# 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
```

References

1. 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 or Clifford or Pauli or QuantumCircuit) â€“ qiskit.circuit.Instruction): Data from which the stabilizer state can be constructed.

• validate (boolean) â€“ validate that the stabilizer state data is a valid Clifford.

Attributes

clifford#

Return StabilizerState Clifford data

dim#

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.

Parameters:

other (StabilizerState) â€“ another StabilizerState.

Returns:

True if other has a generating set that generates the same StabilizerState.

Return type:

bool

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

Evolve a stabilizer state by a Clifford operator.

Parameters:
Returns:

the output stabilizer state.

Return type:

StabilizerState

Raises:
• QiskitError â€“ if other is not a StabilizerState.

• QiskitError â€“ if the operator dimension does not match the specified StabilizerState subsystem dimensions.

expand(other)[source]#

Return the tensor product stabilizer state other âŠ— self.

Parameters:

other (StabilizerState) â€“ a stabilizer state object.

Returns:

the tensor product operator other âŠ— self.

Return type:

StabilizerState

Raises:

QiskitError â€“ if other is not a StabilizerState.

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

Compute the expectation value of a Pauli operator.

Parameters:
• oper (Pauli) â€“ a Pauli operator to evaluate expval.

• qargs (None or list) â€“ 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 â€“ 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.

Parameters:

qargs (list or None) â€“ 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(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) â€“ subsystems to return probabilities for, if None return for all subsystems (Default: None).

• decimals (None or int) â€“ 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) â€“ subsystems to return probabilities for, if None return for all subsystems (Default: None).

• decimals (None or int) â€“ 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:

float

Raises:

QiskitError â€“ if input is not a StabilizerState.

reset(qargs=None)[source]#

Reset state or subsystems to the 0-state.

Parameters:

qargs (list or None) â€“ 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(shots, qargs=None)#

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

Parameters:
• shots (int) â€“ number of samples to generate.

• qargs (None or list) â€“ subsystems to sample measurements for, if None sample measurement of all subsystems (Default: None).

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(shots, qargs=None)[source]#

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

Parameters:
• shots (int) â€“ number of samples to generate.

• qargs (None or list) â€“ 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

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 âŠ— other.

Parameters:

other (StabilizerState) â€“ a stabilizer state object.

Returns:

the tensor product operator self âŠ— other.

Return type:

StabilizerState

Raises:

QiskitError â€“ if other is not a StabilizerState.

to_operator()[source]#

Convert state to matrix operator class

Return type:

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.

Returns:

the trace (should equal 1).

Return type:

float

Raises:

QiskitError â€“ if input is not a StabilizerState.