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}
1Given 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
copy
dims
equiv
equiv(other)
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
evolve
evolve(other, qargs=None)
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
Raises
- QiskitError – if other is not a StabilizerState.
- QiskitError – if the operator dimension does not match the specified StabilizerState subsystem dimensions.
expand
expand(other)
Return the tensor product stabilizer state other ⊗ self.
Parameters
other (StabilizerState) – a stabilizer state object.
Returns
the tensor product operator other ⊗ self.
Return type
Raises
QiskitError – if other is not a StabilizerState.
expectation_value
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
Raises
QiskitError – if oper is not a Pauli operator.
from_stabilizer_list
classmethod from_stabilizer_list(stabilizers, allow_redundant=False, allow_underconstrained=False)
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
is_valid
measure
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
probabilities
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
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
purity
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
Raises
QiskitError – if input is not a StabilizerState.
reset
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
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)
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
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)
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
tensor
tensor(other)
Return the tensor product stabilizer state self ⊗ other.
Parameters
other (StabilizerState) – a stabilizer state object.
Returns
the tensor product operator self ⊗ other.
Return type
Raises
QiskitError – if other is not a StabilizerState.
to_operator
trace
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
Raises
QiskitError – if input is not a StabilizerState.