# StabilizerState

`qiskit.quantum_info.StabilizerState(data, validate=True)` GitHub(opens in a new tab)

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

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.

## Attributes

### clifford

Return StabilizerState Clifford data

### num_qubits

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

## Methods

### conjugate

`conjugate()` GitHub(opens in a new tab)

Return the conjugate of the operator.

### copy

`copy()` GitHub(opens in a new tab)

Make a copy of current operator.

### dims

`dims(qargs=None)` GitHub(opens in a new tab)

Return tuple of input dimension for specified subsystems.

### equiv

`equiv(other)` GitHub(opens in a new tab)

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(opens in a new tab)

### evolve

`evolve(other, qargs=None)` GitHub(opens in a new tab)

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

`expand(other)` GitHub(opens in a new tab)

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(opens in a new tab)

Compute the expectation value of a Pauli operator.

Parameters

Returns

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

Return type

complex(opens in a new tab)

Raises

QiskitError – if oper is not a Pauli operator.

### from_stabilizer_list

`classmethod from_stabilizer_list(stabilizers, allow_redundant=False, allow_underconstrained=False)` GitHub(opens in a new tab)

Create a stabilizer state from the collection of stabilizers.

Parameters

• stabilizers (Collection[str(opens in a new tab)]) – list of stabilizer strings
• allow_redundant (bool(opens in a new tab)) – allow redundant stabilizers (i.e., some stabilizers can be products of the others)
• allow_underconstrained (bool(opens in a new tab)) – 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(opens in a new tab)

Return True if a valid StabilizerState.

### measure

`measure(qargs=None)` GitHub(opens in a new tab)

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(opens in a new tab) 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(opens in a new tab)

### probabilities

`probabilities(qargs=None, decimals=None)` GitHub(opens in a new tab)

Return the subsystem measurement probability vector.

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

Parameters

• qargs (None or list(opens in a new tab)) – subsystems to return probabilities for, if None return for all subsystems (Default: None).
• decimals (None or int(opens in a new tab)) – 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(opens in a new tab)

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(opens in a new tab)) – subsystems to return probabilities for, if None return for all subsystems (Default: None).
• decimals (None or int(opens in a new tab)) – 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(opens in a new tab)

### purity

`purity()` GitHub(opens in a new tab)

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(opens in a new tab)

Raises

QiskitError – if input is not a StabilizerState.

### reset

`reset(qargs=None)` GitHub(opens in a new tab)

Reset state or subsystems to the 0-state.

Parameters

qargs (list(opens in a new tab) 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

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(opens in a new tab)

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

Parameters

Returns

sampled counts dictionary.

Return type

Counts

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(opens in a new tab)

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

Parameters

Returns

list of sampled counts if the order sampled.

Return type

np.array

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

`seed(value=None)` GitHub(opens in a new tab)

Set the seed for the quantum state RNG.

### tensor

`tensor(other)` GitHub(opens in a new tab)

Return the tensor product stabilizer 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

`to_operator()` GitHub(opens in a new tab)

Convert state to matrix operator class

Return type

Operator

### trace

`trace()` GitHub(opens in a new tab)

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

float(opens in a new tab)

Raises

QiskitError – if input is not a StabilizerState.