statevector.hpp File Reference

Statevector-based quantum circuit simulator. More...

#include "core/types.hpp"
#include "core/vector.hpp"
#include <array>
#include <functional>
#include <vector>

Go to the source code of this file.

Namespaces
namespace	num
namespace	num::quantum

Typedefs
using	num::quantum::Statevector = num::CVector
	Dense statevector: complex vector of length 2^n_qubits, backed by num::CVector.
using	num::quantum::Gate = std::array< cplx, 4 >
	2x2 single-qubit gate stored row-major: { G[0,0], G[0,1], G[1,0], G[1,1] }
using	num::quantum::Gate2Q = std::array< cplx, 16 >
	4x4 two-qubit gate stored row-major (16 entries)

Functions
Statevector	num::quantum::zero_state (int n_qubits)
	Returns |0...0> computational basis state for n_qubits qubits.
Statevector	num::quantum::basis_state (int n_qubits, int k)
	Returns the computational basis state |k> for an n_qubits system.
Gate	num::quantum::gate_x ()
	Pauli-X (NOT)
Gate	num::quantum::gate_y ()
	Pauli-Y.
Gate	num::quantum::gate_z ()
	Pauli-Z.
Gate	num::quantum::gate_h ()
	Hadamard.
Gate	num::quantum::gate_s ()
	Phase gate S = diag(1, i)
Gate	num::quantum::gate_sdg ()
	S† = diag(1, -i)
Gate	num::quantum::gate_t ()
	T gate = diag(1, e^{ipi/4})
Gate	num::quantum::gate_tdg ()
	T† gate.
Gate	num::quantum::gate_rx (real theta)
	Rotation about X: R_x(theta) = exp(-ithetaX/2)
Gate	num::quantum::gate_ry (real theta)
	Rotation about Y: R_y(theta) = exp(-ithetaY/2)
Gate	num::quantum::gate_rz (real theta)
	Rotation about Z: R_z(theta) = exp(-ithetaZ/2)
Gate	num::quantum::gate_p (real lambda)
	Phase gate: diag(1, e^{ilambda})
Gate	num::quantum::gate_u (real theta, real phi, real lambda)
	General SU(2) gate.
Gate2Q	num::quantum::gate2q_cnot ()
	CNOT (qubit 0 = control, qubit 1 = target in subspace)
Gate2Q	num::quantum::gate2q_cz ()
	Controlled-Z.
Gate2Q	num::quantum::gate2q_swap ()
	SWAP.
void	num::quantum::apply_1q (Statevector &sv, int n_qubits, const Gate &G, int target)
	Apply a 2x2 gate to a single qubit in-place.
void	num::quantum::apply_2q (Statevector &sv, int n_qubits, const Gate2Q &G, int q0, int q1)
	Apply a general 4x4 two-qubit gate to qubits q0, q1.
void	num::quantum::apply_cnot (Statevector &sv, int n_qubits, int control, int target)
	CNOT with explicit control and target qubits.
void	num::quantum::apply_cz (Statevector &sv, int n_qubits, int control, int target)
	Controlled-Z.
void	num::quantum::apply_swap (Statevector &sv, int n_qubits, int q0, int q1)
	SWAP two qubits.
void	num::quantum::apply_toffoli (Statevector &sv, int n_qubits, int c0, int c1, int target)
	Toffoli (CCX) gate.
void	num::quantum::apply_cy (Statevector &sv, int n_qubits, int control, int target)
	Controlled-Y.
void	num::quantum::apply_cp (Statevector &sv, int n_qubits, real lambda, int control, int target)
	Controlled phase: applies phase e^{ilambda} when both control=1 and target=1.
void	num::quantum::apply_cswap (Statevector &sv, int n_qubits, int ctrl, int q0, int q1)
	Fredkin (CSWAP): swaps q0 and q1 when ctrl=1.
real	num::quantum::norm (const Statevector &sv)
	L2 norm of the statevector (should be 1 for a valid quantum state)
void	num::quantum::normalize (Statevector &sv)
	Normalize statevector in-place.
std::vector< real >	num::quantum::probabilities (const Statevector &sv)
	Measurement probability for each basis state: p_i = |a_i|^2.
real	num::quantum::expectation (const Statevector &sv, std::function< void(const Statevector &, Statevector &)> op)
	Expectation value <psi|O|psi> for a Hermitian operator given as matrix-free matvec.
real	num::quantum::expectation_z (const Statevector &sv, int qubit)
	<Z_q> = P(q=0) - P(q=1) for qubit q
real	num::quantum::expectation_x (const Statevector &sv, int n_qubits, int qubit)
	<X_q> for qubit q
real	num::quantum::expectation_y (const Statevector &sv, int n_qubits, int qubit)
	<Y_q> for qubit q
std::array< std::complex< real >, 4 >	num::quantum::reduced_density_matrix (const Statevector &sv, int n_qubits, int qubit)
	Reduced density matrix for a single qubit (2x2, returned row-major)
real	num::quantum::entanglement_entropy (const Statevector &sv, int n_qubits, int qubit)
	Von Neumann entropy of a single qubit's reduced density matrix.

Detailed Description

Statevector-based quantum circuit simulator.

Simulates an n-qubit system as a dense complex statevector of length 2^n. Qubit indexing is little-endian: qubit 0 is the least-significant bit of the basis-state index.

using namespace num::quantum;
auto sv = zero_state(2);          // |00>
apply_1q(sv, 2, gate_h(), 0);     // H on qubit 0  ->  (|00> + |10>) / sqrt2
apply_cnot(sv, 2, 0, 1);          // CNOT(ctrl=0, tgt=1) -> Bell state
auto p = probabilities(sv);       // {0.5, 0, 0, 0.5}

Definition in file statevector.hpp.