qiskit.quantum_info.StabilizerState¶

class StabilizerState(data, validate=True)[source]¶

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

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

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

__init__(data, validate=True)[source]¶

Initialize a StabilizerState object.

Parameters

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

Methods

`__init__`(data[, validate])	Initialize a StabilizerState object.
`conjugate`()	Return the conjugate of the operator.
`copy`()	Make a copy of current operator.
`dims`([qargs])	Return tuple of input dimension for specified subsystems.
`evolve`(other[, qargs])	Evolve a stabilizer state by a Clifford operator.
`expand`(other)	Return the tensor product stabilzier state other ⊗ self.
`expectation_value`(oper[, qargs])	Compute the expectation value of an operator.
`is_valid`([atol, rtol])	Return True if a valid StabilizerState.
`measure`([qargs])	Measure subsystems and return outcome and post-measure state.
`probabilities`([qargs, decimals])	Return the subsystem measurement probability vector.
`probabilities_dict`([qargs, decimals])	Return the subsystem measurement probability dictionary.
`purity`()	Return the purity of the quantum state, which equals to 1, since it is always a pure state.
`reset`([qargs])	Reset state or subsystems to the 0-state.
`sample_counts`(shots[, qargs])	Sample a dict of qubit measurement outcomes in the computational basis.
`sample_memory`(shots[, qargs])	Sample a list of qubit measurement outcomes in the computational basis.
`seed`([value])	Set the seed for the quantum state RNG.
`tensor`(other)	Return the tensor product stabilzier state self ⊗ other.
`to_operator`()	Convert state to matrix operator class
`trace`()	Return the trace of the stabilizer state as a density matrix, which equals to 1, since it is always a pure state.

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.

property clifford¶: Return StabilizerState Clifford data

conjugate()[source]¶: Return the conjugate of the operator.

copy()¶: Make a copy of current operator.

property dim¶: Return total state dimension.

dims(qargs=None)¶: Return tuple of input dimension for specified subsystems.

evolve(other, qargs=None)[source]¶

Evolve a stabilizer state by a Clifford operator.

Parameters

other (Clifford or QuantumCircuit or qiskit.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(other)[source]¶

Return the tensor product stabilzier 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(oper, qargs=None)[source]¶

Compute the expectation value of an operator.

Parameters

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

Returns

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

Return type

complex

is_valid(atol=None, rtol=None)[source]¶: Return True if a valid StabilizerState.

measure(qargs=None)[source]¶

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

property num_qubits¶: Return the number of qubits if a N-qubit state or None otherwise.

probabilities(qargs=None, decimals=None)[source]¶

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(qargs=None, decimals=None)[source]¶

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()[source]¶

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: double
Raises: QiskitError – if input is not a StabilizerState.

reset(qargs=None)[source]¶

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(shots, qargs=None)¶

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(shots, qargs=None)[source]¶

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.

seed(value=None)¶: Set the seed for the quantum state RNG.

tensor(other)[source]¶

Return the tensor product stabilzier state self ⊗ other.

Parameters: other (StabilizerState) – a stabilizer state object.
Returns: the tensor product operator self ⊗ other.
Return type: StabilizerState
Raises: QiskitError – if other is not a StabilizerState.

to_operator()[source]¶: Convert state to matrix operator class

trace()[source]¶

Return the trace of the stabilizer state as a density matrix, which equals to 1, since it is always a pure state.

Returns: the trace (should equal 1).
Return type: double
Raises: QiskitError – if input is not a StabilizerState.