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StabilizerState

class StabilizerState(data, validate=True)

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Bases: qiskit.quantum_info.states.quantum_state.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

References

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

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.

Methods

conjugate

StabilizerState.conjugate()

Return the conjugate of the operator.

copy

StabilizerState.copy()

Make a copy of current operator.

dims

StabilizerState.dims(qargs=None)

Return tuple of input dimension for specified subsystems.

evolve

StabilizerState.evolve(other, qargs=None)

Evolve a stabilizer state by a Clifford operator.

Parameters

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

StabilizerState.expand(other)

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

StabilizerState.expectation_value(oper, qargs=None)

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.

is_valid

StabilizerState.is_valid(atol=None, rtol=None)

Return True if a valid StabilizerState.

measure

StabilizerState.measure(qargs=None)

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

StabilizerState.probabilities(qargs=None, decimals=None)

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

StabilizerState.probabilities_dict(qargs=None, decimals=None)

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

StabilizerState.purity()

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

StabilizerState.reset(qargs=None)

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

StabilizerState.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

StabilizerState.sample_memory(shots, qargs=None)

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

StabilizerState.seed(value=None)

Set the seed for the quantum state RNG.

tensor

StabilizerState.tensor(other)

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

StabilizerState.to_operator()

Convert state to matrix operator class

trace

StabilizerState.trace()

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.


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.

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