StateVector

A pure quantum state represented as a complex column vector of dimension $2^n$, where $n$ is the number of qubits. Each element corresponds to the probability amplitude of a computational-basis state.

The state vector $|\psi ⟩$ must satisfy the normalization condition:

$$⟨\psi |\psi ⟩=\sum _i|{\psi }_i{|}^2=1$$

Constructors

Default constructor

StateVector()

Constructs a state vector for a single-qubit system in the $|0⟩$ state: $[1+0j,0+0j]$.

Copy constructor

StateVector(other: StateVector)

Construct a StateVector as a copy of another StateVector.

Parameter	Type	Description
other	StateVector	An existing StateVector to copy.

From a dictionary

StateVector(data: dict[int, complex])

Construct a state vector from a dictionary mapping basis-state indices to complex amplitudes. Indices not present in the dictionary are set to zero. The vector is automatically normalized to unit length.

Parameter	Type	Description
data	dict[int, complex]	Mapping from basis-state index to amplitude.

From a complex array

StateVector(data: list[complex])

Construct a state vector from a flat list (or numpy array) of complex amplitudes. The vector is automatically normalized to unit length.

Parameter	Type	Description
data	list[complex]	A 1-D array of complex amplitudes.

From a numpy array

StateVector(data: numpy.ndarray)

Construct a state vector from a 1-D complex numpy array (or Eigen vector). The vector is automatically normalized to unit length.

Parameter	Type	Description
data	numpy.ndarray	A 1-D array of complex amplitudes.

From qubit count

StateVector(qbit_total: int)

Construct a state vector for qbit_total qubits initialized to the all-zeros state $|0{⟩}^{\otimes n}$.

Parameter	Type	Description
qbit_total	int	The number of qubits. The resulting vector has dimension $2^{\mathtt{\text{qbit\_total}}}$.

Methods

ndarray

ndarray() -> numpy.ndarray[numpy.complex128]

Return the internal state-vector data as a 1-D numpy.ndarray.

purity

purity() -> complex

Return the purity $\mathrm{Tr}({\rho }^2)$ of the state. For a pure state represented by a state vector, the purity is always $1+0j$.

evolve

evolve(circuit: QCircuit) -> StateVector

Evolve the state vector under the given quantum circuit. Returns a new StateVector with the result; the original object is not modified.

Parameter	Type	Description
circuit	QCircuit	The quantum circuit to apply.

update_by_evolve

update_by_evolve(circuit: QCircuit) -> StateVector

Evolve the state vector under the given quantum circuit in place, updating the internal data. Also returns the resulting StateVector.

Parameter	Type	Description
circuit	QCircuit	The quantum circuit to apply.

is_valid

is_valid() -> bool

Check whether the internal data constitutes a valid quantum state vector (normalized to unit length).

get_density_matrix

get_density_matrix() -> Matrix

Compute the density matrix $\rho =|\psi ⟩⟨\psi |$ corresponding to this state vector.

at

at(idx: int) -> complex

Return the amplitude at the specified basis-state index.

Parameter	Type	Description
idx	int	The index of the basis state (0-based).

dim

dim() -> int

Return the dimension of the state vector, i.e., $2^n$ for $n$ qubits.

Operators

Equality

sv_a == sv_b -> bool

Return True if the two StateVector objects have identical internal data.

Examples

import numpy as np
from pyqpanda3.quantum_info import StateVector

# Construct from a list (Bell state |00> + |11>)
sv = StateVector([1/np.sqrt(2), 0, 0, 1/np.sqrt(2)])

print(sv.dim())       # 4
print(sv.is_valid())  # True
print(sv.purity())    # (1.0+0j)

# Access an amplitude
amp = sv.at(3)  # (0.7071...+0j)
print("amp:", amp)

# Convert to density matrix
dm = sv.get_density_matrix()

# Get numpy array
arr = sv.ndarray()

Running the example produces:

4
True
(1.0000000000000004+0j)
amp: (0.7071067811865476+0j)

See Also

• DensityMatrix
• Unitary
• Matrix