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clifford_circuits.py
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clifford_circuits.py
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# This code is part of Qiskit.
#
# (C) Copyright IBM 2017--2022
#
# 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.
"""
Circuit simulation for the Clifford class.
"""
from __future__ import annotations
import numpy as np
from qiskit.circuit import Barrier, Delay, Gate
from qiskit.circuit.exceptions import CircuitError
from qiskit.exceptions import QiskitError
def _append_circuit(clifford, circuit, qargs=None):
"""Update Clifford inplace by applying a Clifford circuit.
Args:
clifford (Clifford): The Clifford to update.
circuit (QuantumCircuit): The circuit to apply.
qargs (list or None): The qubits to apply circuit to.
Returns:
Clifford: the updated Clifford.
Raises:
QiskitError: if input circuit cannot be decomposed into Clifford operations.
"""
if qargs is None:
qargs = list(range(clifford.num_qubits))
for instruction in circuit:
if instruction.clbits:
raise QiskitError(
f"Cannot apply Instruction with classical bits: {instruction.operation.name}"
)
# Get the integer position of the flat register
new_qubits = [qargs[circuit.find_bit(bit).index] for bit in instruction.qubits]
clifford = _append_operation(clifford, instruction.operation, new_qubits)
return clifford
def _append_operation(clifford, operation, qargs=None):
"""Update Clifford inplace by applying a Clifford operation.
Args:
clifford (Clifford): The Clifford to update.
operation (Instruction or Clifford or str): The operation or composite operation to apply.
qargs (list or None): The qubits to apply operation to.
Returns:
Clifford: the updated Clifford.
Raises:
QiskitError: if input operation cannot be converted into Clifford operations.
"""
# pylint: disable=too-many-return-statements
if isinstance(operation, (Barrier, Delay)):
return clifford
if qargs is None:
qargs = list(range(clifford.num_qubits))
gate = operation
if isinstance(gate, str):
# Check if gate is a valid Clifford basis gate string
if gate not in _BASIS_1Q and gate not in _BASIS_2Q:
raise QiskitError(f"Invalid Clifford gate name string {gate}")
name = gate
else:
# assert isinstance(gate, Instruction)
name = gate.name
if getattr(gate, "condition", None) is not None:
raise QiskitError("Conditional gate is not a valid Clifford operation.")
# Apply gate if it is a Clifford basis gate
if name in _NON_CLIFFORD:
raise QiskitError(f"Cannot update Clifford with non-Clifford gate {name}")
if name in _BASIS_1Q:
if len(qargs) != 1:
raise QiskitError("Invalid qubits for 1-qubit gate.")
return _BASIS_1Q[name](clifford, qargs[0])
if name in _BASIS_2Q:
if len(qargs) != 2:
raise QiskitError("Invalid qubits for 2-qubit gate.")
return _BASIS_2Q[name](clifford, qargs[0], qargs[1])
# If u gate, check if it is a Clifford, and if so, apply it
if isinstance(gate, Gate) and name == "u" and len(qargs) == 1:
try:
theta, phi, lambd = tuple(_n_half_pis(par) for par in gate.params)
except ValueError as err:
raise QiskitError("U gate angles must be multiples of pi/2 to be a Clifford") from err
if theta == 0:
clifford = _append_rz(clifford, qargs[0], lambd + phi)
elif theta == 1:
clifford = _append_rz(clifford, qargs[0], lambd - 2)
clifford = _append_h(clifford, qargs[0])
clifford = _append_rz(clifford, qargs[0], phi)
elif theta == 2:
clifford = _append_rz(clifford, qargs[0], lambd - 1)
clifford = _append_x(clifford, qargs[0])
clifford = _append_rz(clifford, qargs[0], phi + 1)
elif theta == 3:
clifford = _append_rz(clifford, qargs[0], lambd)
clifford = _append_h(clifford, qargs[0])
clifford = _append_rz(clifford, qargs[0], phi + 2)
return clifford
# If gate is a Clifford, we can either unroll the gate using the "to_circuit"
# method, or we can compose the Cliffords directly. Experimentally, for large
# cliffords the second method is considerably faster.
# pylint: disable=cyclic-import
from qiskit.quantum_info import Clifford
if isinstance(gate, Clifford):
composed_clifford = clifford.compose(gate, qargs=qargs, front=False)
clifford.tableau = composed_clifford.tableau
return clifford
# pylint: disable=cyclic-import
from qiskit.circuit.library import LinearFunction
if isinstance(gate, LinearFunction):
gate_as_clifford = Clifford.from_linear_function(gate)
composed_clifford = clifford.compose(gate_as_clifford, qargs=qargs, front=False)
clifford.tableau = composed_clifford.tableau
return clifford
# pylint: disable=cyclic-import
from qiskit.circuit.library import PermutationGate
if isinstance(gate, PermutationGate):
gate_as_clifford = Clifford.from_permutation(gate)
composed_clifford = clifford.compose(gate_as_clifford, qargs=qargs, front=False)
clifford.tableau = composed_clifford.tableau
return clifford
# If the gate is not directly appendable, we try to unroll the gate with its definition.
# This succeeds only if the gate has all-Clifford definition (decomposition).
# If fails, we need to restore the clifford that was before attempting to unroll and append.
if gate.definition is not None:
try:
return _append_circuit(clifford.copy(), gate.definition, qargs)
except QiskitError:
pass
# As a final attempt, if the gate is up to 3 qubits,
# we try to construct a Clifford to be appended from its matrix representation.
if isinstance(gate, Gate) and len(qargs) <= 3:
try:
matrix = gate.to_matrix()
gate_cliff = Clifford.from_matrix(matrix)
return _append_operation(clifford, gate_cliff, qargs=qargs)
except TypeError as err:
raise QiskitError(f"Cannot apply {gate.name} gate with unbounded parameters") from err
except CircuitError as err:
raise QiskitError(f"Cannot apply {gate.name} gate without to_matrix defined") from err
except QiskitError as err:
raise QiskitError(f"Cannot apply non-Clifford gate: {gate.name}") from err
raise QiskitError(f"Cannot apply {gate}")
def _n_half_pis(param) -> int:
try:
param = float(param)
epsilon = (abs(param) + 0.5 * 1e-10) % (np.pi / 2)
if epsilon > 1e-10:
raise ValueError(f"{param} is not to a multiple of pi/2")
multiple = int(np.round(param / (np.pi / 2)))
return multiple % 4
except TypeError as err:
raise ValueError(f"{param} is not bounded") from err
# ---------------------------------------------------------------------
# Helper functions for applying basis gates
# ---------------------------------------------------------------------
def _append_rz(clifford, qubit, multiple):
"""Apply an Rz gate to a Clifford.
Args:
clifford (Clifford): a Clifford.
qubit (int): gate qubit index.
multiple (int): z-rotation angle in a multiple of pi/2
Returns:
Clifford: the updated Clifford.
"""
if multiple % 4 == 1:
return _append_s(clifford, qubit)
if multiple % 4 == 2:
return _append_z(clifford, qubit)
if multiple % 4 == 3:
return _append_sdg(clifford, qubit)
return clifford
def _append_i(clifford, qubit):
"""Apply an I gate to a Clifford.
Args:
clifford (Clifford): a Clifford.
qubit (int): gate qubit index.
Returns:
Clifford: the updated Clifford.
"""
# pylint: disable=unused-argument
return clifford
def _append_x(clifford, qubit):
"""Apply an X gate to a Clifford.
Args:
clifford (Clifford): a Clifford.
qubit (int): gate qubit index.
Returns:
Clifford: the updated Clifford.
"""
clifford.phase ^= clifford.z[:, qubit]
return clifford
def _append_y(clifford, qubit):
"""Apply a Y gate to a Clifford.
Args:
clifford (Clifford): a Clifford.
qubit (int): gate qubit index.
Returns:
Clifford: the updated Clifford.
"""
x = clifford.x[:, qubit]
z = clifford.z[:, qubit]
clifford.phase ^= x ^ z
return clifford
def _append_z(clifford, qubit):
"""Apply an Z gate to a Clifford.
Args:
clifford (Clifford): a Clifford.
qubit (int): gate qubit index.
Returns:
Clifford: the updated Clifford.
"""
clifford.phase ^= clifford.x[:, qubit]
return clifford
def _append_h(clifford, qubit):
"""Apply a H gate to a Clifford.
Args:
clifford (Clifford): a Clifford.
qubit (int): gate qubit index.
Returns:
Clifford: the updated Clifford.
"""
x = clifford.x[:, qubit]
z = clifford.z[:, qubit]
clifford.phase ^= x & z
tmp = x.copy()
x[:] = z
z[:] = tmp
return clifford
def _append_s(clifford, qubit):
"""Apply an S gate to a Clifford.
Args:
clifford (Clifford): a Clifford.
qubit (int): gate qubit index.
Returns:
Clifford: the updated Clifford.
"""
x = clifford.x[:, qubit]
z = clifford.z[:, qubit]
clifford.phase ^= x & z
z ^= x
return clifford
def _append_sdg(clifford, qubit):
"""Apply an Sdg gate to a Clifford.
Args:
clifford (Clifford): a Clifford.
qubit (int): gate qubit index.
Returns:
Clifford: the updated Clifford.
"""
x = clifford.x[:, qubit]
z = clifford.z[:, qubit]
clifford.phase ^= x & ~z
z ^= x
return clifford
def _append_sx(clifford, qubit):
"""Apply an SX gate to a Clifford.
Args:
clifford (Clifford): a Clifford.
qubit (int): gate qubit index.
Returns:
Clifford: the updated Clifford.
"""
x = clifford.x[:, qubit]
z = clifford.z[:, qubit]
clifford.phase ^= ~x & z
x ^= z
return clifford
def _append_sxdg(clifford, qubit):
"""Apply an SXdg gate to a Clifford.
Args:
clifford (Clifford): a Clifford.
qubit (int): gate qubit index.
Returns:
Clifford: the updated Clifford.
"""
x = clifford.x[:, qubit]
z = clifford.z[:, qubit]
clifford.phase ^= x & z
x ^= z
return clifford
def _append_v(clifford, qubit):
"""Apply a V gate to a Clifford.
This is equivalent to an Sdg gate followed by a H gate.
Args:
clifford (Clifford): a Clifford.
qubit (int): gate qubit index.
Returns:
Clifford: the updated Clifford.
"""
x = clifford.x[:, qubit]
z = clifford.z[:, qubit]
tmp = x.copy()
x ^= z
z[:] = tmp
return clifford
def _append_w(clifford, qubit):
"""Apply a W gate to a Clifford.
This is equivalent to two V gates.
Args:
clifford (Clifford): a Clifford.
qubit (int): gate qubit index.
Returns:
Clifford: the updated Clifford.
"""
x = clifford.x[:, qubit]
z = clifford.z[:, qubit]
tmp = z.copy()
z ^= x
x[:] = tmp
return clifford
def _append_cx(clifford, control, target):
"""Apply a CX gate to a Clifford.
Args:
clifford (Clifford): a Clifford.
control (int): gate control qubit index.
target (int): gate target qubit index.
Returns:
Clifford: the updated Clifford.
"""
x0 = clifford.x[:, control]
z0 = clifford.z[:, control]
x1 = clifford.x[:, target]
z1 = clifford.z[:, target]
clifford.phase ^= (x1 ^ z0 ^ True) & z1 & x0
x1 ^= x0
z0 ^= z1
return clifford
def _append_cz(clifford, control, target):
"""Apply a CZ gate to a Clifford.
Args:
clifford (Clifford): a Clifford.
control (int): gate control qubit index.
target (int): gate target qubit index.
Returns:
Clifford: the updated Clifford.
"""
x0 = clifford.x[:, control]
z0 = clifford.z[:, control]
x1 = clifford.x[:, target]
z1 = clifford.z[:, target]
clifford.phase ^= x0 & x1 & (z0 ^ z1)
z1 ^= x0
z0 ^= x1
return clifford
def _append_cy(clifford, control, target):
"""Apply a CY gate to a Clifford.
Args:
clifford (Clifford): a Clifford.
control (int): gate control qubit index.
target (int): gate target qubit index.
Returns:
Clifford: the updated Clifford.
"""
clifford = _append_sdg(clifford, target)
clifford = _append_cx(clifford, control, target)
clifford = _append_s(clifford, target)
return clifford
def _append_swap(clifford, qubit0, qubit1):
"""Apply a Swap gate to a Clifford.
Args:
clifford (Clifford): a Clifford.
qubit0 (int): first qubit index.
qubit1 (int): second qubit index.
Returns:
Clifford: the updated Clifford.
"""
clifford.x[:, [qubit0, qubit1]] = clifford.x[:, [qubit1, qubit0]]
clifford.z[:, [qubit0, qubit1]] = clifford.z[:, [qubit1, qubit0]]
return clifford
def _append_iswap(clifford, qubit0, qubit1):
"""Apply a iSwap gate to a Clifford.
Args:
clifford (Clifford): a Clifford.
qubit0 (int): first qubit index.
qubit1 (int): second qubit index.
Returns:
Clifford: the updated Clifford.
"""
clifford = _append_s(clifford, qubit0)
clifford = _append_h(clifford, qubit0)
clifford = _append_s(clifford, qubit1)
clifford = _append_cx(clifford, qubit0, qubit1)
clifford = _append_cx(clifford, qubit1, qubit0)
clifford = _append_h(clifford, qubit1)
return clifford
def _append_dcx(clifford, qubit0, qubit1):
"""Apply a DCX gate to a Clifford.
Args:
clifford (Clifford): a Clifford.
qubit0 (int): first qubit index.
qubit1 (int): second qubit index.
Returns:
Clifford: the updated Clifford.
"""
clifford = _append_cx(clifford, qubit0, qubit1)
clifford = _append_cx(clifford, qubit1, qubit0)
return clifford
def _append_ecr(clifford, qubit0, qubit1):
"""Apply an ECR gate to a Clifford.
Args:
clifford (Clifford): a Clifford.
qubit0 (int): first qubit index.
qubit1 (int): second qubit index.
Returns:
Clifford: the updated Clifford.
"""
clifford = _append_s(clifford, qubit0)
clifford = _append_sx(clifford, qubit1)
clifford = _append_cx(clifford, qubit0, qubit1)
clifford = _append_x(clifford, qubit0)
return clifford
# Basis Clifford Gates
_BASIS_1Q = {
"i": _append_i,
"id": _append_i,
"iden": _append_i,
"x": _append_x,
"y": _append_y,
"z": _append_z,
"h": _append_h,
"s": _append_s,
"sdg": _append_sdg,
"sinv": _append_sdg,
"sx": _append_sx,
"sxdg": _append_sxdg,
"v": _append_v,
"w": _append_w,
}
_BASIS_2Q = {
"cx": _append_cx,
"cz": _append_cz,
"cy": _append_cy,
"swap": _append_swap,
"iswap": _append_iswap,
"ecr": _append_ecr,
"dcx": _append_dcx,
}
# Non-clifford gates
_NON_CLIFFORD = {"t", "tdg", "ccx", "ccz"}