# 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**

- 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**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

`conjugate()`

Return the conjugate of the operator.

### copy

`copy()`

Make a copy of current operator.

### dims

`dims(qargs=None)`

Return tuple of input dimension for specified subsystems.

### 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**or**QuantumCircuit**or**qiskit.circuit.Instruction*) – The Clifford operator to evolve by.**qargs**(*list*(opens in a new tab)) – 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*(opens in a new tab)) – 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*(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**

### is_valid

`is_valid(atol=None, rtol=None)`

Return True if a valid StabilizerState.

### 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*(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**

### 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*(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)`

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**

### 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*(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**

**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*(opens in a new tab)) – number of samples to generate.**qargs**(*None or**list*(opens in a new tab)) – subsystems to sample measurements for, if None sample measurement of all subsystems (Default: None).

**Returns**

sampled counts dictionary.

**Return type**

Additional Information:

This function

samplesmeasurement 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*(opens in a new tab)) – number of samples to generate.**qargs**(*None or**list*(opens in a new tab)) – 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

`seed(value=None)`

Set the seed for the quantum state RNG.

### 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

`to_operator()`

Convert state to matrix operator class

**Return type**

### 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.