StabilizerState

class qiskit.quantum_info.StabilizerState(data, validate=True)

Bases: QuantumState

StabilizerState class. Stabilizer simulator using the convention from reference [1]. Based on the internal class Clifford.

from qiskit import QuantumCircuit
from qiskit.quantum_info import StabilizerState, Pauli
 
# Bell state generation circuit
qc = QuantumCircuit(2)
qc.h(0)
qc.cx(0, 1)
stab = StabilizerState(qc)
 
# Print the StabilizerState
print(stab)
 
# Calculate the StabilizerState measurement probabilities dictionary
print (stab.probabilities_dict())
 
# Calculate expectation value of the StabilizerState
print (stab.expectation_value(Pauli('ZZ')))

StabilizerState(StabilizerTable: ['+XX', '+ZZ'])
{'00': 0.5, '11': 0.5}
1

Given a list of stabilizers, qiskit.quantum_info.StabilizerState.from_stabilizer_list() returns a state stabilized by the list

from qiskit.quantum_info import StabilizerState
 
stabilizer_list = ["ZXX", "-XYX", "+ZYY"]
stab = StabilizerState.from_stabilizer_list(stabilizer_list)

References

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

Initialize a StabilizerState object.

Parameters

or (data (StabilizerState orClifford orPauli orQuantumCircuit) – qiskit.circuit.Instruction): Data from which the stabilizer state can be constructed.
validate (boolean) – validate that the stabilizer state data is a valid Clifford.

Attributes

clifford

Return StabilizerState Clifford data

dim

Return total state dimension.

num_qubits

Return the number of qubits if a N-qubit state or None otherwise.

Methods

conjugate

conjugate()

GitHub

Return the conjugate of the operator.

copy

copy()

GitHub

Make a copy of current operator.

dims

dims(qargs=None)

GitHub

Return tuple of input dimension for specified subsystems.

equiv

equiv(other)

GitHub

Return True if the two generating sets generate the same stabilizer group.

Parameters

other (StabilizerState) – another StabilizerState.

Returns

True if other has a generating set that generates the same StabilizerState.

Return type

bool

evolve

evolve(other, qargs=None)

GitHub

Evolve a stabilizer state by a Clifford operator.

Parameters

other (Clifford orQuantumCircuit orqiskit.circuit.Instruction) – The Clifford operator to evolve by.
qargs (list) – a list of stabilizer subsystem positions to apply the operator on.

Returns

the output stabilizer state.

Return type

StabilizerState

Raises

QiskitError – if other is not a StabilizerState.
QiskitError – if the operator dimension does not match the specified StabilizerState subsystem dimensions.

expand

expand(other)

GitHub

Return the tensor product stabilizer state other ⊗ self.

Parameters

other (StabilizerState) – a stabilizer state object.

Returns

the tensor product operator other ⊗ self.

Return type

StabilizerState

Raises

QiskitError – if other is not a StabilizerState.

expectation_value

expectation_value(oper, qargs=None)

GitHub

Compute the expectation value of a Pauli operator.

Parameters

oper (Pauli) – a Pauli operator to evaluate expval.
qargs (None or list) – subsystems to apply the operator on.

Returns

the expectation value (only 0 or 1 or -1 or i or -i).

Return type

complex

Raises

QiskitError – if oper is not a Pauli operator.

from_stabilizer_list

classmethod from_stabilizer_list(stabilizers, allow_redundant=False, allow_underconstrained=False)

GitHub

Create a stabilizer state from the collection of stabilizers.

Parameters

stabilizers (Collection[str]) – list of stabilizer strings
allow_redundant (bool) – allow redundant stabilizers (i.e., some stabilizers can be products of the others)
allow_underconstrained (bool) – allow underconstrained set of stabilizers (i.e., the stabilizers do not specify a unique state)

Returns

a state stabilized by stabilizers.

Return type

StabilizerState

is_valid

is_valid(atol=None, rtol=None)

GitHub

Return True if a valid StabilizerState.

measure

measure(qargs=None)

GitHub

Measure subsystems and return outcome and post-measure state.

Note that this function uses the QuantumStates internal random number generator for sampling the measurement outcome. The RNG seed can be set using the seed() method.

Parameters

qargs (list or None) – subsystems to sample measurements for, if None sample measurement of all subsystems (Default: None).

Returns

the pair (outcome, state) where outcome is the

measurement outcome string label, and state is the collapsed post-measurement stabilizer state for the corresponding outcome.

Return type

tuple

probabilities

probabilities(qargs=None, decimals=None)

GitHub

Return the subsystem measurement probability vector.

Measurement probabilities are with respect to measurement in the computation (diagonal) basis.

Parameters

qargs (None or list) – subsystems to return probabilities for, if None return for all subsystems (Default: None).
decimals (None or int) – the number of decimal places to round values. If None no rounding is done (Default: None).

Returns

The Numpy vector array of probabilities.

Return type

np.array

probabilities_dict

probabilities_dict(qargs=None, decimals=None)

GitHub

Return the subsystem measurement probability dictionary.

Measurement probabilities are with respect to measurement in the computation (diagonal) basis.

This dictionary representation uses a Ket-like notation where the dictionary keys are qudit strings for the subsystem basis vectors. If any subsystem has a dimension greater than 10 comma delimiters are inserted between integers so that subsystems can be distinguished.

Parameters

qargs (None or list) – subsystems to return probabilities for, if None return for all subsystems (Default: None).
decimals (None or int) – the number of decimal places to round values. If None no rounding is done (Default: None).

Returns

The measurement probabilities in dict (ket) form.

Return type

dict

purity

purity()

GitHub

Return the purity of the quantum state, which equals to 1, since it is always a pure state.

Returns

the purity (should equal 1).

Return type

float

Raises

QiskitError – if input is not a StabilizerState.

reset

reset(qargs=None)

GitHub

Reset state or subsystems to the 0-state.

Parameters

qargs (list or None) – subsystems to reset, if None all subsystems will be reset to their 0-state (Default: None).

Returns

the reset state.

Return type

StabilizerState

Additional Information:

If all subsystems are reset this will return the ground state on all subsystems. If only some subsystems are reset this function will perform a measurement on those subsystems and evolve the subsystems so that the collapsed post-measurement states are rotated to the 0-state. The RNG seed for this sampling can be set using the seed() method.

sample_counts

sample_counts(shots, qargs=None)

GitHub

Sample a dict of qubit measurement outcomes in the computational basis.

Parameters

shots (int) – number of samples to generate.
qargs (None or list) – subsystems to sample measurements for, if None sample measurement of all subsystems (Default: None).

Returns

sampled counts dictionary.

Return type

Counts

Additional Information:

This function samples measurement outcomes using the measure probabilities() for the current state and qargs. It does not actually implement the measurement so the current state is not modified.

The seed for random number generator used for sampling can be set to a fixed value by using the stats seed() method.

sample_memory

sample_memory(shots, qargs=None)

GitHub

Sample a list of qubit measurement outcomes in the computational basis.

Parameters

shots (int) – number of samples to generate.
qargs (None or list) – subsystems to sample measurements for, if None sample measurement of all subsystems (Default: None).

Returns

list of sampled counts if the order sampled.

Return type

np.array

Additional Information:

This function implements the measurement measure() method.

The seed for random number generator used for sampling can be set to a fixed value by using the stats seed() method.