Quantum Information (qiskit.quantum_info)

Operators

Operator(data[, input_dims, output_dims])	Matrix operator class
Pauli([data, x, z, label])	N-qubit Pauli operator.
Clifford(data[, validate, copy])	An N-qubit unitary operator from the Clifford group.
ScalarOp([dims, coeff])	Scalar identity operator class.
SparsePauliOp(data[, coeffs, ...])	Sparse N-qubit operator in a Pauli basis representation.
CNOTDihedral([data, num_qubits, validate])	An N-qubit operator from the CNOT-Dihedral group.
PauliList(data)	List of N-qubit Pauli operators.
PauliTable(data)	DEPRECATED: Symplectic representation of a list Pauli matrices.
StabilizerTable(data[, phase])	DEPRECATED: Symplectic representation of a list Stabilizer matrices.
pauli_basis(num_qubits[, weight, pauli_list])	Return the ordered PauliTable or PauliList for the n-qubit Pauli basis.

States

Statevector(data[, dims])	Statevector class
DensityMatrix(data[, dims])	DensityMatrix class
StabilizerState(data[, validate])	StabilizerState class.

Channels

Choi(data[, input_dims, output_dims])	Choi-matrix representation of a Quantum Channel.
SuperOp(data[, input_dims, output_dims])	Superoperator representation of a quantum channel.
Kraus(data[, input_dims, output_dims])	Kraus representation of a quantum channel.
Stinespring(data[, input_dims, output_dims])	Stinespring representation of a quantum channel.
Chi(data[, input_dims, output_dims])	Pauli basis Chi-matrix representation of a quantum channel.
PTM(data[, input_dims, output_dims])	Pauli Transfer Matrix (PTM) representation of a Quantum Channel.

Measures

qiskit.quantum_info.average_gate_fidelity(channel, target=None, require_cp=True, require_tp=False)

Return the average gate fidelity of a noisy quantum channel.

The average gate fidelity \(F_{\text{ave}}\) is given by

\[\begin{split}F_{\text{ave}}(\mathcal{E}, U) &= \int d\psi \langle\psi|U^\dagger \mathcal{E}(|\psi\rangle\!\langle\psi|)U|\psi\rangle \\ &= \frac{d F_{\text{pro}}(\mathcal{E}, U) + 1}{d + 1}\end{split}\]

where \(F_{\text{pro}}(\mathcal{E}, U)\) is the process_fidelity() of the input quantum channel \(\mathcal{E}\) with a target unitary \(U\), and \(d\) is the dimension of the channel.

Parameters:

• channel (QuantumChannel or Operator) -- noisy quantum channel.

• target (Operator or None) -- target unitary operator. If None target is the identity operator [Default: None].

• require_cp (bool) -- check if input and target channels are completely-positive and if non-CP log warning containing negative eigenvalues of Choi-matrix [Default: True].

• require_tp (bool) -- check if input and target channels are trace-preserving and if non-TP log warning containing negative eigenvalues of partial Choi-matrix \(Tr_{\mbox{out}}[\mathcal{E}] - I\) [Default: True].

Returns:

The average gate fidelity \(F_{\text{ave}}\).

Return type:

float

Raises:

QiskitError -- if the channel and target do not have the same dimensions, or have different input and output dimensions.

qiskit.quantum_info.process_fidelity(channel, target=None, require_cp=True, require_tp=True)

Return the process fidelity of a noisy quantum channel.

The process fidelity \(F_{\text{pro}}(\mathcal{E}, \mathcal{F})\) between two quantum channels \(\mathcal{E}, \mathcal{F}\) is given by

\[F_{\text{pro}}(\mathcal{E}, \mathcal{F}) = F(\rho_{\mathcal{E}}, \rho_{\mathcal{F}})\]

where \(F\) is the state_fidelity(), \(\rho_{\mathcal{E}} = \Lambda_{\mathcal{E}} / d\) is the normalized Choi matrix for the channel \(\mathcal{E}\), and \(d\) is the input dimension of \(\mathcal{E}\).

When the target channel is unitary this is equivalent to

\[F_{\text{pro}}(\mathcal{E}, U) = \frac{Tr[S_U^\dagger S_{\mathcal{E}}]}{d^2}\]

where \(S_{\mathcal{E}}, S_{U}\) are the SuperOp matrices for the input quantum channel \(\mathcal{E}\) and target unitary \(U\) respectively, and \(d\) is the input dimension of the channel.

Parameters:

• channel (Operator or QuantumChannel) -- input quantum channel.

• target (Operator or QuantumChannel or None) -- target quantum channel. If None target is the identity operator [Default: None].

• require_cp (bool) -- check if input and target channels are completely-positive and if non-CP log warning containing negative eigenvalues of Choi-matrix [Default: True].

• require_tp (bool) -- check if input and target channels are trace-preserving and if non-TP log warning containing negative eigenvalues of partial Choi-matrix \(Tr_{\mbox{out}}[\mathcal{E}] - I\) [Default: True].

Returns:

The process fidelity \(F_{\text{pro}}\).

Return type:

float

Raises:

QiskitError -- if the channel and target do not have the same dimensions.

qiskit.quantum_info.gate_error(channel, target=None, require_cp=True, require_tp=False)

Return the gate error of a noisy quantum channel.

The gate error \(E\) is given by the average gate infidelity

\[E(\mathcal{E}, U) = 1 - F_{\text{ave}}(\mathcal{E}, U)\]

where \(F_{\text{ave}}(\mathcal{E}, U)\) is the average_gate_fidelity() of the input quantum channel \(\mathcal{E}\) with a target unitary \(U\).

Parameters:

• channel (QuantumChannel) -- noisy quantum channel.

• target (Operator or None) -- target unitary operator. If None target is the identity operator [Default: None].

• require_cp (bool) -- check if input and target channels are completely-positive and if non-CP log warning containing negative eigenvalues of Choi-matrix [Default: True].

• require_tp (bool) -- check if input and target channels are trace-preserving and if non-TP log warning containing negative eigenvalues of partial Choi-matrix \(Tr_{\mbox{out}}[\mathcal{E}] - I\) [Default: True].

Returns:

The average gate error \(E\).

Return type:

float

Raises:

QiskitError -- if the channel and target do not have the same dimensions, or have different input and output dimensions.

qiskit.quantum_info.diamond_norm(choi, solver='SCS', **kwargs)

Return the diamond norm of the input quantum channel object.

This function computes the completely-bounded trace-norm (often referred to as the diamond-norm) of the input quantum channel object using the semidefinite-program from reference [1].

Parameters:

• choi (Choi or QuantumChannel) -- a quantum channel object or Choi-matrix array.

• solver (str) -- The solver to use.

• kwargs -- optional arguments to pass to CVXPY solver.

Returns:

The completely-bounded trace norm \(\|\mathcal{E}\|_{\diamond}\).

Return type:

float

Raises:

QiskitError -- if CVXPY package cannot be found.

Additional Information:

The input to this function is typically not a CPTP quantum channel, but rather the difference between two quantum channels \(\|\Delta\mathcal{E}\|_\diamond\) where \(\Delta\mathcal{E} = \mathcal{E}_1 - \mathcal{E}_2\).

Reference:

J. Watrous. "Simpler semidefinite programs for completely bounded norms", arXiv:1207.5726 [quant-ph] (2012).

Note

This function requires the optional CVXPY package to be installed. Any additional kwargs will be passed to the cvxpy.solve function. See the CVXPY documentation for information on available SDP solvers.

qiskit.quantum_info.state_fidelity(state1, state2, validate=True)

Return the state fidelity between two quantum states.

The state fidelity \(F\) for density matrix input states \(\rho_1, \rho_2\) is given by

\[F(\rho_1, \rho_2) = Tr[\sqrt{\sqrt{\rho_1}\rho_2\sqrt{\rho_1}}]^2.\]

If one of the states is a pure state this simplifies to \(F(\rho_1, \rho_2) = \langle\psi_1|\rho_2|\psi_1\rangle\), where \(\rho_1 = |\psi_1\rangle\!\langle\psi_1|\).

Parameters:

• state1 (Statevector or DensityMatrix) -- the first quantum state.

• state2 (Statevector or DensityMatrix) -- the second quantum state.

• validate (bool) -- check if the inputs are valid quantum states [Default: True]

Returns:

The state fidelity \(F(\rho_1, \rho_2)\).

Return type:

float

Raises:

QiskitError -- if validate=True and the inputs are invalid quantum states.

qiskit.quantum_info.purity(state, validate=True)

Calculate the purity of a quantum state.

The purity of a density matrix \(\rho\) is

\[\text{Purity}(\rho) = Tr[\rho^2]\]

Parameters:

• state (Statevector or DensityMatrix) -- a quantum state.

• validate (bool) -- check if input state is valid [Default: True]

Returns:

the purity \(Tr[\rho^2]\).

Return type:

float

Raises:

QiskitError -- if the input isn't a valid quantum state.

qiskit.quantum_info.concurrence(state)

Calculate the concurrence of a quantum state.

The concurrence of a bipartite Statevector \(|\psi\rangle\) is given by

\[C(|\psi\rangle) = \sqrt{2(1 - Tr[\rho_0^2])}\]

where \(\rho_0 = Tr_1[|\psi\rangle\!\langle\psi|]\) is the reduced state from by taking the partial_trace() of the input state.

For density matrices the concurrence is only defined for 2-qubit states, it is given by:

\[C(\rho) = \max(0, \lambda_1 - \lambda_2 - \lambda_3 - \lambda_4)\]

where \(\lambda _1 \ge \lambda _2 \ge \lambda _3 \ge \lambda _4\) are the ordered eigenvalues of the matrix \(R=\sqrt{\sqrt{\rho }(Y\otimes Y)\overline{\rho}(Y\otimes Y)\sqrt{\rho}}\).

Parameters:

state (Statevector or DensityMatrix) -- a 2-qubit quantum state.

Returns:

The concurrence.

Return type:

float

Raises:

• QiskitError -- if the input state is not a valid QuantumState.

• QiskitError -- if input is not a bipartite QuantumState.

• QiskitError -- if density matrix input is not a 2-qubit state.

qiskit.quantum_info.entropy(state, base=2)

Calculate the von-Neumann entropy of a quantum state.

The entropy \(S\) is given by

\[S(\rho) = - Tr[\rho \log(\rho)]\]

Parameters:

• state (Statevector or DensityMatrix) -- a quantum state.

• base (int) -- the base of the logarithm [Default: 2].

Returns:

The von-Neumann entropy S(rho).

Return type:

float

Raises:

QiskitError -- if the input state is not a valid QuantumState.

qiskit.quantum_info.entanglement_of_formation(state)

Calculate the entanglement of formation of quantum state.

The input quantum state must be either a bipartite state vector, or a 2-qubit density matrix.

Parameters:

state (Statevector or DensityMatrix) -- a 2-qubit quantum state.

Returns:

The entanglement of formation.

Return type:

float

Raises:

• QiskitError -- if the input state is not a valid QuantumState.

• QiskitError -- if input is not a bipartite QuantumState.

• QiskitError -- if density matrix input is not a 2-qubit state.

qiskit.quantum_info.mutual_information(state, base=2)

Calculate the mutual information of a bipartite state.

The mutual information \(I\) is given by:

\[I(\rho_{AB}) = S(\rho_A) + S(\rho_B) - S(\rho_{AB})\]

where \(\rho_A=Tr_B[\rho_{AB}], \rho_B=Tr_A[\rho_{AB}]\), are the reduced density matrices of the bipartite state \(\rho_{AB}\).

Parameters:

• state (Statevector or DensityMatrix) -- a bipartite state.

• base (int) -- the base of the logarithm [Default: 2].

Returns:

The mutual information \(I(\rho_{AB})\).

Return type:

float

Raises:

• QiskitError -- if the input state is not a valid QuantumState.

• QiskitError -- if input is not a bipartite QuantumState.

Utility Functions

qiskit.quantum_info.negativity(state, qargs)

Calculates the negativity.

The mathematical expression for negativity is given by:

\[{\cal{N}}(\rho) = \frac{|| \rho^{T_A}|| - 1 }{2}\]

Parameters:

• state (Statevector or DensityMatrix) -- a quantum state.

• qargs (list) -- The subsystems to be transposed.

Returns:

Negativity value of the quantum state

Return type:

float

Raises:

QiskitError -- if the input state is not a valid QuantumState.

qiskit.quantum_info.partial_trace(state, qargs)

Return reduced density matrix by tracing out part of quantum state.

If all subsystems are traced over this returns the trace() of the input state.

Parameters:

• state (Statevector or DensityMatrix) -- the input state.

• qargs (list) -- The subsystems to trace over.

Returns:

The reduced density matrix.

Return type:

DensityMatrix

Raises:

QiskitError -- if input state is invalid.

qiskit.quantum_info.schmidt_decomposition(state, qargs)

Return the Schmidt Decomposition of a pure quantum state.

For an arbitrary bipartite state:

\[|\psi\rangle_{AB} = \sum_{i,j} c_{ij} |x_i\rangle_A \otimes |y_j\rangle_B,\]

its Schmidt Decomposition is given by the single-index sum over k:

\[|\psi\rangle_{AB} = \sum_{k} \lambda_{k} |u_k\rangle_A \otimes |v_k\rangle_B\]

where \(|u_k\rangle_A\) and \(|v_k\rangle_B\) are an orthonormal set of vectors in their respective spaces \(A\) and \(B\), and the Schmidt coefficients \(\lambda_k\) are positive real values.

Parameters:

• state (Statevector or DensityMatrix) -- the input state.

• qargs (list) -- the list of Input state positions corresponding to subsystem \(B\).

Returns:

list of tuples (s, u, v), where s (float) are the Schmidt coefficients \(\lambda_k\), and u (Statevector), v (Statevector) are the Schmidt vectors \(|u_k\rangle_A\), \(|u_k\rangle_B\), respectively.

Return type:

list

Raises:

• QiskitError -- if Input qargs is not a list of positions of the Input state.

• QiskitError -- if Input qargs is not a proper subset of Input state.

Note

In Qiskit, qubits are ordered using little-endian notation, with the least significant qubits having smaller indices. For example, a four-qubit system is represented as \(|q_3q_2q_1q_0\rangle\). Using this convention, setting qargs=[0] will partition the state as \(|q_3q_2q_1\rangle_A\otimes|q_0\rangle_B\). Furthermore, qubits will be organized in this notation regardless of the order they are passed. For instance, passing either qargs=[1,2] or qargs=[2,1] will result in partitioning the state as \(|q_3q_0\rangle_A\otimes|q_2q_1\rangle_B\).

qiskit.quantum_info.shannon_entropy(pvec, base=2)

Compute the Shannon entropy of a probability vector.

The shannon entropy of a probability vector \(\vec{p} = [p_0, ..., p_{n-1}]\) is defined as

\[H(\vec{p}) = \sum_{i=0}^{n-1} p_i \log_b(p_i)\]

where \(b\) is the log base and (default 2), and \(0 \log_b(0) \equiv 0\).

Parameters:

• pvec (array_like) -- a probability vector.

• base (int) -- the base of the logarithm [Default: 2].

Returns:

The Shannon entropy H(pvec).

Return type:

float

qiskit.quantum_info.commutator(a, b)

Compute commutator of a and b.

\[ab - ba.\]

Parameters:

• a (OperatorTypeT) -- Operator a.

• b (OperatorTypeT) -- Operator b.

Returns:

The commutator

Return type:

OperatorTypeT

qiskit.quantum_info.anti_commutator(a, b)

Compute anti-commutator of a and b.

\[ab + ba.\]

Parameters:

• a (OperatorTypeT) -- Operator a.

• b (OperatorTypeT) -- Operator b.

Returns:

The anti-commutator

Return type:

OperatorTypeT

qiskit.quantum_info.double_commutator(a, b, c, *, commutator=True)

Compute symmetric double commutator of a, b and c.

See also Equation (13.6.18) in [1].

If commutator is True, it returns

\[[[A, B], C]/2 + [A, [B, C]]/2 = (2ABC + 2CBA - BAC - CAB - ACB - BCA)/2.\]

If commutator is False, it returns

\[\lbrace[A, B], C\rbrace/2 + \lbrace A, [B, C]\rbrace/2 = (2ABC - 2CBA - BAC + CAB - ACB + BCA)/2.\]

Parameters:

• a (OperatorTypeT) -- Operator a.

• b (OperatorTypeT) -- Operator b.

• c (OperatorTypeT) -- Operator c.

• commutator (bool) -- If True compute the double commutator, if False the double anti-commutator.

Returns:

The double commutator

Return type:

OperatorTypeT

References

[1]: R. McWeeny.

Methods of Molecular Quantum Mechanics. 2nd Edition, Academic Press, 1992. ISBN 0-12-486552-6.

Random

qiskit.quantum_info.random_statevector(dims, seed=None)

Generator a random Statevector.

The statevector is sampled from the uniform (Haar) measure.

Parameters:

• dims (int or tuple) -- the dimensions of the state.

• seed (int or np.random.Generator) -- Optional. Set a fixed seed or generator for RNG.

Returns:

the random statevector.

Return type:

Statevector

qiskit.quantum_info.random_density_matrix(dims, rank=None, method='Hilbert-Schmidt', seed=None)

Generator a random DensityMatrix.

Parameters:

• dims (int or tuple) -- the dimensions of the DensityMatrix.

• rank (int or None) -- Optional, the rank of the density matrix. The default value is full-rank.

• method (string) -- Optional. The method to use. 'Hilbert-Schmidt': (Default) sample from the Hilbert-Schmidt metric. 'Bures': sample from the Bures metric.

• seed (int or np.random.Generator) -- Optional. Set a fixed seed or generator for RNG.

Returns:

the random density matrix.

Return type:

DensityMatrix

Raises:

QiskitError -- if the method is not valid.

qiskit.quantum_info.random_unitary(dims, seed=None)

Return a random unitary Operator.

The operator is sampled from the unitary Haar measure.

Parameters:

• dims (int or tuple) -- the input dimensions of the Operator.

• seed (int or np.random.Generator) -- Optional. Set a fixed seed or generator for RNG.

Returns:

a unitary operator.

Return type:

Operator

qiskit.quantum_info.random_hermitian(dims, traceless=False, seed=None)

Return a random hermitian Operator.

The operator is sampled from Gaussian Unitary Ensemble.

Parameters:

• dims (int or tuple) -- the input dimension of the Operator.

• traceless (bool) -- Optional. If True subtract diagonal entries to return a traceless hermitian operator (Default: False).

• seed (int or np.random.Generator) -- Optional. Set a fixed seed or generator for RNG.

Returns:

a Hermitian operator.

Return type:

Operator

qiskit.quantum_info.random_pauli(num_qubits, group_phase=False, seed=None)

Return a random Pauli.

Parameters:

• num_qubits (int) -- the number of qubits.

• group_phase (bool) -- Optional. If True generate random phase. Otherwise the phase will be set so that the Pauli coefficient is +1 (default: False).

• seed (int or np.random.Generator) -- Optional. Set a fixed seed or generator for RNG.

Returns:

a random Pauli

Return type:

Pauli

qiskit.quantum_info.random_clifford(num_qubits, seed=None)

Return a random Clifford operator.

The Clifford is sampled using the method of Reference [1].

Parameters:

• num_qubits (int) -- the number of qubits for the Clifford

• seed (int or np.random.Generator) -- Optional. Set a fixed seed or generator for RNG.

Returns:

a random Clifford operator.

Return type:

Clifford

Reference:

1. S. Bravyi and D. Maslov, Hadamard-free circuits expose the structure of the Clifford group. arXiv:2003.09412 [quant-ph]

qiskit.quantum_info.random_quantum_channel(input_dims=None, output_dims=None, rank=None, seed=None)

Return a random CPTP quantum channel.

This constructs the Stinespring operator for the quantum channel by sampling a random isometry from the unitary Haar measure.

Parameters:

• input_dims (int or tuple) -- the input dimension of the channel.

• output_dims (int or tuple) -- the input dimension of the channel.

• rank (int) -- Optional. The rank of the quantum channel Choi-matrix.

• seed (int or np.random.Generator) -- Optional. Set a fixed seed or generator for RNG.

Returns:

a quantum channel operator.

Return type:

Stinespring

Raises:

QiskitError -- if rank or dimensions are invalid.

qiskit.quantum_info.random_cnotdihedral(num_qubits, seed=None)

Return a random CNOTDihedral element.

Parameters:

• num_qubits (int) -- the number of qubits for the CNOTDihedral object.

• seed (int or RandomState) -- Optional. Set a fixed seed or generator for RNG.

Returns:

a random CNOTDihedral element.

Return type:

CNOTDihedral

qiskit.quantum_info.random_pauli_table(num_qubits, size=1, seed=None)

Return a random PauliTable.

Parameters:

• num_qubits (int) -- the number of qubits.

• size (int) -- Optional. The number of rows of the table (Default: 1).

• seed (int or np.random.Generator) -- Optional. Set a fixed seed or generator for RNG.

Returns:

a random PauliTable.

Return type:

PauliTable

qiskit.quantum_info.random_pauli_list(num_qubits, size=1, seed=None, phase=True)

Return a random PauliList.

Parameters:

• num_qubits (int) -- the number of qubits.

• size (int) -- Optional. The length of the Pauli list (Default: 1).

• seed (int or np.random.Generator) -- Optional. Set a fixed seed or generator for RNG.

• phase (bool) -- If True the Pauli phases are randomized, otherwise the phases are fixed to 0. [Default: True]

Returns:

a random PauliList.

Return type:

PauliList

qiskit.quantum_info.random_stabilizer_table(num_qubits, size=1, seed=None)

DEPRECATED: Return a random StabilizerTable.

Deprecated since version 0.22.0: The function qiskit.quantum_info.operators.symplectic.random.random_stabilizer_table() is deprecated as of qiskit-terra 0.22.0. It will be removed no earlier than 3 months after the release date. Instead, use the function random_pauli_list.

Parameters:

• num_qubits (int) -- the number of qubits.

• size (int) -- Optional. The number of rows of the table (Default: 1).

• seed (int or np.random.Generator) -- Optional. Set a fixed seed or generator for RNG.

Returns:

a random StabilizerTable.

Return type:

PauliTable

Analysis

qiskit.quantum_info.hellinger_distance(dist_p, dist_q)

Computes the Hellinger distance between two counts distributions.

Parameters:

• dist_p (dict) -- First dict of counts.

• dist_q (dict) -- Second dict of counts.

Returns:

Distance

Return type:

float

References

Hellinger Distance @ wikipedia

qiskit.quantum_info.hellinger_fidelity(dist_p, dist_q)

Computes the Hellinger fidelity between two counts distributions.

The fidelity is defined as \(\left(1-H^{2}\right)^{2}\) where H is the Hellinger distance. This value is bounded in the range [0, 1].

This is equivalent to the standard classical fidelity \(F(Q,P)=\left(\sum_{i}\sqrt{p_{i}q_{i}}\right)^{2}\) that in turn is equal to the quantum state fidelity for diagonal density matrices.

Parameters:

• dist_p (dict) -- First dict of counts.

• dist_q (dict) -- Second dict of counts.

Returns:

Fidelity

Return type:

float

Example

from qiskit import QuantumCircuit, execute, BasicAer
from qiskit.quantum_info.analysis import hellinger_fidelity

qc = QuantumCircuit(5, 5)
qc.h(2)
qc.cx(2, 1)
qc.cx(2, 3)
qc.cx(3, 4)
qc.cx(1, 0)
qc.measure(range(5), range(5))

sim = BasicAer.get_backend('qasm_simulator')
res1 = execute(qc, sim).result()
res2 = execute(qc, sim).result()

hellinger_fidelity(res1.get_counts(), res2.get_counts())

References

Quantum Fidelity @ wikipedia Hellinger Distance @ wikipedia

Z2Symmetries(symmetries, sq_paulis, sq_list)

The $Z_2$ symmetry converter identifies symmetries from the problem hamiltonian and uses them to provide a tapered - more efficient - representation of operators as Paulis for this problem.

Synthesis

OneQubitEulerDecomposer([basis, use_dag])	A class for decomposing 1-qubit unitaries into Euler angle rotations.
TwoQubitBasisDecomposer(gate[, ...])	A class for decomposing 2-qubit unitaries into minimal number of uses of a 2-qubit basis gate.
Quaternion(data)	A class representing a Quaternion.
XXDecomposer([basis_fidelity, euler_basis, ...])	A class for optimal decomposition of 2-qubit unitaries into 2-qubit basis gates of XX type (i.e., each locally equivalent to CAN(alpha, 0, 0) for a possibly varying alpha).

qiskit.quantum_info.two_qubit_cnot_decompose(*args, **kwargs)

Return type:

QuantumCircuit

qiskit.quantum_info.decompose_clifford(clifford, method=None)

DEPRECATED: Decompose a Clifford operator into a QuantumCircuit.

For N <= 3 qubits this is based on optimal CX cost decomposition from reference [1]. For N > 3 qubits this is done using the general non-optimal greedy compilation routine from reference [3], which typically yields better CX cost compared to the AG method in [2].

Deprecated since version 0.23.0: The function qiskit.quantum_info.synthesis.clifford_decompose.decompose_clifford() is deprecated as of qiskit-terra 0.23.0. It will be removed no earlier than 3 months after the release date. Instead, use the function qiskit.synthesis.synth_clifford_full.

Parameters:

• clifford (Clifford) -- a clifford operator.

• method (str) -- Optional, a synthesis method ('AG' or 'greedy'). If set this overrides optimal decomposition for N <=3 qubits.

Returns:

a circuit implementation of the Clifford.

Return type:

QuantumCircuit

References

1. S. Bravyi, D. Maslov, Hadamard-free circuits expose the structure of the Clifford group, arXiv:2003.09412 [quant-ph]

2. S. Aaronson, D. Gottesman, Improved Simulation of Stabilizer Circuits, Phys. Rev. A 70, 052328 (2004). arXiv:quant-ph/0406196

3. Sergey Bravyi, Shaohan Hu, Dmitri Maslov, Ruslan Shaydulin, Clifford Circuit Optimization with Templates and Symbolic Pauli Gates, arXiv:2105.02291 [quant-ph]