85 lines
3.4 KiB
Plaintext
85 lines
3.4 KiB
Plaintext
---
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title: calculate_1q_epg
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description: API reference for qiskit.ignis.verification.calculate_1q_epg
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in_page_toc_min_heading_level: 1
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python_api_type: function
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python_api_name: qiskit.ignis.verification.calculate_1q_epg
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---
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# qiskit.ignis.verification.calculate\_1q\_epg
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<Function id="qiskit.ignis.verification.calculate_1q_epg" isDedicatedPage={true} github="https://github.com/qiskit-community/qiskit-ignis/tree/stable/0.7/qiskit/ignis/verification/randomized_benchmarking/rb_utils.py" signature="calculate_1q_epg(gate_per_cliff, epc_1q, qubit)">
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Convert error per Clifford (EPC) into error per gates (EPGs) of single qubit basis gates.
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Given that a standard 1Q RB sequences consist of `u1`, `u2` and `u3` gates, the EPC can be written using those EPGs:
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$$
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EPC = 1 - (1 - EPG_{U1})^{N_{U1}} (1 - EPG_{U2})^{N_{U2}} (1 - EPG_{U3})^{N_{U3}}.
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$$
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where $N_{x}$ is the number of gate $x$ per Clifford. Assuming `u1` composed of virtual-Z gate, ie FrameChange instruction, the $EPG_{U1}$ is estimated to be zero within the range of quantization error. Therefore the EPC can be written as:
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$$
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EPC = 1 - (1 - EPG_{U2})^{N_{U2}} (1 - EPG_{U3})^{N_{U3}}.
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$$
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Because `u2` and `u3` gates are respectively implemented by a single and two half-pi pulses with virtual-Z rotations, we assume $EPG_{U3} = 2EPG_{U2}$. Using this relation in the limit of $EPG_{U2} \ll 1$:
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$$
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\begin{split}EPC & = 1 - (1 - EPG_{U2})^{N_{U2}} (1 - 2 EPG_{U2})^{N_{U3}} \\
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& \simeq EPG_{U2}(N_{U2} + 2 N_{U3}).\end{split}
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$$
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Finally the EPG of each basis gate can be written using EPC and number of gates:
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$$
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\begin{split}EPG_{U1} &= 0 \\
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EPG_{U2} &= EPC / (N_{U2} + 2 N_{U3}) \\
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EPG_{U3} &= 2 EPC / (N_{U2} + 2 N_{U3})\end{split}
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$$
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To run this function, you first need to run a standard 1Q RB experiment with transpiled `QuantumCircuit` and count the number of basis gates composing the RB circuits.
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```python
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import pprint
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import qiskit.ignis.verification.randomized_benchmarking as rb
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# assuming we ran 1Q RB experiment for qubit 0
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gpc = {0: {'cx': 0, 'u1': 0.13, 'u2': 0.31, 'u3': 0.51}}
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epc = 1.5e-3
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# calculate 1Q EPGs
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epgs = rb.rb_utils.calculate_1q_epg(gate_per_cliff=gpc, epc_1q=epc, qubit=0)
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pprint.pprint(epgs)
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```
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```python
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{'u1': 0, 'u2': 0.0011278195488721805, 'u3': 0.002255639097744361}
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```
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In the example, `gpc` can be generated by [`gates_per_clifford()`](qiskit.ignis.verification.gates_per_clifford "qiskit.ignis.verification.gates_per_clifford"). The output of the function `epgs` can be used to calculate EPG of CNOT gate in conjugation with 2Q RB results, see [`calculate_2q_epg()`](qiskit.ignis.verification.calculate_2q_epg "qiskit.ignis.verification.calculate_2q_epg").
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<Admonition title="Note" type="note">
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This function presupposes the basis gate consists of `u1`, `u2` and `u3`.
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</Admonition>
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**Parameters**
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* **gate\_per\_cliff** (`Dict`\[`int`, `Dict`\[`str`, `float`]]) – dictionary of gate per Clifford. see [`gates_per_clifford()`](qiskit.ignis.verification.gates_per_clifford "qiskit.ignis.verification.gates_per_clifford").
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* **epc\_1q** (`float`) – EPC fit from 1Q RB experiment data.
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* **qubit** (`int`) – index of qubit to calculate EPGs.
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**Return type**
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`Dict`\[`str`, `float`]
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**Returns**
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Dictionary of EPGs of single qubit basis gates.
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**Raises**
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**QiskitError** – when `u2` or `u3` is not found, `cx` gate count is nonzero, or specified qubit is not included in the gate count dictionary.
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</Function>
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