Methods to calculate the cost function of the final optimization problem (supporting parallel computations). More...

#include "N_Qubit_Decomposition_Cost_Function.h"
#include "QGDTypes.h"
#include <vector>
#include <algorithm>

Include dependency graph for N_Qubit_Decomposition_Cost_Function.cpp:

Classes
struct	OSRTriplet< ComplexT >

Macros
#define	LAPACK_COL_MAJOR 102

#define	LAPACK_ROW_MAJOR 101

#define	USE_COL_MAJ

#define	USE_SDD

Functions
template<class MatrixT , class ComplexT >
static void	accumulate_grad_for_cut (MatrixT &accum, const std::vector< double > &G, const std::vector< ComplexT > &Umat, const std::vector< ComplexT > &VTmat, int n, const std::vector< int > &A, int rank=-1)

double	avg_loss_for_rank (const std::vector< std::vector< double >> &cuts_S, int rank)

double	avg_tail_loss (const std::vector< std::vector< double >> &cuts_S, double rho=0.1)

template<class MatrixT , class ComplexT >
static std::vector< ComplexT >	build_osr_matrix (const MatrixT &U, int n, const std::vector< int > &A, int &m_rows, int &m_cols)

static void	combinations_recursive (int n, int r, int start, std::vector< int > &current, std::vector< std::vector< int >> &out)

std::vector< std::vector< double > >	cuts_avg_rank_grad (const std::vector< std::vector< double >> &cuts_S, int rank, double Fnorm)

std::vector< std::vector< double > >	cuts_avg_tail_grad (const std::vector< std::vector< double >> &cuts_S, double Fnorm, double rho=0.1)

double	cuts_softmax_rank_cost (const std::vector< std::vector< double >> &cuts_S, int rank, double tau=1e-2)

std::vector< std::vector< double > >	cuts_softmax_rank_grad (const std::vector< std::vector< double >> &cuts_S, int rank, double Fnorm, double tau=1e-2)

double	cuts_softmax_tail_cost (const std::vector< std::vector< double >> &cuts_S, double rho=0.1, double tau=1e-2)

std::vector< std::vector< double > >	cuts_softmax_tail_grad (const std::vector< std::vector< double >> &cuts_S, double Fnorm, double rho=0.1, double tau=1e-2)

static int	extract_bits (int x, const std::vector< int > &pos)

double	get_cost_function (const Matrix &matrix, int trace_offset)
	Call co calculate the cost function during the final optimization process. More...

double	get_cost_function (const Matrix_float &matrix, int trace_offset)

double	get_cost_function_sum_of_squares (Matrix &matrix)

Matrix_real	get_cost_function_with_correction (const Matrix &matrix, int qbit_num, int trace_offset)
	Call co calculate the cost function of the optimization process, and the first correction to the cost finction according to https://arxiv.org/pdf/2210.09191.pdf. More...

Matrix_real_float	get_cost_function_with_correction (const Matrix_float &matrix, int qbit_num, int trace_offset)

Matrix_real	get_cost_function_with_correction2 (const Matrix &matrix, int qbit_num, int trace_offset)
	Call co calculate the cost function of the optimization process, and the first correction to the cost finction according to https://arxiv.org/pdf/2210.09191.pdf. More...

Matrix_real_float	get_cost_function_with_correction2 (const Matrix_float &matrix, int qbit_num, int trace_offset)

Matrix	get_deriv_osr_entanglement (Matrix &matrix, std::vector< std::vector< int >> &use_cuts, int rank, bool use_softmax)

Matrix_float	get_deriv_osr_entanglement (Matrix_float &matrix, std::vector< std::vector< int >> &use_cuts, int rank, bool use_softmax)

template<class MatrixT , class ComplexT , class RealT >
static MatrixT	get_deriv_osr_entanglement_impl (MatrixT &matrix, std::vector< std::vector< int >> &use_cuts, int rank, bool use_softmax)

Matrix	get_deriv_sum_of_squares (Matrix &matrix)

double	get_hilbert_schmidt_test (Matrix &matrix)
	Call co calculate the cost function of the optimization process according to https://arxiv.org/pdf/2210.09191.pdf. More...

double	get_hilbert_schmidt_test (Matrix_float &matrix)

double	get_infidelity (Matrix &matrix)
	Call to calculate infidelity. More...

double	get_infidelity (Matrix_float &matrix)

double	get_osr_entanglement_test (Matrix &matrix, std::vector< std::vector< int >> &use_cuts, int rank, bool use_softmax)

double	get_osr_entanglement_test (Matrix_float &matrix, std::vector< std::vector< int >> &use_cuts, int rank, bool use_softmax)

template<class MatrixT , class ComplexT , class RealT >
static double	get_osr_entanglement_test_impl (MatrixT &matrix, std::vector< std::vector< int >> &use_cuts, int rank, bool use_softmax)

QGD_Complex16	get_trace (Matrix &matrix)
	Call to calculate the real and imaginary parts of the trace. More...

QGD_Complex16	get_trace (Matrix_float &matrix)

Matrix	get_trace_with_correction (Matrix &matrix, int qbit_num)
	Call co calculate the Hilbert Schmidt testof the optimization process, and the first correction to the cost finction according to https://arxiv.org/pdf/2210.09191.pdf. More...

Matrix	get_trace_with_correction2 (Matrix &matrix, int qbit_num)
	Call co calculate the Hilbert Schmidt testof the optimization process, and the first correction to the cost finction according to https://arxiv.org/pdf/2210.09191.pdf. More...

static int	lapack_gesdd_dispatch (int lapack_layout, char jobz, int m, int n, QGD_Complex16 a, int lda, double s, QGD_Complex16 u, int ldu, QGD_Complex16 vt, int ldvt)

static int	lapack_gesdd_dispatch (int lapack_layout, char jobz, int m, int n, QGD_Complex8 a, int lda, float s, QGD_Complex8 u, int ldu, QGD_Complex8 vt, int ldvt)

int	LAPACKE_cgesdd (int matrix_order, char jobz, int m, int n, QGD_Complex8 a, int lda, float s, QGD_Complex8 u, int ldu, QGD_Complex8 vt, int ldvt)

int	LAPACKE_cgesvd (int matrix_order, char jobu, char jobvt, int m, int n, QGD_Complex8 a, int lda, float s, QGD_Complex8 u, int ldu, QGD_Complex8 vt, int ldvt, float *superb)

int	LAPACKE_zgesdd (int matrix_order, char jobz, int m, int n, QGD_Complex16 a, int lda, double s, QGD_Complex16 u, int ldu, QGD_Complex16 vt, int ldvt)

int	LAPACKE_zgesvd (int matrix_order, char jobu, char jobvt, int m, int n, QGD_Complex16 a, int lda, double s, QGD_Complex16 u, int ldu, QGD_Complex16 vt, int ldvt, double *superb)

static uint32_t	lg_down (uint32_t v)

static uint32_t	lg_up (uint32_t x)

double	logsumexp_smoothmax (const std::vector< double > &Lc, double tau=1e-2)

double	loss_for_rank (const std::vector< double > &S, int rank)

std::vector< double >	loss_for_rank_grad_diag (const std::vector< double > &S, int rank, double Fnorm)

static size_t	mat_idx (int row, int col, int nrows, int ncols)

static int	numerical_rank_osr (std::vector< double > S, double tol)

std::pair< int, double >	operator_schmidt_rank (const Matrix &U, int n, const std::vector< int > &A_qubits, double Fnorm, double tol)

std::pair< int, double >	operator_schmidt_rank (const Matrix_float &U, int n, const std::vector< int > &A_qubits, double Fnorm, double tol)

template<class ComplexT , class RealT >
static std::vector< double >	osr (std::vector< ComplexT > &A, int m_rows, int m_cols, double Fnorm)

double	real_trace_conj_dot (Matrix &A, Matrix &B)

double	real_trace_conj_dot (Matrix_float &A, Matrix_float &B)

double	tail_loss (const std::vector< double > &S, int max_dyadic, double rho=0.1, double tol=1e-4)

std::vector< double >	tail_loss_grad_diag (const std::vector< double > &S, int max_dyadic, double Fnorm, double rho=0.1, double tol=1e-4)

template<class MatrixT , class ComplexT , class RealT >
static OSRTriplet< ComplexT >	top_k_triplet_for_cut (const MatrixT &U, int q, const std::vector< int > &A, double Fnorm, int &m_rows, int &m_cols)

std::vector< std::vector< int > >	unique_cuts (int n)

double	weighted_loss_for_rank (const std::vector< double > &S, int rank, double rho=0.1, double tol=1e-4)

Detailed Description

Methods to calculate the cost function of the final optimization problem (supporting parallel computations).

Definition in file N_Qubit_Decomposition_Cost_Function.cpp.

Macro Definition Documentation

◆ LAPACK_COL_MAJOR

#define LAPACK_COL_MAJOR 102

Definition at line 30 of file N_Qubit_Decomposition_Cost_Function.cpp.

◆ LAPACK_ROW_MAJOR

#define LAPACK_ROW_MAJOR 101

Definition at line 29 of file N_Qubit_Decomposition_Cost_Function.cpp.

◆ USE_COL_MAJ

#define USE_COL_MAJ

Definition at line 59 of file N_Qubit_Decomposition_Cost_Function.cpp.

◆ USE_SDD

#define USE_SDD

Definition at line 58 of file N_Qubit_Decomposition_Cost_Function.cpp.

Function Documentation

◆ accumulate_grad_for_cut()

template<class MatrixT , class ComplexT >

static void accumulate_grad_for_cut	(	MatrixT &	accum,
		const std::vector< double > &	G,
		const std::vector< ComplexT > &	Umat,
		const std::vector< ComplexT > &	VTmat,
		int	n,
		const std::vector< int > &	A,
		int	rank = `-1`
	)

static

Definition at line 810 of file N_Qubit_Decomposition_Cost_Function.cpp.

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◆ avg_loss_for_rank()

double avg_loss_for_rank	(	const std::vector< std::vector< double >> &	cuts_S,
		int	rank
	)

Definition at line 1037 of file N_Qubit_Decomposition_Cost_Function.cpp.

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◆ avg_tail_loss()

double avg_tail_loss	(	const std::vector< std::vector< double >> &	cuts_S,
		double	rho = `0.1`
	)

Definition at line 1155 of file N_Qubit_Decomposition_Cost_Function.cpp.

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◆ build_osr_matrix()

template<class MatrixT , class ComplexT >

static std::vector<ComplexT> build_osr_matrix	(	const MatrixT &	U,
		int	n,
		const std::vector< int > &	A,
		int &	m_rows,
		int &	m_cols
	)

static

Definition at line 773 of file N_Qubit_Decomposition_Cost_Function.cpp.

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◆ combinations_recursive()

static void combinations_recursive	(	int	n,
		int	r,
		int	start,
		std::vector< int > &	current,
		std::vector< std::vector< int >> &	out
	)

static

Definition at line 959 of file N_Qubit_Decomposition_Cost_Function.cpp.

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◆ cuts_avg_rank_grad()

std::vector<std::vector<double> > cuts_avg_rank_grad	(	const std::vector< std::vector< double >> &	cuts_S,
		int	rank,
		double	Fnorm
	)

Definition at line 1076 of file N_Qubit_Decomposition_Cost_Function.cpp.

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◆ cuts_avg_tail_grad()

std::vector<std::vector<double> > cuts_avg_tail_grad	(	const std::vector< std::vector< double >> &	cuts_S,
		double	Fnorm,
		double	rho = `0.1`
	)

Definition at line 1201 of file N_Qubit_Decomposition_Cost_Function.cpp.

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◆ cuts_softmax_rank_cost()

double cuts_softmax_rank_cost	(	const std::vector< std::vector< double >> &	cuts_S,
		int	rank,
		double	tau = `1e-2`
	)

Definition at line 1047 of file N_Qubit_Decomposition_Cost_Function.cpp.

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◆ cuts_softmax_rank_grad()

std::vector<std::vector<double> > cuts_softmax_rank_grad	(	const std::vector< std::vector< double >> &	cuts_S,
		int	rank,
		double	Fnorm,
		double	tau = `1e-2`
	)

Definition at line 1097 of file N_Qubit_Decomposition_Cost_Function.cpp.

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◆ cuts_softmax_tail_cost()

double cuts_softmax_tail_cost	(	const std::vector< std::vector< double >> &	cuts_S,
		double	rho = `0.1`,
		double	tau = `1e-2`
	)

Definition at line 1168 of file N_Qubit_Decomposition_Cost_Function.cpp.

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◆ cuts_softmax_tail_grad()

std::vector<std::vector<double> > cuts_softmax_tail_grad	(	const std::vector< std::vector< double >> &	cuts_S,
		double	Fnorm,
		double	rho = `0.1`,
		double	tau = `1e-2`
	)

Definition at line 1219 of file N_Qubit_Decomposition_Cost_Function.cpp.

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◆ extract_bits()

static int extract_bits	(	int	x,
		const std::vector< int > &	pos
	)

inlinestatic

Definition at line 751 of file N_Qubit_Decomposition_Cost_Function.cpp.

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◆ get_cost_function() [1/2]

double get_cost_function	(	const Matrix &	matrix,
		int	trace_offset
	)

Call co calculate the cost function during the final optimization process.

Parameters

matrix	The square shaped complex matrix from which the cost function is calculated.
trace_offset	The offset in the first columns from which the "trace" is calculated. In this case Tr(A) = sum_(i-offset=j) A_{ij}

Returns: Returns with the calculated cost function.

Definition at line 73 of file N_Qubit_Decomposition_Cost_Function.cpp.

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◆ get_cost_function() [2/2]

double get_cost_function	(	const Matrix_float &	matrix,
		int	trace_offset
	)

Definition at line 164 of file N_Qubit_Decomposition_Cost_Function.cpp.

◆ get_cost_function_sum_of_squares()

double get_cost_function_sum_of_squares ( Matrix & matrix )

Definition at line 443 of file N_Qubit_Decomposition_Cost_Function.cpp.

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◆ get_cost_function_with_correction() [1/2]

Matrix_real get_cost_function_with_correction	(	const Matrix &	matrix,
		int	qbit_num,
		int	trace_offset
	)

Call co calculate the cost function of the optimization process, and the first correction to the cost finction according to https://arxiv.org/pdf/2210.09191.pdf.

Parameters

matrix	The square shaped complex matrix from which the cost function is calculated.
qbit_num	The number of qubits

Returns: Returns with the matrix containing the cost function (index 0) and the first correction (index 1).

Definition at line 191 of file N_Qubit_Decomposition_Cost_Function.cpp.

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◆ get_cost_function_with_correction() [2/2]

Matrix_real_float get_cost_function_with_correction	(	const Matrix_float &	matrix,
		int	qbit_num,
		int	trace_offset
	)

Definition at line 254 of file N_Qubit_Decomposition_Cost_Function.cpp.

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◆ get_cost_function_with_correction2() [1/2]

Matrix_real get_cost_function_with_correction2	(	const Matrix &	matrix,
		int	qbit_num,
		int	trace_offset
	)

Call co calculate the cost function of the optimization process, and the first correction to the cost finction according to https://arxiv.org/pdf/2210.09191.pdf.

Parameters

matrix	The square shaped complex matrix from which the cost function is calculated.
qbit_num	The number of qubits

Returns: Returns with the matrix containing the cost function (index 0), the first correction (index 1) and the second correction (index 2).

Definition at line 295 of file N_Qubit_Decomposition_Cost_Function.cpp.

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◆ get_cost_function_with_correction2() [2/2]

Matrix_real_float get_cost_function_with_correction2	(	const Matrix_float &	matrix,
		int	qbit_num,
		int	trace_offset
	)

Definition at line 406 of file N_Qubit_Decomposition_Cost_Function.cpp.

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◆ get_deriv_osr_entanglement() [1/2]

Matrix get_deriv_osr_entanglement	(	Matrix &	matrix,
		std::vector< std::vector< int >> &	use_cuts,
		int	rank,
		bool	use_softmax
	)

Definition at line 1441 of file N_Qubit_Decomposition_Cost_Function.cpp.

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◆ get_deriv_osr_entanglement() [2/2]

Matrix_float get_deriv_osr_entanglement	(	Matrix_float &	matrix,
		std::vector< std::vector< int >> &	use_cuts,
		int	rank,
		bool	use_softmax
	)

Definition at line 1445 of file N_Qubit_Decomposition_Cost_Function.cpp.

◆ get_deriv_osr_entanglement_impl()

template<class MatrixT , class ComplexT , class RealT >

static MatrixT get_deriv_osr_entanglement_impl	(	MatrixT &	matrix,
		std::vector< std::vector< int >> &	use_cuts,
		int	rank,
		bool	use_softmax
	)

static

Definition at line 1399 of file N_Qubit_Decomposition_Cost_Function.cpp.

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◆ get_deriv_sum_of_squares()

Matrix get_deriv_sum_of_squares ( Matrix & matrix )

Definition at line 459 of file N_Qubit_Decomposition_Cost_Function.cpp.

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◆ get_hilbert_schmidt_test() [1/2]

double get_hilbert_schmidt_test ( Matrix & matrix )

Call co calculate the cost function of the optimization process according to https://arxiv.org/pdf/2210.09191.pdf.

Parameters

matrix	The square shaped complex matrix from which the cost function is calculated.
qbit_num	The number of qubits

Returns: Returns the cost function

Definition at line 524 of file N_Qubit_Decomposition_Cost_Function.cpp.

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◆ get_hilbert_schmidt_test() [2/2]

double get_hilbert_schmidt_test ( Matrix_float & matrix )

Definition at line 534 of file N_Qubit_Decomposition_Cost_Function.cpp.

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◆ get_infidelity() [1/2]

double get_infidelity ( Matrix & matrix )

Call to calculate infidelity.

Parameters

matrix	The square shaped complex matrix from which the cost function is calculated.
qbit_num	The number of qubits

Returns: Returns the cost function

Definition at line 541 of file N_Qubit_Decomposition_Cost_Function.cpp.

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◆ get_infidelity() [2/2]

double get_infidelity ( Matrix_float & matrix )

Definition at line 551 of file N_Qubit_Decomposition_Cost_Function.cpp.

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◆ get_osr_entanglement_test() [1/2]

double get_osr_entanglement_test	(	Matrix &	matrix,
		std::vector< std::vector< int >> &	use_cuts,
		int	rank,
		bool	use_softmax
	)

Definition at line 1308 of file N_Qubit_Decomposition_Cost_Function.cpp.

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◆ get_osr_entanglement_test() [2/2]

double get_osr_entanglement_test	(	Matrix_float &	matrix,
		std::vector< std::vector< int >> &	use_cuts,
		int	rank,
		bool	use_softmax
	)

Definition at line 1312 of file N_Qubit_Decomposition_Cost_Function.cpp.

◆ get_osr_entanglement_test_impl()

template<class MatrixT , class ComplexT , class RealT >

static double get_osr_entanglement_test_impl	(	MatrixT &	matrix,
		std::vector< std::vector< int >> &	use_cuts,
		int	rank,
		bool	use_softmax
	)

static

Definition at line 1284 of file N_Qubit_Decomposition_Cost_Function.cpp.

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◆ get_trace() [1/2]

QGD_Complex16 get_trace ( Matrix & matrix )

Call to calculate the real and imaginary parts of the trace.

Parameters

matrix The square shaped complex matrix from which the trace is calculated.

Returns: Returns with the calculated trace.

Definition at line 482 of file N_Qubit_Decomposition_Cost_Function.cpp.

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◆ get_trace() [2/2]

QGD_Complex16 get_trace ( Matrix_float & matrix )

Definition at line 501 of file N_Qubit_Decomposition_Cost_Function.cpp.

◆ get_trace_with_correction()

Matrix get_trace_with_correction	(	Matrix &	matrix,
		int	qbit_num
	)

Call co calculate the Hilbert Schmidt testof the optimization process, and the first correction to the cost finction according to https://arxiv.org/pdf/2210.09191.pdf.

Parameters

matrix	The square shaped complex matrix from which the cost function is calculated.
qbit_num	The number of qubits

Returns: Returns with the matrix containing the cost function (index 0-1) and the first correction (index 2-3).

Definition at line 564 of file N_Qubit_Decomposition_Cost_Function.cpp.

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◆ get_trace_with_correction2()

Matrix get_trace_with_correction2	(	Matrix &	matrix,
		int	qbit_num
	)

Call co calculate the Hilbert Schmidt testof the optimization process, and the first correction to the cost finction according to https://arxiv.org/pdf/2210.09191.pdf.

Parameters

matrix	The square shaped complex matrix from which the cost function is calculated.
qbit_num	The number of qubits

Returns: Returns with the matrix containing the cost function (index 0-1), the first correction (index 2-3) and the second correction (index 4-5).

Definition at line 604 of file N_Qubit_Decomposition_Cost_Function.cpp.

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◆ lapack_gesdd_dispatch() [1/2]

static int lapack_gesdd_dispatch	(	int	lapack_layout,
		char	jobz,
		int	m,
		int	n,
		QGD_Complex16 *	a,
		int	lda,
		double *	s,
		QGD_Complex16 *	u,
		int	ldu,
		QGD_Complex16 *	vt,
		int	ldvt
	)

static

Definition at line 878 of file N_Qubit_Decomposition_Cost_Function.cpp.

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◆ lapack_gesdd_dispatch() [2/2]

static int lapack_gesdd_dispatch	(	int	lapack_layout,
		char	jobz,
		int	m,
		int	n,
		QGD_Complex8 *	a,
		int	lda,
		float *	s,
		QGD_Complex8 *	u,
		int	ldu,
		QGD_Complex8 *	vt,
		int	ldvt
	)

static

Definition at line 884 of file N_Qubit_Decomposition_Cost_Function.cpp.

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◆ LAPACKE_cgesdd()

int LAPACKE_cgesdd	(	int	matrix_order,
		char	jobz,
		int	m,
		int	n,
		QGD_Complex8 *	a,
		int	lda,
		float *	s,
		QGD_Complex8 *	u,
		int	ldu,
		QGD_Complex8 *	vt,
		int	ldvt
	)

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◆ LAPACKE_cgesvd()

int LAPACKE_cgesvd	(	int	matrix_order,
		char	jobu,
		char	jobvt,
		int	m,
		int	n,
		QGD_Complex8 *	a,
		int	lda,
		float *	s,
		QGD_Complex8 *	u,
		int	ldu,
		QGD_Complex8 *	vt,
		int	ldvt,
		float *	superb
	)

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◆ LAPACKE_zgesdd()

int LAPACKE_zgesdd	(	int	matrix_order,
		char	jobz,
		int	m,
		int	n,
		QGD_Complex16 *	a,
		int	lda,
		double *	s,
		QGD_Complex16 *	u,
		int	ldu,
		QGD_Complex16 *	vt,
		int	ldvt
	)

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◆ LAPACKE_zgesvd()

int LAPACKE_zgesvd	(	int	matrix_order,
		char	jobu,
		char	jobvt,
		int	m,
		int	n,
		QGD_Complex16 *	a,
		int	lda,
		double *	s,
		QGD_Complex16 *	u,
		int	ldu,
		QGD_Complex16 *	vt,
		int	ldvt,
		double *	superb
	)