ts-quantum/dist/geometry/quantumDistance.d.ts

TypeScript library for quantum mechanics calculations and utilities

/**
 * Quantum state geometry - distances and metrics on quantum state manifolds
 * Based on Provost & Vallee (1980) "Riemannian structure on manifolds of quantum states"
 */
import { StateVector } from '../states/stateVector';
import { IStateVector } from '../core/types';
/**
 * Calculates the quantum distance between two normalized state vectors
 * Formula: D²(ψ₁,ψ₂) = 2 - 2|⟨ψ₁|ψ₂⟩| (Provost-Vallee Eq. 2.14)
 *
 * This distance is gauge-invariant and represents the geometric distance
 * on the projective Hilbert space of quantum states.
 *
 * @param state1 First quantum state (should be normalized)
 * @param state2 Second quantum state (should be normalized)
 * @returns Quantum distance between the states
 */
export declare function quantumDistance(state1: IStateVector, state2: IStateVector): number;
/**
 * Calculates quantum distance for states that may not be normalized
 * Automatically normalizes before computing distance
 *
 * @param state1 First quantum state
 * @param state2 Second quantum state
 * @returns Quantum distance between normalized states
 */
export declare function quantumDistanceUnnormalized(state1: IStateVector, state2: IStateVector): number;
/**
 * Calculates the quantum fidelity between two states
 * Fidelity F = |⟨ψ₁|ψ₂⟩|²
 * Related to distance by: D² = 2(1 - √F)
 *
 * @param state1 First quantum state (should be normalized)
 * @param state2 Second quantum state (should be normalized)
 * @returns Fidelity between states (0 to 1)
 */
export declare function quantumFidelity(state1: IStateVector, state2: IStateVector): number;
/**
 * Creates a simple two-level quantum system for testing
 * |0⟩ and |1⟩ basis states
 */
export declare class TwoLevelSystem {
    /**
     * Ground state |0⟩
     */
    static ground(): StateVector;
    /**
     * Excited state |1⟩
     */
    static excited(): StateVector;
    /**
     * Plus state |+⟩ = (|0⟩ + |1⟩)/√2
     */
    static plus(): StateVector;
    /**
     * Minus state |-⟩ = (|0⟩ - |1⟩)/√2
     */
    static minus(): StateVector;
    /**
     * General qubit state cos(θ/2)|0⟩ + e^(iφ)sin(θ/2)|1⟩
     * @param theta Polar angle (0 to π)
     * @param phi Azimuthal angle (0 to 2π)
     */
    static blochState(theta: number, phi: number): StateVector;
}
/**
 * Bloch sphere geometry utilities
 */
export declare class BlochSphere {
    /**
     * Calculates the quantum distance on the Bloch sphere
     * This matches the Provost-Vallee quantum distance for qubit states
     *
     * The relationship is: D_quantum = √2 * sin(θ_bloch/2)
     * where θ_bloch is the angle between Bloch vectors
     *
     * @param theta1 Polar angle of first state
     * @param phi1 Azimuthal angle of first state
     * @param theta2 Polar angle of second state
     * @param phi2 Azimuthal angle of second state
     * @returns Quantum distance between states
     */
    static geodesicDistance(theta1: number, phi1: number, theta2: number, phi2: number): number;
    /**
     * Verifies that quantum distance matches Bloch sphere calculation
     * @param theta1 Polar angle of first state
     * @param phi1 Azimuthal angle of first state
     * @param theta2 Polar angle of second state
     * @param phi2 Azimuthal angle of second state
     * @param tolerance Numerical tolerance for comparison
     * @returns True if distances match within tolerance
     */
    static verifyQuantumDistance(theta1: number, phi1: number, theta2: number, phi2: number, tolerance?: number): boolean;
}