# -*- coding: utf-8 -*-
# This code is part of Qiskit.
#
# (C) Copyright IBM 2019.
#
# This code is licensed under the Apache License, Version 2.0. You may
# obtain a copy of this license in the LICENSE.txt file in the root directory
# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0.
#
# Any modifications or derivative works of this code must retain this
# copyright notice, and modified files need to carry a notice indicating
# that they have been altered from the originals.
# TODO(mtreinish): Remove these disables when implementation is finished
# pylint: disable=unused-argument,unnecessary-pass,invalid-name
"""
RB Helper functions
"""
from typing import List, Union, Dict, Optional
from warnings import warn
import numpy as np
from qiskit import QuantumCircuit, QiskitError
from qiskit.qobj import QasmQobj
[docs]def count_gates(qobj, basis, qubits):
"""
Take a compiled qobj and output the number of gates in each circuit.
Args:
qobj (QasmQObj): compiled qobj.
basis (list): gates basis for the qobj.
qubits (list): qubits to count over.
Returns:
list: n x l x m list of number of gates.
* n: number of circuits,
* l: number of qubits,
* m: number of gates in basis.
Additional Information:
nQ gates are counted in each qubit's set of gates.
"""
warn('The function `count_gates` will be deprecated. '
'Gate count is integrated into `gates_per_clifford` function.',
category=DeprecationWarning)
nexp = len(qobj.experiments)
ngates = np.zeros([nexp, len(qubits), len(basis)], dtype=int)
basis_ind = {basis[i]: i for i in range(len(basis))}
for i in range(nexp):
for instr in qobj.experiments[i].instructions:
if instr.name in basis:
for qind, qubit in enumerate(qubits):
if qubit in instr.qubits:
ngates[i][qind][basis_ind[instr.name]] += 1
return ngates
[docs]def gates_per_clifford(
transpiled_circuits_list: Union[List[List[QuantumCircuit]], List[QasmQobj]],
clifford_lengths: Union[np.ndarray, List[int]],
basis: List[str],
qubits: List[int]) -> Dict[int, Dict[str, float]]:
"""Take a list of transpiled ``QuantumCircuit`` and use these to calculate
the number of gates per Clifford. Each ``QuantumCircuit`` should be transpiled into
given ``basis`` set. The result can be used to convert a value of error per Clifford
into error per basis gate under appropriate assumption.
Example:
This example shows how to calculate gate per Clifford of 2Q RB sequence for
qubit 0 and qubit 1. You can refer to the function
:mod:`~qiskit.ignis.verification.randomized_benchmarking.randomized_benchmarking_seq`
for the detail of RB circuit generation.
.. jupyter-execute::
import pprint
import qiskit
import qiskit.ignis.verification.randomized_benchmarking as rb
from qiskit.test.mock.backends import FakeAlmaden
rb_circs_list, xdata = rb.randomized_benchmarking_seq(
nseeds=5,
length_vector=[1, 20, 50, 100],
rb_pattern=[[0, 1]])
basis = FakeAlmaden().configuration().basis_gates
# transpile
transpiled_circuits_list = []
for rb_circs in rb_circs_list:
rb_circs_transpiled = qiskit.transpile(rb_circs, basis_gates=basis)
transpiled_circuits_list.append(rb_circs_transpiled)
# count gate per Clifford
ngates = rb.rb_utils.gates_per_clifford(
transpiled_circuits_list=transpiled_circuits_list,
clifford_lengths=xdata[0],
basis=basis, qubits=[0, 1])
pprint.pprint(ngates)
The gate counts for qubit 0 (1) is obtained by ``ngates[0]`` (``ngates[1]``)
as usual python dictionary. If all gate counts are zero,
you might specify wrong ``basis`` or input circuit list is not transpiled into basis gates.
Args:
transpiled_circuits_list: List of transpiled RB circuit for each seed.
clifford_lengths: number of Cliffords in each circuit
basis: gates basis for the qobj
qubits: qubits to count over
Returns:
Nested dictionary of gate counts per Clifford.
Raises:
QiskitError: when input object is not a list of `QuantumCircuit`.
"""
ngates = {qubit: {base: 0 for base in basis} for qubit in qubits}
if isinstance(transpiled_circuits_list[0], QasmQobj):
warn('`QasmQobj` input will be deprecated. Use transpiled `QuantumCircuit` instead. '
'Gate counts based on `QasmQobj` has no unittest and may return wrong counts.',
category=DeprecationWarning)
for transpiled_circuits in transpiled_circuits_list:
if isinstance(transpiled_circuits, QasmQobj):
# TODO: remove this code block after deprecation period
for experiment in transpiled_circuits.experiments:
for instr in experiment.instructions:
for q_ind in instr.qubits:
try:
ngates[q_ind][instr.name] += 1
except KeyError:
pass
else:
for transpiled_circuit in transpiled_circuits:
if isinstance(transpiled_circuit, QuantumCircuit):
for instr, qregs, _ in transpiled_circuit.data:
for qreg in qregs:
try:
ngates[qreg.index][instr.name] += 1
except KeyError:
pass
else:
raise QiskitError('Input object is not `QuantumCircuit`.')
# include inverse, ie + 1 for all clifford length
total_ncliffs = len(transpiled_circuits_list) * np.sum(np.array(clifford_lengths) + 1)
for qubit in qubits:
for base in basis:
ngates[qubit][base] /= total_ncliffs
return ngates
[docs]def coherence_limit(nQ=2, T1_list=None, T2_list=None,
gatelen=0.1):
"""
The error per gate (1-average_gate_fidelity) given by the T1,T2 limit.
Args:
nQ (int): number of qubits (1 and 2 supported).
T1_list (list): list of T1's (Q1,...,Qn).
T2_list (list): list of T2's (as measured, not Tphi).
If not given assume T2=2*T1 .
gatelen (float): length of the gate.
Returns:
float: coherence limited error per gate.
Raises:
ValueError: if there are invalid inputs
"""
T1 = np.array(T1_list)
if T2_list is None:
T2 = 2*T1
else:
T2 = np.array(T2_list)
if len(T1) != nQ or len(T2) != nQ:
raise ValueError("T1 and/or T2 not the right length")
coherence_limit_err = 0
if nQ == 1:
coherence_limit_err = 0.5*(1.-2./3.*np.exp(-gatelen/T2[0]) -
1./3.*np.exp(-gatelen/T1[0]))
elif nQ == 2:
T1factor = 0
T2factor = 0
for i in range(2):
T1factor += 1./15.*np.exp(-gatelen/T1[i])
T2factor += 2./15.*(np.exp(-gatelen/T2[i]) +
np.exp(-gatelen*(1./T2[i]+1./T1[1-i])))
T1factor += 1./15.*np.exp(-gatelen*np.sum(1/T1))
T2factor += 4./15.*np.exp(-gatelen*np.sum(1/T2))
coherence_limit_err = 0.75*(1.-T1factor-T2factor)
else:
raise ValueError('Not a valid number of qubits')
return coherence_limit_err
[docs]def twoQ_clifford_error(ngates: Dict[int, Dict[str, float]],
gate_qubit: List[int],
gate_err: List[float]):
"""
The two qubit Clifford gate error given measured errors in the primitive
gates used to construct the Clifford (see arxiv:1712.06550). Assumes the
error in the underlying gates is depolarizing.
Args:
ngates: list of the number of gates per 2Q Clifford.
gate_qubit: list of the qubit corresponding to the gate (0, 1 or -1).
`-1` corresponds to the 2Q gate. Note that `0` (`1`) corresponds to the
single qubit gate counts in ``ngates`` which has smaller (larger) qubit index.
gate_err: list of the gate errors.
Note:
This function presupposes the basis gate consists
of ``u1``, ``u2``, ``u3`` and ``cx``.
Returns:
float: Error per 2Q Clifford.
Raises:
QiskitError: when number of qubit contained in ``ngates`` is not 2.
"""
warn('The function `twoQ_clifford_error` will be deprecated. '
'Use `calculate_2q_epc` instead.', category=DeprecationWarning)
gpc_per_qubits = sorted(ngates.items())
if len(gpc_per_qubits) != 2:
raise QiskitError('Number of qubits contained in the `ngates` dictionary is not 2. ',
'Rerun `gate_per_clifford` with `qubits` used for 2Q RB experiment.')
ngates_lists = np.zeros(7)
ngates_lists[0] = gpc_per_qubits[0][1].get('u1', 0)
ngates_lists[1] = gpc_per_qubits[0][1].get('u2', 0)
ngates_lists[2] = gpc_per_qubits[0][1].get('u3', 0)
ngates_lists[3] = gpc_per_qubits[1][1].get('u1', 0)
ngates_lists[4] = gpc_per_qubits[1][1].get('u2', 0)
ngates_lists[5] = gpc_per_qubits[1][1].get('u3', 0)
ngates_lists[6] = gpc_per_qubits[0][1].get('cx', 0)
alpha1Q = [1.0, 1.0]
alpha2Q = 1.0
for gate_ind, ngate in enumerate(ngates_lists):
if gate_qubit[gate_ind] == -1:
alpha2Q *= (1-4/3*gate_err[gate_ind])**ngate
else:
alpha1Q[gate_qubit[gate_ind]] *= \
(1-2*gate_err[gate_ind])**ngate
alpha2Q_cliff = 1/5*(np.sum(alpha1Q)+3*np.prod(alpha1Q))*alpha2Q
return (1-alpha2Q_cliff)*3/4
[docs]def calculate_1q_epg(gate_per_cliff: Dict[int, Dict[str, float]],
epc_1q: float,
qubit: int) -> Dict[str, float]:
r"""
Convert error per Clifford (EPC) into error per gates (EPGs) of single qubit basis gates.
Given that a standard 1Q RB sequences consist of ``u1``, ``u2`` and ``u3`` gates,
the EPC can be written using those EPGs:
.. math::
EPC = 1 - (1 - EPG_{U1})^{N_{U1}} (1 - EPG_{U2})^{N_{U2}} (1 - EPG_{U3})^{N_{U3}}.
where :math:`N_{x}` is the number of gate :math:`x` per Clifford.
Assuming ``u1`` composed of virtual-Z gate, ie FrameChange instruction,
the :math:`EPG_{U1}` is estimated to be zero within the range of quantization error.
Therefore the EPC can be written as:
.. math::
EPC = 1 - (1 - EPG_{U2})^{N_{U2}} (1 - EPG_{U3})^{N_{U3}}.
Because ``u2`` and ``u3`` gates are respectively implemented by a single and two
half-pi pulses with virtual-Z rotations, we assume :math:`EPG_{U3} = 2EPG_{U2}`.
Using this relation in the limit of :math:`EPG_{U2} \ll 1`:
.. math::
EPC & = 1 - (1 - EPG_{U2})^{N_{U2}} (1 - 2 EPG_{U2})^{N_{U3}} \\
& \simeq EPG_{U2}(N_{U2} + 2 N_{U3}).
Finally the EPG of each basis gate can be written using EPC and number of gates:
.. math::
EPG_{U1} &= 0 \\
EPG_{U2} &= EPC / (N_{U2} + 2 N_{U3}) \\
EPG_{U3} &= 2 EPC / (N_{U2} + 2 N_{U3})
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.
.. jupyter-execute::
import pprint
import qiskit.ignis.verification.randomized_benchmarking as rb
# assuming we ran 1Q RB experiment for qubit 0
gpc = {0: {'cx': 0, 'u1': 0.13, 'u2': 0.31, 'u3': 0.51}}
epc = 1.5e-3
# calculate 1Q EPGs
epgs = rb.rb_utils.calculate_1q_epg(gate_per_cliff=gpc, epc_1q=epc, qubit=0)
pprint.pprint(epgs)
In the example, ``gpc`` can be generated by :func:`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 :func:`calculate_2q_epg`.
Note:
This function presupposes the basis gate consists
of ``u1``, ``u2`` and ``u3``.
Args:
gate_per_cliff: dictionary of gate per Clifford. see :func:`gates_per_clifford`.
epc_1q: EPC fit from 1Q RB experiment data.
qubit: index of qubit to calculate EPGs.
Returns:
Dictionary of EPGs of single qubit basis gates.
Raises:
QiskitError: when ``u2`` or ``u3`` is not found, ``cx`` gate count is nonzero,
or specified qubit is not included in the gate count dictionary.
"""
if qubit not in gate_per_cliff:
raise QiskitError('Qubit %d is not included in the `gate_per_cliff`' % qubit)
gpc_per_qubit = gate_per_cliff[qubit]
if 'u3' not in gpc_per_qubit or 'u2' not in gpc_per_qubit:
raise QiskitError('Invalid basis set is given. Use `u1`, `u2`, `u3` for basis gates.')
n_u2 = gpc_per_qubit['u2']
n_u3 = gpc_per_qubit['u3']
if gpc_per_qubit.get('cx', 0) > 0:
raise QiskitError('Two qubit gate is included in the RB sequence.')
return {'u1': 0, 'u2': epc_1q / (n_u2 + 2 * n_u3), 'u3': 2 * epc_1q / (n_u2 + 2 * n_u3)}
[docs]def calculate_2q_epg(gate_per_cliff: Dict[int, Dict[str, float]],
epc_2q: float,
qubit_pair: List[int],
list_epgs_1q: Optional[List[Dict[str, float]]] = None,
two_qubit_name: Optional[str] = 'cx') -> float:
r"""
Convert error per Clifford (EPC) into error per gate (EPG) of two qubit ``cx`` gates.
Given that a standard 2Q RB sequences consist of ``u1``, ``u2``, ``u3``, and ``cx`` gates,
the EPG of ``cx`` gate can be roughly approximated by :math:`EPG_{CX} = EPC/N_{CX}`,
where :math:`N_{CX}` is number of ``cx`` gates per Clifford which is designed to be 1.5.
Because an error from two qubit gates are usually dominant and the contribution of
single qubit gates in 2Q RB experiments is thus able to be ignored.
If ``list_epgs_1q`` is not provided, the function returns
the EPG calculated based upon this assumption.
When we know the EPG of every single qubit gates used in the 2Q RB experiment,
we can isolate the EPC of the two qubit gate, ie :math:`EPG_{CX} = EPC_{CX}/N_{CX}` [1].
This will give you more accurate estimation of EPG, especially when the ``cx``
gate fidelity is close to that of single qubit gate.
To evaluate EPGs of single qubit gates, you first need to run standard 1Q RB experiments
separately and feed the fit result and gate counts to :func:`calculate_1q_epg`.
.. jupyter-execute::
import qiskit.ignis.verification.randomized_benchmarking as rb
# assuming we ran 1Q RB experiment for qubit 0 and qubit 1
gpc = {0: {'cx': 0, 'u1': 0.13, 'u2': 0.31, 'u3': 0.51},
1: {'cx': 0, 'u1': 0.10, 'u2': 0.33, 'u3': 0.51}}
epc_q0 = 1.5e-3
epc_q1 = 5.8e-4
# calculate 1Q EPGs
epgs_q0 = rb.rb_utils.calculate_1q_epg(gate_per_cliff=gpc, epc_1q=epc_q0, qubit=0)
epgs_q1 = rb.rb_utils.calculate_1q_epg(gate_per_cliff=gpc, epc_1q=epc_q1, qubit=1)
# assuming we ran 2Q RB experiment for qubit 0 and qubit 1
gpc = {0: {'cx': 1.49, 'u1': 0.25, 'u2': 0.95, 'u3': 0.56},
1: {'cx': 1.49, 'u1': 0.24, 'u2': 0.98, 'u3': 0.49}}
epc = 2.4e-2
# calculate 2Q EPG
epg_no_comp = rb.rb_utils.calculate_2q_epg(
gate_per_cliff=gpc,
epc_2q=epc,
qubit_pair=[0, 1])
epg_comp = rb.rb_utils.calculate_2q_epg(
gate_per_cliff=gpc,
epc_2q=epc,
qubit_pair=[0, 1],
list_epgs_1q=[epgs_q0, epgs_q1])
print('EPG without `list_epgs_1q`: %f, with `list_epgs_1q`: %f' % (epg_no_comp, epg_comp))
Note:
This function presupposes the basis gate consists
of ``u1``, ``u2``, ``u3`` and ``cx``.
References:
[1] D. C. McKay, S. Sheldon, J. A. Smolin, J. M. Chow,
and J. M. Gambetta, “Three-Qubit Randomized Benchmarking,”
Phys. Rev. Lett., vol. 122, no. 20, 2019 (arxiv:1712.06550).
Args:
gate_per_cliff: dictionary of gate per Clifford. see :func:`gates_per_clifford`.
epc_2q: EPC fit from 2Q RB experiment data.
qubit_pair: index of two qubits to calculate EPG.
list_epgs_1q: list of single qubit EPGs of qubit listed in ``qubit_pair``.
two_qubit_name: name of two qubit gate in ``basis gates``.
Returns:
EPG of 2Q gate.
Raises:
QiskitError: when ``cx`` is not found, specified ``qubit_pair`` is not included
in the gate count dictionary, or length of ``qubit_pair`` is not 2.
"""
list_epgs_1q = list_epgs_1q or []
if len(qubit_pair) != 2:
raise QiskitError('Number of qubit is not 2.')
# estimate single qubit gate error contribution
alpha_1q = [1.0, 1.0]
for ind, (qubit, epg_1q) in enumerate(zip(qubit_pair, list_epgs_1q)):
if qubit not in gate_per_cliff:
raise QiskitError('Qubit %d is not included in the `gate_per_cliff`' % qubit)
gpc_per_qubit = gate_per_cliff[qubit]
for gate_name, epg in epg_1q.items():
n_gate = gpc_per_qubit.get(gate_name, 0)
alpha_1q[ind] *= (1 - 2 * epg) ** n_gate
alpha_c_1q = 1 / 5 * (alpha_1q[0] + alpha_1q[1] + 3 * alpha_1q[0] * alpha_1q[1])
alpha_c_2q = (1 - 4 / 3 * epc_2q) / alpha_c_1q
n_gate_2q = gate_per_cliff[qubit_pair[0]].get(two_qubit_name, 0)
if n_gate_2q > 0:
return 3 / 4 * (1 - alpha_c_2q) / n_gate_2q
raise QiskitError('Two qubit gate %s is not included in the `gate_per_cliff`. '
'Set correct `two_qubit_name` or use 2Q RB gate count.' % two_qubit_name)
[docs]def calculate_1q_epc(gate_per_cliff: Dict[int, Dict[str, float]],
epg_1q: Dict[str, float],
qubit: int) -> float:
r"""
Convert error per gate (EPG) into error per Clifford (EPC) of single qubit basis gates.
Given that we know the number of gates per Clifford :math:`N_i` and those EPGs,
we can predict EPC of that RB sequence:
.. math::
EPC = 1 - \prod_i \left( 1 - EPG_i \right)^{N_i}
To run this function, you need to know EPG of every single qubit basis gates.
For example, when you prepare 1Q RB experiment with appropriate error model,
you can define EPG of those basis gate set. Then you can estimate the EPC of
prepared RB sequence without running experiment.
.. jupyter-execute::
import qiskit.ignis.verification.randomized_benchmarking as rb
# gate counts of your 1Q RB experiment
gpc = {0: {'cx': 0, 'u1': 0.13, 'u2': 0.31, 'u3': 0.51}}
# EPGs from error model
epgs_q0 = {'u1': 0, 'u2': 0.001, 'u3': 0.002}
# calculate 1Q EPC
epc = rb.rb_utils.calculate_1q_epc(
gate_per_cliff=gpc,
epg_1q=epgs_q0,
qubit=0)
print(epc)
Args:
gate_per_cliff: dictionary of gate per Clifford. see :func:`gates_per_clifford`.
epg_1q: EPG of single qubit gates estimated by error model.
qubit: index of qubit to calculate EPC.
Returns:
EPG of 2Q gate.
Raises:
QiskitError: when specified ``qubit`` is not included in the gate count dictionary
"""
if qubit not in gate_per_cliff:
raise QiskitError('Qubit %d is not included in the `gate_per_cliff`' % qubit)
fid = 1
gpc_per_qubit = gate_per_cliff[qubit]
for gate_name, epg in epg_1q.items():
n_gate = gpc_per_qubit.get(gate_name, 0)
fid *= (1 - epg) ** n_gate
return 1 - fid
[docs]def calculate_2q_epc(gate_per_cliff: Dict[int, Dict[str, float]],
epg_2q: float,
qubit_pair: List[int],
list_epgs_1q: List[Dict[str, float]],
two_qubit_name: Optional[str] = 'cx') -> float:
r"""
Convert error per gate (EPG) into error per Clifford (EPC) of two qubit ``cx`` gates.
Given that we know the number of gates per Clifford :math:`N_i` and those EPGs,
we can predict EPC of that RB sequence:
.. math::
EPC = 1 - \prod_i \left( 1 - EPG_i \right)^{N_i}
This function isolates the contribution of two qubit gate to the EPC [1].
This will give you more accurate estimation of EPC, especially when the ``cx``
gate fidelity is close to that of single qubit gate.
To run this function, you need to know EPG of both single and two qubit gates.
For example, when you prepare 2Q RB experiment with appropriate error model,
you can define EPG of those basis gate set. Then you can estimate the EPC of
prepared RB sequence without running experiment.
.. jupyter-execute::
import qiskit.ignis.verification.randomized_benchmarking as rb
# gate counts of your 2Q RB experiment
gpc = {0: {'cx': 1.49, 'u1': 0.25, 'u2': 0.95, 'u3': 0.56},
1: {'cx': 1.49, 'u1': 0.24, 'u2': 0.98, 'u3': 0.49}}
# EPGs from error model
epgs_q0 = {'u1': 0, 'u2': 0.001, 'u3': 0.002}
epgs_q1 = {'u1': 0, 'u2': 0.002, 'u3': 0.004}
epg_q01 = 0.03
# calculate 2Q EPC
epc_2q = rb.rb_utils.calculate_2q_epc(
gate_per_cliff=gpc,
epg_2q=epg_q01,
qubit_pair=[0, 1],
list_epgs_1q=[epgs_q0, epgs_q1])
# calculate EPC according to the definition
fid = 1
for qubit in (0, 1):
for epgs in (epgs_q0, epgs_q1):
for gate, val in epgs.items():
fid *= (1 - val) ** gpc[qubit][gate]
fid *= (1 - epg_q01) ** 1.49
epc = 1 - fid
print('Total sequence EPC: %f, 2Q gate contribution: %f' % (epc, epc_2q))
As you can see two qubit gate contribution is dominant in this RB sequence.
References:
[1] D. C. McKay, S. Sheldon, J. A. Smolin, J. M. Chow,
and J. M. Gambetta, “Three-Qubit Randomized Benchmarking,”
Phys. Rev. Lett., vol. 122, no. 20, 2019 (arxiv:1712.06550).
Args:
gate_per_cliff: dictionary of gate per Clifford. see :func:`gates_per_clifford`.
epg_2q: EPG estimated by error model.
qubit_pair: index of two qubits to calculate EPC.
list_epgs_1q: list of single qubit EPGs of qubit listed in ``qubit_pair``.
two_qubit_name: name of two qubit gate in ``basis gates``.
Returns:
EPG of 2Q gate.
Raises:
QiskitError: when ``cx`` is not found, specified ``qubit_pair`` is not included
in the gate count dictionary, or length of ``qubit_pair`` is not 2.
"""
if len(qubit_pair) != 2:
raise QiskitError('Number of qubit is not 2.')
n_gate_2q = gate_per_cliff[qubit_pair[0]].get(two_qubit_name, 0)
if n_gate_2q == 0:
raise QiskitError('Two qubit gate %s is not included in the `gate_per_cliff`. '
'Set correct `two_qubit_name` or use 2Q RB gate count.' % two_qubit_name)
# estimate single qubit gate error contribution
alpha_1q = [1.0, 1.0]
alpha_2q = (1 - 4 / 3 * epg_2q) ** n_gate_2q
for ind, (qubit, epg_1q) in enumerate(zip(qubit_pair, list_epgs_1q)):
if qubit not in gate_per_cliff:
raise QiskitError('Qubit %d is not included in the `gate_per_cliff`' % qubit)
gpc_per_qubit = gate_per_cliff[qubit]
for gate_name, epg in epg_1q.items():
n_gate = gpc_per_qubit.get(gate_name, 0)
alpha_1q[ind] *= (1 - 2 * epg) ** n_gate
alpha_c_2q = 1 / 5 * (alpha_1q[0] + alpha_1q[1] + 3 * alpha_1q[0] * alpha_1q[1]) * alpha_2q
return 3 / 4 * (1 - alpha_c_2q)