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Module quantum

numrs2::new_modules

Module quantum 

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Quantum Computing Simulation

This module provides comprehensive quantum computing simulation capabilities for NumRS2, including state vector simulation, quantum gates, circuit construction, measurements, and quantum algorithms.

§Overview

The quantum module enables:

  • State Vector Simulation: Exact simulation of quantum states using complex amplitudes
  • Quantum Gates: Complete set of single and multi-qubit gates
  • Circuit Building: Fluent API for constructing quantum circuits
  • Measurements: Computational and Pauli basis measurements with sampling
  • Quantum Algorithms: QFT, Grover’s search, VQE, and QPE implementations

§Module Organization

  • statevector: Quantum state representation and density matrices
  • gates: Standard quantum gates (Pauli, Hadamard, rotations, controlled gates)
  • circuit: Quantum circuit builder with optimization
  • measurement: Measurement operations and statistics
  • algorithms: Quantum algorithms (QFT, Grover, VQE, QPE)

§Examples

§Creating a Bell State

use numrs2::new_modules::quantum::circuit::QuantumCircuit;

// Create Bell state (|00⟩ + |11⟩)/√2
let mut circuit = QuantumCircuit::<f64>::new(2).expect("valid qubit count");
circuit.h(0).expect("valid qubit index");  // Hadamard on qubit 0
circuit.cnot(0, 1).expect("valid qubit indices");  // CNOT with control=0, target=1

let state = circuit.execute().expect("circuit execution succeeds");
use numrs2::new_modules::quantum::algorithms::GroverSearch;
use numrs2::new_modules::quantum::circuit::QuantumCircuit;

// Oracle that marks state |11⟩
let oracle = |circuit: &mut QuantumCircuit<f64>| {
    circuit.cz(0, 1)?;
    Ok(())
};

let iterations = GroverSearch::optimal_iterations(2, 1);
let result_state = GroverSearch::search(2, oracle, iterations).expect("valid Grover search");

§Quantum Fourier Transform

use numrs2::new_modules::quantum::circuit::QuantumCircuit;
use numrs2::new_modules::quantum::algorithms::QuantumFourierTransform;

let mut circuit = QuantumCircuit::<f64>::new(3).expect("valid qubit count");
QuantumFourierTransform::apply(&mut circuit).expect("valid QFT application");

let state = circuit.execute().expect("circuit execution succeeds");

§Mathematical Background

§Quantum States

A quantum state of n qubits is represented as a normalized vector in 2ⁿ-dimensional complex Hilbert space:

|ψ⟩ = Σᵢ αᵢ|i⟩ where Σᵢ|αᵢ|² = 1

§Quantum Gates

Quantum gates are unitary transformations U satisfying U†U = I. Common gates include:

  • Pauli-X: Bit flip, X|0⟩ = |1⟩, X|1⟩ = |0⟩
  • Pauli-Y: Y = iXZ
  • Pauli-Z: Phase flip, Z|0⟩ = |0⟩, Z|1⟩ = -|1⟩
  • Hadamard: Creates superposition, H|0⟩ = (|0⟩ + |1⟩)/√2
  • CNOT: Controlled-NOT, entanglement gate

§Measurement

Measurement follows the Born rule: P(outcome i) = |⟨i|ψ⟩|² = |αᵢ|²

§SCIRS2 Integration

This module strictly follows NumRS2’s SCIRS2 ecosystem policy:

  • Complex numbers via scirs2_core::Complex
  • Random number generation via scirs2_core::random
  • Array operations via NumRS2’s Array type
  • No direct external dependencies (ndarray, rand, etc.)

§Performance Considerations

  • State vector simulation is exact but memory-intensive: O(2ⁿ) for n qubits
  • Practical limit: ~20-25 qubits on typical systems
  • Gate operations: O(2ⁿ) time complexity
  • Measurement sampling: O(1) per shot after O(2ⁿ) probability computation

§References

  • Nielsen & Chuang, “Quantum Computation and Quantum Information” (2010)
  • Grover, “Quantum Mechanics Helps in Searching for a Needle in a Haystack” (1997)
  • Peruzzo et al., “A variational eigenvalue solver on a photonic quantum processor” (2014)
  • Shor, “Polynomial-Time Algorithms for Prime Factorization” (1997)

Re-exports§

pub use algorithms::GroverSearch;
pub use algorithms::QuantumFourierTransform;
pub use algorithms::QuantumPhaseEstimation;
pub use algorithms::VQE;
pub use circuit::QuantumCircuit;
pub use measurement::Measurement;
pub use measurement::MeasurementResult;
pub use measurement::MeasurementStatistics;
pub use statevector::DensityMatrix;
pub use statevector::StateVector;
pub use unitarity::create_validated_gate;
pub use unitarity::disable_runtime_validation;
pub use unitarity::enable_runtime_validation;
pub use unitarity::is_unitary;
pub use unitarity::unitarity_error;
pub use unitarity::validate_all_standard_gates;
pub use unitarity::validate_gate_unitarity;
pub use unitarity::GateValidationResult;
pub use unitarity::StandardGatesValidation;

Modules§

algorithms
Quantum Algorithms
circuit
Quantum Circuit Builder
gates
Quantum Gates
measurement
Quantum Measurement Operations
statevector
Quantum State Vector Simulation
unitarity
Quantum Gate Unitarity Verification