Typedefs
using	Statevector = num::CVector
	Dense statevector: complex vector of length 2^n_qubits, backed by num::CVector.

using	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	Gate2Q = std::array< cplx, 16 >
	4x4 two-qubit gate stored row-major (16 entries)

using	cplx = std::complex< real >

Functions
Statevector	zero_state (int n_qubits)
	Returns \|0...0> computational basis state for n_qubits qubits.

Statevector	basis_state (int n_qubits, int k)
	Returns the computational basis state \|k> for an n_qubits system.

Gate	gate_x ()
	Pauli-X (NOT)

Gate	gate_y ()
	Pauli-Y.

Gate	gate_z ()
	Pauli-Z.

Gate	gate_h ()
	Hadamard.

Gate	gate_s ()
	Phase gate S = diag(1, i)

Gate	gate_sdg ()
	S† = diag(1, -i)

Gate	gate_t ()
	T gate = diag(1, e^{ipi/4})

Gate	gate_tdg ()
	T† gate.

Gate	gate_rx (real theta)
	Rotation about X: R_x(theta) = exp(-ithetaX/2)

Gate	gate_ry (real theta)
	Rotation about Y: R_y(theta) = exp(-ithetaY/2)

Gate	gate_rz (real theta)
	Rotation about Z: R_z(theta) = exp(-ithetaZ/2)

Gate	gate_p (real lambda)
	Phase gate: diag(1, e^{ilambda})

Gate	gate_u (real theta, real phi, real lambda)
	General SU(2) gate.

Gate2Q	gate2q_cnot ()
	CNOT (qubit 0 = control, qubit 1 = target in subspace)

Gate2Q	gate2q_cz ()
	Controlled-Z.

Gate2Q	gate2q_swap ()
	SWAP.

void	apply_1q (Statevector &sv, int n_qubits, const Gate &G, int target)
	Apply a 2x2 gate to a single qubit in-place.

void	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	apply_cnot (Statevector &sv, int n_qubits, int control, int target)
	CNOT with explicit control and target qubits.

void	apply_cz (Statevector &sv, int n_qubits, int control, int target)
	Controlled-Z.

void	apply_swap (Statevector &sv, int n_qubits, int q0, int q1)
	SWAP two qubits.

void	apply_toffoli (Statevector &sv, int n_qubits, int c0, int c1, int target)
	Toffoli (CCX) gate.

void	apply_cy (Statevector &sv, int n_qubits, int control, int target)
	Controlled-Y.

void	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	apply_cswap (Statevector &sv, int n_qubits, int ctrl, int q0, int q1)
	Fredkin (CSWAP): swaps q0 and q1 when ctrl=1.

real	norm (const Statevector &sv)
	L2 norm of the statevector (should be 1 for a valid quantum state)

void	normalize (Statevector &sv)
	Normalize statevector in-place.

std::vector< real >	probabilities (const Statevector &sv)
	Measurement probability for each basis state: p_i = \|a_i\|^2.

real	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	expectation_z (const Statevector &sv, int qubit)
	<Z_q> = P(q=0) - P(q=1) for qubit q

real	expectation_x (const Statevector &sv, int n_qubits, int qubit)
	<X_q> for qubit q

real	expectation_y (const Statevector &sv, int n_qubits, int qubit)
	<Y_q> for qubit q

std::array< std::complex< real >, 4 >	reduced_density_matrix (const Statevector &sv, int n_qubits, int qubit)
	Reduced density matrix for a single qubit (2x2, returned row-major)

real	entanglement_entropy (const Statevector &sv, int n_qubits, int qubit)
	Von Neumann entropy of a single qubit's reduced density matrix.

Typedef Documentation

◆ cplx

using num::quantum::cplx = typedef std::complex<real>

Definition at line 7 of file statevector.cpp.

◆ Gate

using num::quantum::Gate = typedef std::array<cplx, 4>

2x2 single-qubit gate stored row-major: { G[0,0], G[0,1], G[1,0], G[1,1] }

Definition at line 31 of file statevector.hpp.

◆ Gate2Q

using num::quantum::Gate2Q = typedef std::array<cplx, 16>

4x4 two-qubit gate stored row-major (16 entries)

Definition at line 34 of file statevector.hpp.

◆ Statevector

using num::quantum::Statevector = typedef num::CVector

Dense statevector: complex vector of length 2^n_qubits, backed by num::CVector.

Definition at line 28 of file statevector.hpp.

Function Documentation

◆ apply_1q()

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.

Parameters

sv	Statevector of length 2^n_qubits (modified in-place)
n_qubits	Total number of qubits
G	2x2 gate (row-major)
target	Target qubit index (0 = LSB)

Definition at line 107 of file statevector.cpp.

References num::ipow().

Referenced by expectation_x(), and expectation_y().

◆ apply_2q()

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.

Parameters

sv	Statevector
n_qubits	Total number of qubits
G	4x4 gate acting on (q0, q1) in little-endian order
q0	First qubit (LSB of the 2-qubit subspace)
q1	Second qubit (MSB of the 2-qubit subspace)

Definition at line 122 of file statevector.cpp.

References num::ipow().

◆ apply_cnot()

void num::quantum::apply_cnot	(	Statevector &	sv,
		int	n_qubits,
		int	control,
		int	target
	)

CNOT with explicit control and target qubits.

Definition at line 139 of file statevector.cpp.

References num::ipow().

◆ apply_cp()

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.

Definition at line 277 of file statevector.cpp.

References num::ipow().

◆ apply_cswap()

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.

Definition at line 288 of file statevector.cpp.

References num::ipow().

◆ apply_cy()

void num::quantum::apply_cy	(	Statevector &	sv,
		int	n_qubits,
		int	control,
		int	target
	)

Controlled-Y.

Definition at line 262 of file statevector.cpp.

References num::ipow().

◆ apply_cz()

void num::quantum::apply_cz	(	Statevector &	sv,
		int	n_qubits,
		int	control,
		int	target
	)

Controlled-Z.

Definition at line 148 of file statevector.cpp.

References num::ipow().

◆ apply_swap()

void num::quantum::apply_swap	(	Statevector &	sv,
		int	n_qubits,
		int	q0,
		int	q1
	)

SWAP two qubits.

Definition at line 157 of file statevector.cpp.

References num::ipow().

◆ apply_toffoli()

void num::quantum::apply_toffoli	(	Statevector &	sv,
		int	n_qubits,
		int	c0,
		int	c1,
		int	target
	)

Toffoli (CCX) gate.

Definition at line 166 of file statevector.cpp.

References num::ipow().

◆ basis_state()

Statevector num::quantum::basis_state	(	int	n_qubits,
		int	k
	)

Returns the computational basis state |k> for an n_qubits system.

Definition at line 18 of file statevector.cpp.

References num::ipow().

◆ entanglement_entropy()

real num::quantum::entanglement_entropy	(	const Statevector &	sv,
		int	n_qubits,
		int	qubit
	)

Von Neumann entropy of a single qubit's reduced density matrix.

Definition at line 248 of file statevector.cpp.

References num::e, num::ipow(), and reduced_density_matrix().

Referenced by main().

◆ expectation()

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.

Definition at line 192 of file statevector.cpp.

References num::ipow(), and num::BasicVector< T >::size().

◆ expectation_x()

real num::quantum::expectation_x	(	const Statevector &	sv,
		int	n_qubits,
		int	qubit
	)

<X_q> for qubit q

Definition at line 211 of file statevector.cpp.

References apply_1q(), gate_x(), num::ipow(), and num::BasicVector< T >::size().

◆ expectation_y()

real num::quantum::expectation_y	(	const Statevector &	sv,
		int	n_qubits,
		int	qubit
	)

<Y_q> for qubit q

Definition at line 220 of file statevector.cpp.

References apply_1q(), gate_y(), num::ipow(), and num::BasicVector< T >::size().

◆ expectation_z()

real num::quantum::expectation_z	(	const Statevector &	sv,
		int	qubit
	)

<Z_q> = P(q=0) - P(q=1) for qubit q

Definition at line 201 of file statevector.cpp.

References num::ipow(), and num::BasicVector< T >::size().

◆ gate2q_cnot()

Gate2Q num::quantum::gate2q_cnot ( )

CNOT (qubit 0 = control, qubit 1 = target in subspace)

Definition at line 78 of file statevector.cpp.

◆ gate2q_cz()

Gate2Q num::quantum::gate2q_cz ( )

Controlled-Z.

Definition at line 87 of file statevector.cpp.

◆ gate2q_swap()

Gate2Q num::quantum::gate2q_swap ( )

SWAP.

Definition at line 96 of file statevector.cpp.

◆ gate_h()

Gate num::quantum::gate_h ( )

Hadamard.

Definition at line 30 of file statevector.cpp.

◆ gate_p()

Gate num::quantum::gate_p ( real lambda )

Phase gate: diag(1, e^{ilambda})

Definition at line 60 of file statevector.cpp.

◆ gate_rx()

Gate num::quantum::gate_rx ( real theta )

Rotation about X: R_x(theta) = exp(-ithetaX/2)

Definition at line 47 of file statevector.cpp.

◆ gate_ry()

Gate num::quantum::gate_ry ( real theta )

Rotation about Y: R_y(theta) = exp(-ithetaY/2)

Definition at line 51 of file statevector.cpp.

◆ gate_rz()

Gate num::quantum::gate_rz ( real theta )

Rotation about Z: R_z(theta) = exp(-ithetaZ/2)

Definition at line 55 of file statevector.cpp.

◆ gate_s()

Gate num::quantum::gate_s ( )

Phase gate S = diag(1, i)

Definition at line 35 of file statevector.cpp.

◆ gate_sdg()

Gate num::quantum::gate_sdg ( )

S† = diag(1, -i)

Definition at line 36 of file statevector.cpp.

◆ gate_t()

Gate num::quantum::gate_t ( )

T gate = diag(1, e^{ipi/4})

Definition at line 38 of file statevector.cpp.

References num::pi.

◆ gate_tdg()

Gate num::quantum::gate_tdg ( )

T† gate.

Definition at line 42 of file statevector.cpp.

References num::pi.

◆ gate_u()

Gate num::quantum::gate_u	(	real	theta,
		real	phi,
		real	lambda
	)

General SU(2) gate.

Definition at line 65 of file statevector.cpp.

References num::ipow(), and num::phi.

◆ gate_x()

Gate num::quantum::gate_x ( )

Pauli-X (NOT)

Definition at line 26 of file statevector.cpp.

Referenced by expectation_x().

◆ gate_y()

Gate num::quantum::gate_y ( )

Pauli-Y.

Definition at line 27 of file statevector.cpp.

Referenced by expectation_y().

◆ gate_z()

Gate num::quantum::gate_z ( )

Pauli-Z.

Definition at line 28 of file statevector.cpp.

◆ norm()

real num::quantum::norm ( const Statevector & sv )

L2 norm of the statevector (should be 1 for a valid quantum state)

Definition at line 177 of file statevector.cpp.

References num::norm().

Referenced by main().

◆ normalize()

void num::quantum::normalize ( Statevector & sv )

Normalize statevector in-place.

Definition at line 181 of file statevector.cpp.

References num::ipow(), and num::norm().

◆ probabilities()

std::vector< real > num::quantum::probabilities ( const Statevector & sv )

Measurement probability for each basis state: p_i = |a_i|^2.

Definition at line 186 of file statevector.cpp.

References num::ipow(), and num::BasicVector< T >::size().

Referenced by main(), and num::Circuit::run().

◆ reduced_density_matrix()

std::array< cplx, 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)

Definition at line 228 of file statevector.cpp.

References num::ipow().

Referenced by entanglement_entropy().

◆ zero_state()

Statevector num::quantum::zero_state ( int n_qubits )

Returns |0...0> computational basis state for n_qubits qubits.

Definition at line 12 of file statevector.cpp.

Referenced by num::Circuit::statevector_at().

Typedefs

Functions

Typedef Documentation

◆ cplx

◆ Gate

◆ Gate2Q

◆ Statevector

Function Documentation

◆ apply_1q()

◆ apply_2q()

◆ apply_cnot()

◆ apply_cp()

◆ apply_cswap()

◆ apply_cy()

◆ apply_cz()

◆ apply_swap()

◆ apply_toffoli()

◆ basis_state()

◆ entanglement_entropy()

◆ expectation()

◆ expectation_x()

◆ expectation_y()

◆ expectation_z()

◆ gate2q_cnot()

◆ gate2q_cz()

◆ gate2q_swap()

◆ gate_h()

◆ gate_p()

◆ gate_rx()

◆ gate_ry()

◆ gate_rz()

◆ gate_s()

◆ gate_sdg()

◆ gate_t()

◆ gate_tdg()

◆ gate_u()

◆ gate_x()

◆ gate_y()

◆ gate_z()

◆ norm()

◆ normalize()

◆ probabilities()

◆ reduced_density_matrix()

◆ zero_state()