States

StateAnalysis inspects statevectors and density matrices in a backend-independent way.

Inputs

A BackendResult, an ExecutionRecord, a StateVector / ~microquantum.DensityMatrix, a raw NumPy array (1-D = statevector, 2-D = density matrix), or a serialized dict carrying statevector / density_matrix.

Statevectors

from microquantum import QuantumCircuit, StateAnalysis

qc = QuantumCircuit(2).h(0).cx(0, 1)
state = qc.run()                      # StateVector

analysis = StateAnalysis(state)
print(analysis.kind)                  # "statevector"
print(analysis.dim)                   # 4
print(analysis.norm_squared())        # 1.0
print(analysis.is_normalized())       # True
print(analysis.probabilities())       # {'00': 0.5, '11': 0.5}
print(analysis.most_probable_state()) # 0 or 3 (index)
print(analysis.most_probable_bitstring())  # '00' or '11'

Density matrices

For a result carrying a density matrix (or a DensityMatrix directly):

import numpy as np

# density matrix for the Bell state prepared above
density_matrix_result = np.outer(state.amplitudes,
                                 np.conjugate(state.amplitudes))

dm_analysis = StateAnalysis(density_matrix_result)
print(dm_analysis.kind)                # "density_matrix"
print(dm_analysis.trace())             # 1.0
print(dm_analysis.purity())            # 1.0 pure / <1 mixed
print(dm_analysis.is_pure())           # True
print(dm_analysis.diagonal_probabilities())

Observables

A diagonal observable may be given as a 1-D array of dim real numbers, or a callable basis_index -> real:

print(analysis.expectation([0.0, 1.0, 1.0, 0.0]))   # ~1.0 for '11'
print(analysis.expectation(lambda i: i % 2))         # callable form

Notes

• kind / dim report what was analysed.

• Everything persists via to_dict() / to_json().