 13 13\\n 0.02386454932121322 16 12 14 4\\n 0.04683595810183153 16 12 14 10\\n 1.276115389668579e-15 16 12 14 14\\n -0.02179737382377572 16 12 15 1\\n 1.856803597162178e-15 16 12 15 2\\n 0.0264119391333841 16 12 15 3\\n -1.25333291974904e-14 16 12 15 8\\n 0.01288433222568699 16 12 15 9\\n -0.03421263480964471 16 12 15 12\\n 3.604755383079805e-15 16 12 15 15\\n -0.02855049523302051 16 12 16 1\\n -5.219375524274725e-15 16 12 16 2\\n 0.01651322398521536 16 12 16 3\\n 4.362257616865854e-14 16 12 16 8\\n 0.01542447990351162 16 12 16 9\\n 0.02682900793297205 16 12 16 12\\n -0.05668006138333965 16 13 5 1\\n -0.0161562579681439 16 13 5 3\\n 0.0458493427584348 16 13 6 2\\n -0.02133831631236967 16 13 8 6\\n -0.01242301321668599 16 13 9 5\\n -0.01829474708738727 16 13 11 1\\n 0.007411196438025029 16 13 11 3\\n 0.0195624809948784 16 13 11 9\\n -0.00273197443016854 16 13 12 5\\n 0.04251675853009274 16 13 12 11\\n 0.01216894721678041 16 13 13 2\\n -0.02205337167814066 16 13 13 8\\n 0.02403042546124195 16 13 15 6\\n -0.008850108812868383 16 13 15 13\\n 0.007384989569455208 16 13 16 6\\n 0.04513224232659596 16 13 16 13\\n -0.05668006138333961 16 14 4 1\\n -0.01615625796814387 16 14 4 3\\n 0.04584934275843478 16 14 7 2\\n -0.02133831631236992 16 14 8 7\\n -0.01242301321668604 16 14 9 4\\n -0.01829474708738724 16 14 10 1\\n 0.007411196438025063 16 14 10 3\\n 0.01956248099487841 16 14 10 9\\n -0.002731974430168641 16 14 12 4\\n 0.04251675853009265 16 14 12 10\\n 0.01216894721678029 16 14 14 2\\n -0.02205337167814028 16 14 14 8\\n 0.02403042546124205 16 14 15 7\\n -0.00885010881286854 16 14 15 14\\n 0.00738498956945486 16 14 16 7\\n 0.04513224232659604 16 14 16 14\\n 0.1569633113847971 16 15 1 1\\n 0.05787714956534407 16 15 2 2\\n -0.04994490156642798 16 15 3 1\\n 0.07686411480382442 16 15 3 3\\n 0.08303790680849328 16 15 4 4\\n 0.08303790680849335 16 15 5 5\\n 0.06081298889881077 16 15 6 6\\n 0.06081298889880927 16 15 7 7\\n 5.310399066097946e-15 16 15 8 1\\n -0.0231604828365148 16 15 8 2\\n 2.712708624576935e-15 16 15 8 3\\n 0.03639814722352972 16 15 8 8\\n -0.03902419268036143 16 15 9 1\\n 1.59899267460415e-15 16 15 9 2\\n 0.0351701600430642 16 15 9 3\\n -4.436474560991833e-15 16 15 9 8\\n 0.04604524611495352 16 15 9 9\\n 0.0525136519141776 16 15 10 4\\n 0.05544937108918365 16 15 10 10\\n 0.05251365191417747 16 15 11 5\\n 0.05544937108918409 16 15 11 11\\n -0.02729364114267291 16 15 12 1\\n -0.02046989051649213 16 15 12 3\\n 3.954528327059162e-15 16 15 12 8\\n 0.004497148195492229 16 15 12 9\\n 0.04149040805239823 16 15 12 12\\n 0.05596924463339107 16 15 13 6\\n 0.0635965839010509 16 15 13 13\\n 0.05596924463339334 16 15 14 7\\n 0.06359658390104776 16 15 14 14\\n -1.950499113974221e-15 16 15 15 1\\n -0.01336194832617421 16 15 15 2\\n -1.272433537729245e-15 16 15 15 3\\n -0.0252597323102154 16 15 15 8\\n 4.745472317309655e-15 16 15 15 9\\n -1.032702527524231e-15 16 15 15 12\\n 0.0930165819216586 16 15 15 15\\n 8.703197119210286e-15 16 15 16 1\\n 0.03023672607424808 16 15 16 2\\n 4.801543401410668e-15 16 15 16 3\\n -0.04266373857922931 16 15 16 8\\n -8.944651560152458e-15 16 15 16 9\\n 4.54937645014102e-15 16 15 16 12\\n 0.06578256216923312 16 15 16 15\\n 0.6095177502791381 16 16 1 1\\n 3.413477667354715e-15 16 16 2 1\\n 0.4514856598796156 16 16 2 2\\n -0.07283207717602366 16 16 3 1\\n 0.4694776049347383 16 16 3 3\\n 0.499413913175186 16 16 4 4\\n 0.4994139131751858 16 16 5 5\\n 0.4561590215966879 16 16 6 6\\n 1.668732234451617e-15 16 16 7 4\\n 0.4561590215966919 16 16 7 7\\n -2.137924509739039e-14 16 16 8 1\\n -0.0645202770416191 16 16 8 2\\n -5.628194789149302e-15 16 16 8 3\\n 0.3505526213192748 16 16 8 8\\n -0.05255663699969248 16 16 9 1\\n -4.88449799296871e-15 16 16 9 2\\n 0.07246707264790894 16 16 9 3\\n 2.338442757089573e-14 16 16 9 8\\n 0.388479126897645 16 16 9 9\\n 0.09884064916343566 16 16 10 4\\n 0.4293099836227132 16 16 10 10\\n 0.09884064916343638 16 16 11 5\\n 1.741943194642991e-15 16 16 11 6\\n 0.4293099836227113 16 16 11 11\\n -0.0489141873120035 16 16 12 1\\n -0.05002398657977705 16 16 12 3\\n -7.816833871831079e-15 16 16 12 8\\n 0.0299487240229355 16 16 12 9\\n 0.4061588202601188 16 16 12 12\\n 0.1158501412475767 16 16 13 6\\n -3.710521830287963e-15 16 16 13 11\\n 0.4362464030193691 16 16 13 13\\n -1.1187828317558e-15 16 16 14 4\\n 0.1158501412475714 16 16 14 7\\n -1.418465610520137e-15 16 16 14 10\\n 0.4362464030193751 16 16 14 14\\n 7.77876570191495e-15 16 16 15 1\\n -0.02772008861884064 16 16 15 2\\n 4.027542590396144e-15 16 16 15 3\\n -0.05828834141623013 16 16 15 8\\n -2.004025150191673e-14 16 16 15 9\\n 0.493391201597973 16 16 15 15\\n -2.887579115224201e-14 16 16 16 1\\n 0.04957040081284462 16 16 16 2\\n -1.198756349736642e-14 16 16 16 3\\n -0.09244148681404396 16 16 16 8\\n 3.20929905823288e-14 16 16 16 9\\n -8.789410358037327e-15 16 16 16 12\\n 0.09929387371351053 16 16 16 15\\n 0.4988558024531632 16 16 16 16\\n -6.683210272480665 1 1 0 0\\n -5.05801991735896 2 2 0 0\\n 0.5093740535790473 3 1 0 0\\n -5.060718004401872 3 3 0 0\\n -5.241594321289754 4 4 0 0\\n -5.241594321289755 5 5 0 0\\n -4.495352077885957 6 6 0 0\\n 1.031276567087045e-15 7 1 0 0\\n -4.495352077885959 7 7 0 0\\n -1.852207064622862e-15 8 1 0 0\\n 0.5862891072481656 8 2 0 0\\n 5.217912372939835e-15 8 3 0 0\\n -4.174967908523783e-15 8 4 0 0\\n -3.004188106134393 8 8 0 0\\n 0.353765259990788 9 1 0 0\\n -0.6083289518389058 9 3 0 0\\n 2.666971454264797e-15 9 8 0 0\\n -3.157845111668903 9 9 0 0\\n -0.9400165388605516 10 4 0 0\\n 1.175322440382098e-15 10 8 0 0\\n -3.516783993981039 10 10 0 0\\n -0.9400165388605513 11 5 0 0\\n -3.51678399398104 11 11 0 0\\n 0.4229990555408695 12 1 0 0\\n -1.905974893100913e-15 12 2 0 0\\n 0.626081952156225 12 3 0 0\\n 5.823279594237991e-15 12 8 0 0\\n -0.2288000350163298 12 9 0 0\\n -3.333008040651025 12 12 0 0\\n -1.174115690312534 13 6 0 0\\n 1.462965175656052e-15 13 11 0 0\\n -3.451001907784892 13 13 0 0\\n -1.174115690312534 14 7 0 0\\n 2.097688254432345e-15 14 10 0 0\\n -3.451001907784885 14 14 0 0\\n 1.510890214156748e-15 15 1 0 0\\n 0.4323970482854796 15 2 0 0\\n -1.262860516547564e-15 15 3 0 0\\n 1.982594591989286e-15 15 4 0 0\\n 0.4973837150599378 15 8 0 0\\n -4.330965086964359e-15 15 9 0 0\\n -3.214794676707322e-15 15 12 0 0\\n -3.961405744595176 15 15 0 0\\n -0.4289222488017268 16 2 0 0\\n 5.039051098775309e-15 16 3 0 0\\n -3.293855240294314e-15 16 4 0 0\\n 0.8512656679561205 16 8 0 0\\n 5.29294696293402e-15 16 9 0 0\\n 1.301363795748629e-15 16 10 0 0\\n 2.727924913158556e-15 16 12 0 0\\n -0.838369929881854 16 15 0 0\\n -3.317587539899629 16 16 0 0\\n -77.40622425962903 0 0 0 0\"\n",
|
|
"\n",
|
|
"\n",
|
|
"with open(\"n2_fci.txt\", \"w\") as output_file:\n",
|
|
" output_file.write(orbital_string)"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 2,
|
|
"id": "a41617e6-bc0b-48a9-9fe6-de7cfd84f9f6",
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"Parsing n2_fci.txt\n"
|
|
]
|
|
}
|
|
],
|
|
"source": [
|
|
"from pyscf import ao2mo, tools\n",
|
|
"\n",
|
|
"# Specify molecule properties\n",
|
|
"num_orbitals = 16\n",
|
|
"num_alpha = num_beta = 5\n",
|
|
"open_shell = False\n",
|
|
"spin_sq = 0\n",
|
|
"\n",
|
|
"# Read in molecule from disk\n",
|
|
"molecule_scf = tools.fcidump.to_scf(\"n2_fci.txt\")\n",
|
|
"\n",
|
|
"# Core Hamiltonian representing the single-electron integrals\n",
|
|
"core_hamiltonian = molecule_scf.get_hcore()\n",
|
|
"\n",
|
|
"# Electron repulsion integrals representing the two-electron integrals\n",
|
|
"electron_repulsion_integrals = ao2mo.restore(\n",
|
|
" 1, molecule_scf._eri, num_orbitals\n",
|
|
")\n",
|
|
"\n",
|
|
"# Nuclear repulsion energy of the molecule\n",
|
|
"nuclear_repulsion_energy = molecule_scf.mol.energy_nuc()"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "0f6239eb-d7f5-40ff-9e7a-262cf4fbe613",
|
|
"metadata": {},
|
|
"source": [
|
|
"## Obtain samples from an ansatz\n",
|
|
"\n",
|
|
"Once the molecule information has been loaded in, you should specify an ansatz circuit and optimize it for execution. This involves considering any symmetries of your problem, the choice of ansatz, and optimize it to run on quantum hardware.\n",
|
|
"\n",
|
|
"However, these choices are problem specific and out of scope for this guide. Instead, to demonstrate the SQD workflow, we will generate a random set of counts for the configuration recovery loop to post-process. This simulates the measurement data of a 32-qubit circuit sampled with 10,000 shots. After the count data has been generated, the `recover_configurations()` method requires that you convert the count data into a matrix of the bitstrings measured at each shot, as well as an array of probabilities for each state that was measured.\n",
|
|
"\n",
|
|
"<Admonition type = \"note\">\n",
|
|
"The artificial generation of samples is only used as a means to demonstrate the tooling of `qiskit-addon-sqd`. The package is meant to be used as part of a larger workflow wherein an ansatz or other circuit is defined, optimized, and executed using the Sampler primitive. The code cell below contains commented-out code demonstrating what a typical workflow might look like given a circuit ansatz transpiled to an ISA circuit.\n",
|
|
"</Admonition>"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 3,
|
|
"id": "004ea9de-413c-41d5-9208-a6981166f252",
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"# from qiskit_ibm_runtime import SamplerV2 as Sampler\n",
|
|
"\n",
|
|
"# sampler = Sampler(mode=backend)\n",
|
|
"# job = sampler.run([isa_circuit], shots=10_000)\n",
|
|
"# primitive_result = job.result()\n",
|
|
"# pub_result = primitive_result[0]\n",
|
|
"# counts = pub_result.data.meas.get_counts()\n",
|
|
"\n",
|
|
"from qiskit_addon_sqd.counts import generate_counts_uniform\n",
|
|
"from qiskit_addon_sqd.counts import counts_to_arrays\n",
|
|
"import numpy as np\n",
|
|
"\n",
|
|
"\n",
|
|
"rng = np.random.default_rng(24)\n",
|
|
"counts = generate_counts_uniform(10_000, num_orbitals * 2, rand_seed=rng)\n",
|
|
"\n",
|
|
"# rand_seed = 42\n",
|
|
"# counts = generate_counts_uniform(\n",
|
|
"# 10_000, num_orbitals * 2, rand_seed=rand_seed\n",
|
|
"# )\n",
|
|
"# Convert counts into bitstring and probability arrays\n",
|
|
"bitstring_matrix_full, probs_array_full = counts_to_arrays(counts)"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "c36a8888-42fa-4c60-9290-45d35f585c4e",
|
|
"metadata": {},
|
|
"source": [
|
|
"## Run configuration recovery loop\n",
|
|
"\n",
|
|
"The measurement samples can then be refined by repeating the configuration recovery and diagonalizing sets of subsamples to approximate the ground state until convergence.\n",
|
|
"\n",
|
|
"First, specify the following options:\n",
|
|
"\n",
|
|
"- `ITERATIONS`: The number of self-consistent configuration recovery iterations\n",
|
|
"- `NUM_BATCHES`: The number of sets of subsamples to diagonalize\n",
|
|
"- `SAMPLES_PER_BATCH`: The number of samples to include in each batch\n",
|
|
"- `MAX_DAVIDSON_CYCLES`: The number of iterations for the eigenstate solver"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 4,
|
|
"id": "d10aeaee-c20f-421c-94d1-a1e829dcaab5",
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"# SQD options\n",
|
|
"ITERATIONS = 5\n",
|
|
"\n",
|
|
"# Eigenstate solver options\n",
|
|
"NUM_BATCHES = 10\n",
|
|
"SAMPLES_PER_BATCH = 300\n",
|
|
"MAX_DAVIDSON_CYCLES = 200"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "d977f0e1-0e21-45d0-8971-92e1773f418b",
|
|
"metadata": {},
|
|
"source": [
|
|
"Next, in order to plot the convergence, define arrays to store the approximation of the ground state energy, expectation value of the $\\langle S \\rangle ^2$, and the orbital occupancy of the molecule."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 5,
|
|
"id": "a02aaca2-bca2-4531-b49a-3718a37de948",
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"# Self-consistent configuration recovery loop\n",
|
|
"energy_hist = np.zeros((ITERATIONS, NUM_BATCHES)) # energy history\n",
|
|
"spin_sq_hist = np.zeros((ITERATIONS, NUM_BATCHES)) # spin history\n",
|
|
"occupancy_hist = np.zeros((ITERATIONS, 2 * num_orbitals))\n",
|
|
"occupancies_bitwise = (\n",
|
|
" None # Orbital i corresponds to column i in bitstring matrix\n",
|
|
")"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "05823f66-cf57-43e0-bd9a-a77c6b6f8786",
|
|
"metadata": {},
|
|
"source": [
|
|
"Now, run the configuration recovery loop. Each loop consists of three steps:\n",
|
|
"\n",
|
|
"1. Use the `recover_configurations()` method to obtain a refined bitstring matrix and probability array based on the average orbital occupancy.\n",
|
|
"1. Use the `postselect_and_subsample()` to collect batches of subsamples to diagonalize over.\n",
|
|
"1. Then use the batches of subsamples as arguments to the `solve_fermion()` method to obtain an approximation of the ground state."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 7,
|
|
"id": "a6d492b5-d86b-43cd-9171-4add0903fe84",
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"Starting configuration recovery iteration 0\n",
|
|
"Starting configuration recovery iteration 1\n",
|
|
"Starting configuration recovery iteration 2\n",
|
|
"Starting configuration recovery iteration 3\n",
|
|
"Starting configuration recovery iteration 4\n"
|
|
]
|
|
}
|
|
],
|
|
"source": [
|
|
"from qiskit_addon_sqd.configuration_recovery import recover_configurations\n",
|
|
"from qiskit_addon_sqd.subsampling import postselect_and_subsample\n",
|
|
"from qiskit_addon_sqd.fermion import flip_orbital_occupancies, solve_fermion\n",
|
|
"\n",
|
|
"for i in range(ITERATIONS):\n",
|
|
" print(f\"Starting configuration recovery iteration {i}\")\n",
|
|
" # On the first iteration, we have no orbital occupancy information from the\n",
|
|
" # solver, so we just post-select from the full bitstring set based on Hamming weight.\n",
|
|
" if occupancies_bitwise is None:\n",
|
|
" bitstring_matrix_tmp = bitstring_matrix_full\n",
|
|
" probs_array_tmp = probs_array_full\n",
|
|
"\n",
|
|
" # If there is average orbital occupancy information, use it to refine the full set of noisy configurations\n",
|
|
" else:\n",
|
|
" bitstring_matrix_tmp, probs_array_tmp = recover_configurations(\n",
|
|
" bitstring_matrix_full,\n",
|
|
" probs_array_full,\n",
|
|
" occupancies_bitwise,\n",
|
|
" num_alpha,\n",
|
|
" num_beta,\n",
|
|
" rand_seed=rng,\n",
|
|
" )\n",
|
|
"\n",
|
|
" # Throw out configurations with an incorrect particle number in either the spin-up or spin-down systems\n",
|
|
" batches = postselect_and_subsample(\n",
|
|
" bitstring_matrix_tmp,\n",
|
|
" probs_array_tmp,\n",
|
|
" hamming_right=5,\n",
|
|
" hamming_left=5,\n",
|
|
" samples_per_batch=SAMPLES_PER_BATCH,\n",
|
|
" num_batches=NUM_BATCHES,\n",
|
|
" rand_seed=rng,\n",
|
|
" )\n",
|
|
"\n",
|
|
" # Run eigenstate solvers in a loop. This loop should be parallelized for larger problems.\n",
|
|
" e_tmp = np.zeros(NUM_BATCHES)\n",
|
|
" s_tmp = np.zeros(NUM_BATCHES)\n",
|
|
" occs_tmp = np.zeros((NUM_BATCHES, 2 * num_orbitals))\n",
|
|
" coeffs = []\n",
|
|
" for j in range(NUM_BATCHES):\n",
|
|
" energy_sci, coeffs_sci, avg_occs, spin = solve_fermion(\n",
|
|
" batches[j],\n",
|
|
" core_hamiltonian,\n",
|
|
" electron_repulsion_integrals,\n",
|
|
" open_shell=open_shell,\n",
|
|
" spin_sq=spin_sq,\n",
|
|
" max_davidson=MAX_DAVIDSON_CYCLES,\n",
|
|
" )\n",
|
|
" energy_sci += nuclear_repulsion_energy\n",
|
|
" e_tmp[j] = energy_sci\n",
|
|
" s_tmp[j] = spin\n",
|
|
" occs_tmp[j, :num_orbitals] = avg_occs[0]\n",
|
|
" occs_tmp[j, num_orbitals:] = avg_occs[1]\n",
|
|
" coeffs.append(coeffs_sci)\n",
|
|
"\n",
|
|
" # Combine batch results\n",
|
|
" avg_occupancy = np.mean(occs_tmp, axis=0)\n",
|
|
" # The occupancies from the solver should be flipped to match the bits in the bitstring matrix.\n",
|
|
" occupancies_bitwise = flip_orbital_occupancies(avg_occupancy)\n",
|
|
"\n",
|
|
" # Track optimization history\n",
|
|
" energy_hist[i, :] = e_tmp\n",
|
|
" spin_sq_hist[i, :] = s_tmp\n",
|
|
" occupancy_hist[i, :] = avg_occupancy"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "39b08afb-82f8-4622-b300-4509fd056917",
|
|
"metadata": {},
|
|
"source": [
|
|
"### Visualize the results\n",
|
|
"\n",
|
|
"Lastly, the results can be visualized by examining the approximated energy and average orbital occupancy at each iteration of the configuration recovery loop. The first plot shows that after a few iterations, the ground state energy is estimated to within approximately `200 mH` (chemical accuracy is typically accepted to be `1 kcal/mol` $\\approx$ `1.6 mH`). Recall that this demonstration used pure noise, and that the ability to approximate the energy to this degree comes from prior knowledge about the molecule and its electronic structure.\n",
|
|
"\n",
|
|
"The second plot shows the average occupancy of each spatial orbital after the final iteration. Notice that both the spin-up and spin-down electrons occupy the first five orbitals with high probability in the solutions."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 8,
|
|
"id": "dcd4ed70-89a0-44f4-b4b0-6270bbeb0c13",
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
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68PX1zVLcu++++xx+22Cmw4cPa82aNRo4cKDD+xoxYoRGjhypnj17ql69enrmmWf00ksvKSIiwuF9V69eXevWrdOlS5f0xx9/aMuWLbp27ZqqVavm8L4zj0WF6TiVWZA6fPiwVq9ebcpVUpJUokQJ1ahRQw888IDmzJmjIkWKaM6cOQ7p66efftLJkydVpUoV63Hq8OHD+r//+z/5+/s7pM+cVKtWTZ6eng49VuUVRal8wM3NTY0aNVJMTIy1LSMjQzExMcxxAjiZYRgaNmyYli5dqh9++EEBAQHOTgkOkJGRobS0NGengTxo166ddu3apfj4eOurcePG6t27t+Lj4/PdJeowX2EbZ+WX7y1HH1fzy2f/0qVLOnDggHx9fR3Wx0MPPaS9e/fatP3++++qWrWqw/q80bx58+Tl5aXOnTs7vK/Lly/LxcX2T1RXV1dlZGQ4vO9MJUqUkK+vr86dO6eVK1fq0UcfdXifAQEB8vHxsTlOpaSkaPPmzQXyOJVZkNq3b5/WrFmj8uXLOy0XRx6rnnnmGe3cudPmOOXn56cRI0Zo5cqVDukzJ0ePHtWZM2cceqzKK27fyyfCwsIUEhKixo0bq2nTppo6dapSU1PVr18/Z6eGPLh06ZJNFToxMVHx8fEqV66cqlSp4tTccHtCQ0P12Wef6euvv1bJkiWt9/WXLl1axYoVc3Z6yINRo0apU6dOqlKlii5evKjPPvtMsbGxpg8OYB8lS5bMMldOiRIlVL58eeZ+g5WzxlnOGA8443vLGcdVZ332X375ZXXp0kVVq1bV8ePHFR4eLldXV/Xq1cthfb700kt68MEHNXHiRD355JPasmWLZs2apVmzZjmsz0wZGRmaN2+eQkJCVKSI4/907NKli9566y1VqVJFderU0Y4dO/Tee++pf//+Du975cqVMgxDtWrV0v79+zVixAjVrl3bbseJWx0Phg8frjfffFM1a9ZUQECAxowZIz8/P3Xt2tWh/Z49e1ZHjhzR8ePHJclaAPXx8cnzVVo369PX11fdu3fX9u3b9e233yo9Pd16nCpXrpzc3Nwcsq/ly5fXW2+9pUceeUS+vr46ffq0IiMjdezYMT3xxBMO6bNKlSpZCm5FixaVj4+PatWqlec+b9VvuXLlNG7cOD3++OPy8fHRgQMH9Morr6hGjRoKDg6+o34dwtmP/8P/TJ8+3ahSpYrh5uZmNG3a1Ni0aZOzU0IerV271pCU5RUSEuLs1HCbsvs9SjLmzZvn7NSQR/379zeqVq1quLm5GRUqVDDatWtnrFq1ytlpwY7MeCw87j7OGGc5YzzgjO+t/HJcNeOz36NHD8PX19dwc3MzKlasaPTo0cPYv3+/Q/s0DMNYvny5UbduXcPd3d2oXbu2MWvWLIf3aRiGsXLlSkOSsXfvXlP6S0lJMV588UWjSpUqhoeHh1GtWjXj9ddfN9LS0hze9+LFi41q1aoZbm5uho+PjxEaGmqcP3/ebtu/1fEgIyPDGDNmjOHt7W24u7sb7dq1s8vP/Vb9zps3L9v14eHhDukzMTExx+PU2rVrHbavf/75p/HYY48Zfn5+hpubm+Hr62s88sgjxpYtWxzWZ3aqVq1qvP/++3fU5636vXz5stGhQwejQoUKRtGiRY2qVasagwYNMpKSku64X0ewGP/98gIAAAAAAABMw5xSAAAAAAAAMB1FKQAAAAAAAJiOohQAAAAAAABMR1EKAAAAAAAApqMoBQAAAAAAANNRlAIAAAAAAIDpKEoBAAAAAADAdBSlAAAAAAAAYDqKUgAKndjYWFksFsXGxjo7Fbt44403ZLFYnJ0GAADIZ/r27at77rknV7EWi0VvvPGGXftv3bq1Wrdubddt5lbfvn3l7+/vlL4B5B5FKQB3ZP78+bJYLNq6dau17bvvvrP7oCYv/v3vf2v+/PnOTsNG69atVbduXWenAQAA8rFff/1VTz/9tCpWrCh3d3f5+fmpd+/e+vXXX03LYcOGDXrjjTd0/vx5h/fl7++vf/3rXw7vB0D+Q1EKgN199913GjdunLPTyLEo9fDDD+vPP//Uww8/7JS8AAAAcrJkyRI1bNhQMTEx6tevn/79739rwIABWrt2rRo2bKilS5c6pN8///xTo0ePti5v2LBB48aNM6UoBaDwKuLsBAAgNwzD0JUrV1SsWLE73paLi4s8PDzskhcAAIC9HDhwQM8884yqVaumH3/8URUqVLCue/HFF9WyZUs988wz2rlzp6pVq5bjdlJTU1WiRInb6puxEQBn4EopAHbVt29fRUZGSn/NTZD5ypSRkaGpU6eqTp068vDwkLe3twYPHqxz587ZbCfzMu6VK1eqcePGKlasmD788ENJ0rx589S2bVt5eXnJ3d1dgYGBmjlzZpb3//rrr1q3bp01h8w5DXKaU+rLL79Uo0aNVKxYMXl6eurpp5/WsWPHsuzfPffco2PHjqlr16665557VKFCBb388stKT0/P08/MYrFo2LBhWrZsmerWrSt3d3fVqVNH0dHRWWLXr1+vJk2ayMPDQ9WrV7f+TLLz6aefWvenXLly6tmzp/744w/r+nnz5slisWju3Lk275s4caIsFou+++67PO0PAADImylTpujy5cuaNWuWTUFKkjw9PfXhhx8qNTVVkydPtrZnzi2ZkJCgp556SmXLllWLFi1s3nvw4EEFBwerRIkS8vPz0/jx42UYhk3MjXNKvfHGGxoxYoQkKSAgwDqWOnTokJTLsdidOHTokCwWi9555x3NmjVL1atXl7u7u5o0aaK4uLgs8ZljKA8PD9WtWzfHq8lyMw4NDw+Xi4uLYmJibN777LPPys3NTb/88ovd9hMAV0oBsLPBgwfr+PHjWr16tT755JNs18+fP1/9+vXTCy+8oMTERM2YMUM7duzQzz//rKJFi1pj9+7dq169emnw4MEaNGiQatWqJUmaOXOm6tSpo0ceeURFihTR8uXLNXToUGVkZCg0NFSSNHXqVD3//PO655579Prrr0uSvL29c8w7M6cmTZooIiJCycnJmjZtmn7++Wft2LFDZcqUscamp6crODhYzZo10zvvvKM1a9bo3XffVfXq1TVkyJA8/dzWr1+vJUuWaOjQoSpZsqQ++OADPf744zpy5IjKly8vSdq1a5c6dOigChUq6I033tD169cVHh6e7X699dZbGjNmjJ588kkNHDhQp06d0vTp0/Xwww9b96dfv35asmSJwsLC9I9//EOVK1fWrl27NG7cOA0YMED//Oc/87QvAAAgb5YvXy5/f3+1bNky2/UPP/yw/P39tWLFiizrnnjiCdWsWVMTJ060KTilp6erY8eOeuCBBzR58mRFR0crPDxc169f1/jx47Ptp1u3bvr999/1+eef6/3335enp6ckWQtluRmL2cNnn32mixcvavDgwbJYLJo8ebK6deumgwcPWseMq1at0uOPP67AwEBFRETozJkz6tevnypVqpRle7kZh44ePVrLly/XgAEDtGvXLpUsWVIrV67U7NmzNWHCBDVo0MBu+wfgv7fEAECezZs3z5BkxMXFWdtCQ0ON7A4vP/30kyHJWLhwoU17dHR0lvaqVasakozo6Ogs27l8+XKWtuDgYKNatWo2bXXq1DFatWqVJXbt2rWGJGPt2rWGYRjG1atXDS8vL6Nu3brGn3/+aY379ttvDUnG2LFjrW0hISGGJGP8+PE227z//vuNRo0aZfMTstWqVSujTp06Nm2SDDc3N2P//v3Wtl9++cWQZEyfPt3a1rVrV8PDw8M4fPiwtS0hIcFwdXW1+XkfOnTIcHV1Nd566y2bfnbt2mUUKVLEpv3EiRNGuXLljH/84x9GWlqacf/99xtVqlQxLly4cMt9AQAA9nP+/HlDkvHoo4/eNO6RRx4xJBkpKSmGYRhGeHi4Icno1atXltjMccvzzz9vbcvIyDA6d+5suLm5GadOnbK2SzLCw8Oty1OmTDEkGYmJiVm2m9uxWKtWrbIdi/1d1apVjc6dO1uXExMTDUlG+fLljbNnz1rbv/76a0OSsXz5cmtbUFCQ4evra5w/f97atmrVKkOSUbVqVWvb7YxDd+3aZbi5uRkDBw40zp07Z1SsWNFo3Lixce3atVvuC4Dbw+17AEzz5ZdfqnTp0vrHP/6h06dPW1+NGjXSPffco7Vr19rEBwQEKDg4OMt2bpxX6sKFCzp9+rRatWqlgwcP6sKFC7ed19atW3Xy5EkNHTrUZj6Fzp07q3bt2tmejXzuuedsllu2bKmDBw/edt+Z2rdvr+rVq1uX69evr1KlSlm3mZ6erpUrV6pr166qUqWKNe6+++7L8jNasmSJMjIy9OSTT9r8nH18fFSzZk2bn7OPj48iIyO1evVqtWzZUvHx8Zo7d65KlSqV530BAAC37+LFi5KkkiVL3jQuc31KSopN+9/HJjcaNmyY9d+Z0wZcvXpVa9asyVOu9h6L5aRHjx4qW7asdTnzCrLM8dGJEycUHx+vkJAQlS5d2hr3j3/8Q4GBgTbbup1xaN26dTVu3Dh99NFHCg4O1unTp7VgwQIVKcKNRoC98akCYJp9+/bpwoUL8vLyynb9yZMnbZYDAgKyjfv5558VHh6ujRs36vLlyzbrLly4YDMoyY3Dhw9LkvX2wBvVrl1b69evt2nz8PDIMs9D2bJls8yLdTtuLDRlt81Tp07pzz//VM2aNbPE1apVy2b+p3379skwjGxjJdncIilJPXv21KeffqoVK1bo2WefVbt27fK8HwAAIG8yi02Zxamc5FS8ymnc5OLikmVS9HvvvVf6a+6mvLD3WCwnfx8fZRaoMsdHmWO4nMZH27dvty7f7jh0xIgRWrRokbZs2aKJEydmKXIBsA+KUgBMk5GRIS8vLy1cuDDb9X8v9GT3pL0DBw6oXbt2ql27tt577z1VrlxZbm5u+u677/T+++8rIyPDYflncnV1NW2bf5+ENDcyMjJksVj0/fffZ7vde+65x2b5zJkz2rp1qyQpISFBGRkZcnHhQloAAMxUunRp+fr6aufOnTeN27lzpypWrJjlqmZ7PKE4N8wci9l7fHQ749CDBw9q37590l/zegJwDIpSAOzuxqft3ah69epas2aNHnrooTwPnJYvX660tDR98803NmfP/n7r383y+LuqVatKf02s3rZtW5t1e/futa53pgoVKqhYsWLWwdGN9u7da7NcvXp1GYahgIAA65nQmwkNDdXFixcVERGhUaNGaerUqQoLC7Nr/gAA4Nb+9a9/afbs2Vq/fn2WJ+hJ0k8//aRDhw5p8ODBud5mRkaGDh48aDMm+P3336W/nlack5zGUbczFnO0zDFabsdHuR2HZmRkqG/fvipVqpSGDx+uiRMnqnv37urWrZud9wAAp8IB2F2JEiUkSefPn7dpf/LJJ5Wenq4JEyZkec/169ezxGcn84zZjWfILly4oHnz5mWbR2622bhxY3l5eSkqKkppaWnW9u+//1579uxR586db7kNR3N1dVVwcLCWLVumI0eOWNv37NmjlStX2sR269ZNrq6uGjduXJYziYZh6MyZM9blr776SosXL9bbb7+tkSNHqmfPnho9erR1sAoAAMwzYsQIFStWTIMHD7b5vpaks2fP6rnnnlPx4sU1YsSI29rujBkzrP82DEMzZsxQ0aJFb3rLfk7judsZizmar6+vgoKCtGDBApu5rFavXq2EhASb2NsZh7733nvasGGDZs2apQkTJujBBx/UkCFDdPr0aQfvEVD4cKUUALtr1KiRJOmFF15QcHCwXF1d1bNnT7Vq1UqDBw9WRESE4uPj1aFDBxUtWlT79u3Tl19+qWnTpql79+433XaHDh3k5uamLl26aPDgwbp06ZJmz54tLy8vnThxIkseM2fO1JtvvqkaNWrIy8sry5VQ+muOpUmTJqlfv35q1aqVevXqpeTkZE2bNk3+/v566aWX7PwTyptx48YpOjpaLVu21NChQ3X9+nVNnz5dderUsbnUv3r16nrzzTc1atQoHTp0SF27dlXJkiWVmJiopUuX6tlnn9XLL7+skydPasiQIWrTpo11AtQZM2Zo7dq16tu3r9avX89tfAAAmKhmzZpasGCBevfurXr16mnAgAEKCAjQoUOHNGfOHJ0+fVqff/65zcNRbsXDw0PR0dEKCQlRs2bN9P3332vFihV67bXXstyydqPM8dzrr7+unj17qmjRourSpcttjcXMEBERoc6dO6tFixbq37+/zp49ax0fXbp0yRqX23Honj17NGbMGPXt21ddunSRJM2fP19BQUEaOnSovvjiC9P3ESjQnP34PwB3t3nz5hmSjLi4OGvb9evXjeeff96oUKGCYbFYjL8fambNmmU0atTIKFasmFGyZEmjXr16xiuvvGIcP37cGvP3RwPf6JtvvjHq169veHh4GP7+/sakSZOMuXPnZnlscVJSktG5c2ejZMmShiTrI4nXrl1rSDLWrl1rs93Fixcb999/v+Hu7m6UK1fO6N27t3H06FGbmJCQEKNEiRJZcsp8HPOttGrVyqhTp45NmyQjNDQ0S2zVqlWNkJAQm7Z169YZjRo1Mtzc3Ixq1aoZUVFROfb9n//8x2jRooVRokQJo0SJEkbt2rWN0NBQY+/evYZhGEa3bt2MkiVLGocOHbJ5X+bjlidNmnTL/QEAAPa3c+dOo1evXoavr69RtGhRw8fHx+jVq5exa9euLLGZ44BTp05lWZc5bjlw4IDRoUMHo3jx4oa3t7cRHh5upKen28RKMsLDw23aJkyYYFSsWNFwcXGxGWfldizWqlUr6/jrZv4+7ktMTDQkGVOmTMkSm12e//nPf4z77rvPcHd3NwIDA40lS5YYISEhRtWqVbO8/2bj0OvXrxtNmjQxKlWqZJw/f97mfdOmTTMkGYsXL77l/gDIPYuRl1niAAAAAAAAgDvAfRkAAAAAAAAwHUUpAAAAAAAAmI6iFAAAAAAAAExHUQoAAAAAAACmoygFAAAAAAAA01GUAgAAAAAAgOkoSgEAAAAAAMB0FKUAAAAAAABgOopSAAAAAAAAMB1FKQAAAAAAAJiOohQAAAAAAABMR1EKAAAAAAAApqMoBQAAAAAAANP9P2sWrlMc34MZAAAAAElFTkSuQmCC",
|
|
"text/plain": [
|
|
"<Figure size 1200x600 with 2 Axes>"
|
|
]
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
|
"source": [
|
|
"import matplotlib.pyplot as plt\n",
|
|
"\n",
|
|
"# Data for energies plot\n",
|
|
"n2_exact = -109.10288938\n",
|
|
"x1 = range(ITERATIONS)\n",
|
|
"e_diff = [abs(np.min(energies) - n2_exact) for energies in energy_hist]\n",
|
|
"yt1 = [1.0, 1e-1, 1e-2, 1e-3, 1e-4]\n",
|
|
"\n",
|
|
"# Chemical accuracy (+/- 1 milli-Hartree)\n",
|
|
"chem_accuracy = 0.001\n",
|
|
"\n",
|
|
"# Data for avg spatial orbital occupancy\n",
|
|
"y2 = avg_occupancy[:num_orbitals] + avg_occupancy[num_orbitals:]\n",
|
|
"x2 = range(len(y2))\n",
|
|
"\n",
|
|
"fig, axs = plt.subplots(1, 2, figsize=(12, 6))\n",
|
|
"\n",
|
|
"# Plot energies\n",
|
|
"axs[0].plot(x1, e_diff, label=\"energy error\", marker=\"o\")\n",
|
|
"axs[0].set_xticks(x1)\n",
|
|
"axs[0].set_xticklabels(x1)\n",
|
|
"axs[0].set_yticks(yt1)\n",
|
|
"axs[0].set_yticklabels(yt1)\n",
|
|
"axs[0].set_yscale(\"log\")\n",
|
|
"axs[0].set_ylim(1e-4)\n",
|
|
"axs[0].axhline(\n",
|
|
" y=chem_accuracy,\n",
|
|
" color=\"#BF5700\",\n",
|
|
" linestyle=\"--\",\n",
|
|
" label=\"chemical accuracy\",\n",
|
|
")\n",
|
|
"axs[0].set_title(\"Approximated Ground State Energy vs SQD Iterations\")\n",
|
|
"axs[0].set_xlabel(\"Iteration Index\", fontdict={\"fontsize\": 12})\n",
|
|
"axs[0].set_ylabel(\"Energy Error (Ha)\", fontdict={\"fontsize\": 12})\n",
|
|
"axs[0].legend()\n",
|
|
"\n",
|
|
"# Plot orbital occupancy\n",
|
|
"axs[1].bar(x2, y2, width=0.8)\n",
|
|
"axs[1].set_xticks(x2)\n",
|
|
"axs[1].set_xticklabels(x2)\n",
|
|
"axs[1].set_title(\"Avg Occupancy per Spatial Orbital\")\n",
|
|
"axs[1].set_xlabel(\"Orbital Index\", fontdict={\"fontsize\": 12})\n",
|
|
"axs[1].set_ylabel(\"Avg Occupancy\", fontdict={\"fontsize\": 12})\n",
|
|
"\n",
|
|
"plt.tight_layout()\n",
|
|
"plt.show()"
|
|
]
|
|
}
|
|
],
|
|
"metadata": {
|
|
"description": "Get started with the SQD addon and how to post-process results",
|
|
"kernelspec": {
|
|
"display_name": "Python 3",
|
|
"language": "python",
|
|
"name": "python3"
|
|
},
|
|
"language_info": {
|
|
"codemirror_mode": {
|
|
"name": "ipython",
|
|
"version": 3
|
|
},
|
|
"file_extension": ".py",
|
|
"mimetype": "text/x-python",
|
|
"name": "python",
|
|
"nbconvert_exporter": "python",
|
|
"pygments_lexer": "ipython3",
|
|
"version": "3"
|
|
},
|
|
"title": "Getting started with SQD"
|
|
},
|
|
"nbformat": 4,
|
|
"nbformat_minor": 2
|
|
}
|