StabilizerState#

class qiskit.quantum_info.StabilizerState(data, validate=True)[source]#

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

Références

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

Initialize a StabilizerState object.

Paramètres:

or (data (StabilizerState or Clifford or Pauli or QuantumCircuit) – 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()[source]#: Return the conjugate of the operator.

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

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

equiv(other)[source]#

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

Paramètres:: other (StabilizerState) – another StabilizerState.
Renvoie:: True if other has a generating set that generates the same StabilizerState.
Type renvoyé:: bool

evolve(other, qargs=None)[source]#

Evolve a stabilizer state by a Clifford operator.

Paramètres:

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.

Renvoie:

the output stabilizer state.

Type renvoyé:

StabilizerState

Lève:

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 stabilizer state other ⊗ self.

Paramètres:: other (StabilizerState) – a stabilizer state object.
Renvoie:: the tensor product operator other ⊗ self.
Type renvoyé:: StabilizerState
Lève:: QiskitError – if other is not a StabilizerState.

expectation_value(oper, qargs=None)[source]#

Compute the expectation value of a Pauli operator.

Paramètres:

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

Renvoie:

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

Type renvoyé:

complex

Lève:

QiskitError – if oper is not a Pauli operator.

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.

Paramètres:

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

Renvoie:

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.

Type renvoyé:

tuple

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

Return the subsystem measurement probability vector.

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

Paramètres:

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).

Renvoie:

The Numpy vector array of probabilities.

Type renvoyé:

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.

Paramètres:

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).

Renvoie:

The measurement probabilities in dict (ket) form.

Type renvoyé:

dict

purity()[source]#

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

Renvoie:: the purity (should equal 1).
Type renvoyé:: float
Lève:: QiskitError – if input is not a StabilizerState.

reset(qargs=None)[source]#

Reset state or subsystems to the 0-state.

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

Paramètres:

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).

Renvoie:

sampled counts dictionary.

Type renvoyé:

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.

Paramètres:

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).

Renvoie:

list of sampled counts if the order sampled.

Type renvoyé:

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 stabilizer state self ⊗ other.

Paramètres:: other (StabilizerState) – a stabilizer state object.
Renvoie:: the tensor product operator self ⊗ other.
Type renvoyé:: StabilizerState
Lève:: QiskitError – if other is not a StabilizerState.

to_operator()[source]#

Convert state to matrix operator class

Type renvoyé:: Operator

trace()[source]#

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

Renvoie:: the trace (should equal 1).
Type renvoyé:: float
Lève:: QiskitError – if input is not a StabilizerState.