Struct QuantumState 

pub struct QuantumState {
    pub amplitudes: Array1<QuantumAmplitude>,
    pub numqubits: usize,
}

Quantum state vector representation

A quantum state is represented as a vector of complex amplitudes in the computational basis. The state |ψ⟩ = Σᵢ αᵢ|i⟩ where αᵢ are the complex amplitudes and |i⟩ are the computational basis states.

Properties

• The state is normalized: Σᵢ |αᵢ|² = 1
• The number of amplitudes must be a power of 2 (2ⁿ for n qubits)
• Supports common quantum gates and operations

Example

use scirs2_spatial::quantum_inspired::concepts::QuantumState;
use scirs2_core::ndarray::Array1;
use scirs2_core::numeric::Complex64;

// Create a 2-qubit zero state |00⟩
let zero_state = QuantumState::zero_state(2);
assert_eq!(zero_state.num_qubits(), 2);
assert_eq!(zero_state.probability(0), 1.0);

// Create uniform superposition |+⟩⊗²
let superposition = QuantumState::uniform_superposition(2);
assert_eq!(superposition.probability(0), 0.25);

Fields

amplitudes: Array1<QuantumAmplitude>

Amplitudes for each basis state

numqubits: usize

Number of qubits

Implementations

impl QuantumState

pub fn new(amplitudes: Array1<QuantumAmplitude>) -> SpatialResult<Self>

Create a new quantum state with given amplitudes

Arguments

• amplitudes - Complex amplitudes for each computational basis state

Returns

A new QuantumState if the amplitudes vector has a power-of-2 length

Errors

Returns SpatialError::InvalidInput if the number of amplitudes is not a power of 2

pub fn zero_state(numqubits: usize) -> Self

Create a quantum state in computational basis |0⟩⊗ⁿ

Creates an n-qubit state where all qubits are in the |0⟩ state. This corresponds to the basis state |00…0⟩.

Arguments

• numqubits - Number of qubits in the state

Returns

A new QuantumState in the |0⟩⊗ⁿ state

pub fn uniform_superposition(numqubits: usize) -> Self

Create a uniform superposition state |+⟩⊗ⁿ

Creates an n-qubit state where each qubit is in the |+⟩ = (|0⟩ + |1⟩)/√2 state. This results in a uniform superposition over all 2ⁿ computational basis states.

Arguments

• numqubits - Number of qubits in the state

Returns

A new QuantumState in uniform superposition

pub fn measure(&self) -> usize

Measure the quantum state and collapse to classical state

Performs a measurement in the computational basis, collapsing the quantum state to a classical state according to the Born rule. The probability of measuring state |i⟩ is |αᵢ|².

Returns

The index of the measured computational basis state

pub fn probability(&self, state: usize) -> f64

Get the probability of measuring a specific state

Calculates the probability of measuring the quantum state in a specific computational basis state according to the Born rule.

Arguments

• state - Index of the computational basis state

Returns

Probability of measuring the given state (between 0.0 and 1.0)

pub fn hadamard(&mut self, qubit: usize) -> SpatialResult<()>

Apply Hadamard gate to specific qubit

The Hadamard gate creates superposition by mapping:

• |0⟩ → (|0⟩ + |1⟩)/√2
• |1⟩ → (|0⟩ - |1⟩)/√2

Arguments

• qubit - Index of the qubit to apply the gate to (0-indexed)

Errors

Returns SpatialError::InvalidInput if the qubit index is out of range

pub fn phase_rotation(&mut self, qubit: usize, angle: f64) -> SpatialResult<()>

Apply phase rotation gate

The phase rotation gate applies a phase e^(iθ) to the |1⟩ component of the specified qubit, leaving the |0⟩ component unchanged.

Arguments

• qubit - Index of the qubit to apply the gate to
• angle - Rotation angle in radians

Errors

Returns SpatialError::InvalidInput if the qubit index is out of range

pub fn controlled_rotation( &mut self, control: usize, target: usize, angle: f64, ) -> SpatialResult<()>

Apply controlled rotation between two qubits

Applies a rotation to the target qubit conditioned on the control qubit being in the |1⟩ state. This creates entanglement between the qubits.

Arguments

• control - Index of the control qubit
• target - Index of the target qubit
• angle - Rotation angle in radians

Errors

Returns SpatialError::InvalidInput if either qubit index is out of range

pub fn pauli_x(&mut self, qubit: usize) -> SpatialResult<()>

Apply Pauli-X gate (bit flip) to specific qubit

The Pauli-X gate performs a bit flip: |0⟩ ↔ |1⟩

Arguments

• qubit - Index of the qubit to apply the gate to

Errors

Returns SpatialError::InvalidInput if the qubit index is out of range

pub fn pauli_y(&mut self, qubit: usize) -> SpatialResult<()>

Apply Pauli-Y gate to specific qubit

The Pauli-Y gate performs: |0⟩ → i|1⟩, |1⟩ → -i|0⟩

Arguments

• qubit - Index of the qubit to apply the gate to

Errors

Returns SpatialError::InvalidInput if the qubit index is out of range

pub fn pauli_z(&mut self, qubit: usize) -> SpatialResult<()>

Apply Pauli-Z gate (phase flip) to specific qubit

The Pauli-Z gate performs a phase flip: |0⟩ → |0⟩, |1⟩ → -|1⟩

Arguments

• qubit - Index of the qubit to apply the gate to

Errors

Returns SpatialError::InvalidInput if the qubit index is out of range

pub fn num_qubits(&self) -> usize

Get number of qubits

pub fn num_states(&self) -> usize

Get number of basis states (2^n)

pub fn is_normalized(&self) -> bool

Check if the state is normalized

pub fn normalize(&mut self)

Normalize the quantum state

pub fn amplitude(&self, state: usize) -> Option<QuantumAmplitude>

Get the amplitude for a specific basis state

pub fn set_amplitude( &mut self, state: usize, amplitude: QuantumAmplitude, ) -> SpatialResult<()>

Set the amplitude for a specific basis state

Trait Implementations

impl Clone for QuantumState

fn clone(&self) -> QuantumState

Returns a duplicate of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl Debug for QuantumState

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.