header.h File Reference

Main header file which specifies arguments for the program. More...

Go to the source code of this file.

Defines

#define CUT_ITER   1

Boolean to stop iteration if MLE function starts to decrease by some very small amount.

#define DATA   "/home/max/Desktop/2/"

Output location for the matrices produced by the program.

#define DO_MLE   1

Boolean to specify whether MLE should be performed.

#define EPS   0.05

Experimental State Error value.

#define KEEP_GOING   1

Boolean to cutoff MLE based on MAX_FIDELITY.

#define MAX_FIDELITY   0.90

Max fidelity cutoff point. If fidelity is over this value, simulations stops.

#define MAXCHAR   512

Defines the numerical value of a character - do not alter.

#define MAXITER   100

Maximum number of iterations of MLE function, an integer.

#define MILLION   1000000

Defines the numerical value of one million - do not alter.

#define NQ   2

Number of Qubits.

#define NUMTRIALS   1

Number of times tomography is repeated.

#define STATE   5

Main control which selects what kind of tomography will be perfomred.

#define VERBOSE   1

Boolean extra verboseness level toggle.

#define WRITE_DENSITY   1

Boolean toggle for density matrices to be written to disc.

Functions

double abs_val (gsl_vector *vec)

Returns absolute value (length) of vector vec.

void base_4_rep_inc (int counter[], int n)

Input array has base-4 rep of n-1, it's incremented to n.

double concurrence (gsl_matrix_complex *matrix)

Returns concurrence of the input density matrix.

void display_matrix (gsl_matrix_complex *data)

Prints complex matrix to screen.

void display_matrix_real (gsl_matrix *data)

Prints real matrix to screen.

void display_vector_real (gsl_vector *data)

Prints real-valued vector to screen.

double entropy_linear (gsl_matrix_complex *matrix)

Returns entropy of the input complex-valued density matrix.

double fidelity (gsl_matrix_complex *m1, gsl_matrix_complex *m2)

Returns fidelity between two density matrices m1 and m2.

int Fwrite (const void *ptr, size_t size, size_t nmemb, FILE *stream)

Wrapper function for fwrite to handle return codes.

void gsl_vector_add_element (gsl_vector *vector, double element)

Adds element as last element in vector, after re-allocating size of vector.

void kron (gsl_matrix_complex *a, gsl_matrix_complex *b, gsl_matrix_complex *c)

Performs tensor product on matrices A and B storing the output into pre-allocated matrix C.

void make_T (const gsl_vector *t, gsl_matrix_complex *T)

Seeds in values from vector t into Cholesky lower-diagonal matrix T, like described in the paper.

void matrix_complex_random_init (gsl_matrix_complex *random)

Fills a pre-allocated matrix with random values sampled from U(-1,1).

void mu_tensor (gsl_matrix_complex *mu_cell[], gsl_matrix_complex *mu_array[], int mu_counter[], int counter[])

Shortcut algorithm for tensoring on additional mu matrices to save computation time.

void outer_product (gsl_vector_complex *a, gsl_matrix_complex *outp)

Performs outer product |a><a| into pre-allocated output matrix.

void PSI_matrix (gsl_matrix_complex *psi, double theta)

Adjusts the density matrix psi to fall on the Werner state line by using the paramter theta, which is delta in the paper.

void random_density_matrix (gsl_matrix_complex *density_random)

Creates a random density matrix out of a pre-allocated complex matrix.

int read_vector_real (char *fname, gsl_vector *data)

Reads in real valued vector into data from ASCII file fname.

void rho_MEMS (gsl_matrix_complex *rho_mems, double gamma)

Density matrix rho_mems fall on MEMS line by varying parameter gamma, as described in the paper.

void sig_tensor (gsl_matrix_complex *sigma_cell[], gsl_matrix_complex *sig_array[], int mu_counter[], int counter[])

Shortcut algorithm for tensoring on additional sigma matrices to save computation time, see mu_tensor function description.

void sqrtm (gsl_matrix_complex *matrix)

Computes square root of complex matrix, stores output in originally pre-allocated matrix.

gsl_complex trace (gsl_matrix_complex *m)

Computes trace of a complex matrix and returns a complex number.

void W_state (gsl_matrix_complex *density)

Creates a W state density matrix.

int write_data (char *name, gsl_matrix_complex *data)

Writes complex matrix data into ASCII file specified by name, standard return codes for write.

int write_matrix_real (char *name, gsl_matrix *data)

Writes real matrix data into ASCII file name.

int write_vector_real (char *name, gsl_vector *data)

Writes real vector into ASCII file specified by name char string.

Variables

gsl_matrix_complex * mu_array [4]

Stores the Stokes measurement basis matrices.

gsl_matrix_complex * mu_cell [NQ]

Stores tensored mu matrices to compute the projection operators for >1 qubits, as described in the paper.

double N

Specifies the simulated number of times an experiment is performed.

gsl_complex one

Computational constant.

gsl_matrix_complex * ones

Matrix full of ones.

gsl_matrix_complex * sig_array [4]

Stores the 4 Pauli matrices.

gsl_matrix_complex * sigma_cell [NQ]

Stores tensored sigma matrices to compute the Pauli operators for >1 qubits, as described in the paper.

double theta_handle

Used to adjust the tangle value.

double Werner_handle

State handle used to adjust the Werner state.

gsl_complex zero

Computational constant.

Detailed Description

Main header file which specifies arguments for the program.

This program is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation;

AUTHOR Max S Kaznady, [EMAIL PROTECTED] max.kaznady@gmail.com Summer, 2007

This header file is used to specify all the parameters for the program instead of using command line arguments. This is not a very good software practice but saved a lot of time while developing the code.

Definition in file header.h.

Define Documentation

#define DATA "/home/max/Desktop/2/"

Output location for the matrices produced by the program.

Valid directory with sufficient space and write permissions is a must for this setting. All the simulation data would be outputted there as ASCII files.

Definition at line 298 of file header.h.

Referenced by write_data(), write_matrix_real(), and write_vector_real().

#define EPS 0.05

Experimental State Error value.

Used to adjust the "coherence" of the state rho_out = (1-EPS)*rho_state + EPS*rho_random do not set equal to zero

Definition at line 329 of file header.h.

Referenced by measure_state().

#define KEEP_GOING 1

Boolean to cutoff MLE based on MAX_FIDELITY.

For MLE Optimisation routine
if 0, then will stop iterating as soon as fidelity will start to decrease
if 1, then will keep iterating until either MLE Objective function stops decreasing, or gradient is close to zero, or some other GSL-induced condition.

Definition at line 347 of file header.h.

Referenced by MLE().

#define NQ 2

Number of Qubits.

This is the main control used to specify the number of qubits. The amount of memory on a regular PC (2 GB) should handle 1-15 qubits with this setting. Going over 15 qubits may result in memory overflow, as the density matrix itself would become a problem.

Definition at line 296 of file header.h.

Referenced by apply_noise(), base_4_rep_inc(), concurrence(), entropy_linear(), fill_tangle_entropy_plane(), find_N(), init(), linear_estimate(), main(), make_T(), measure_state(), MLE(), mu_tensor(), my_df(), my_f(), my_fdf(), prepare_state(), quick_and_dirty(), quick_and_dirty_2(), random_density_matrix(), sig_tensor(), sqrtm(), states_1_to_10(), and W_state().

#define NUMTRIALS 1

Number of times tomography is repeated.

Used to define how many times tomography is performed on an identical state and has many uses in the code.

Definition at line 301 of file header.h.

Referenced by find_N(), and states_1_to_10().

#define STATE 5

Main control which selects what kind of tomography will be perfomred.

The numerical value of this variable selects the type of tomography:
1 - GHZ state -- obsolete: it's just state 5
2 - tau = 0, S_l = 0
3 - Werner state, epsilon ~= 0 (low tau, high S)
4 - Werner state, epsilon ~= 0.5-0.0123 (middle)
5 - Werner state, epsilon ~= 1 (high tau, low S)
6 - MEMS State - only available for 2 QB
7 - tau = 0; S_l = 1
8 - W state
9 - completely random state
10 - Werner state, epsilon is being adjusted from 0 to 1 each time
11 - not really a state - for 2 qubits, this is used to fill the tangle/entropy plane - only defined for 2 qubits
12 - cycle through all tangle values for a pure state (S_l = 0) and and apply a different Quick and Dirty routine
13 - not a state - vary experimental error for many pure states, see how this scales with the number of qubits
14 - middle tangle value, pure state
15 - determine value for N which results in 90% Fidelity for pure states
16 - W state density matrix

Definition at line 324 of file header.h.

Referenced by main(), prepare_state(), and states_1_to_10().

Function Documentation

void mu_tensor	(	gsl_matrix_complex *	mu_cell[],
		gsl_matrix_complex *	mu_array[],
		int	mu_counter[],
		int	counter[]
	)

Shortcut algorithm for tensoring on additional mu matrices to save computation time.

Mu_cell contains pointers to gsl mu matrices that make up the final mu matrix which corresponds to base-4 representation in mu_counter. The function corrects mu_cell to represent "counter" base-4 representation by location the index of the mu matrix in mu_cell starting from which new matrices need to be tensored on from mu_array.

Basically this is an update function which computes the final mu_matrix corresponding to the correct base-4 representation in counter without recomputing everything from scratch.

Definition at line 185 of file utilities.c.

References kron(), and NQ.

Referenced by measure_state(), my_df(), my_f(), and my_fdf().

00185                                                                                                           {
00186     //gsl_matrix_complex *mu_nu = gsl_matrix_complex_alloc(pow(2, NQ), pow(2, NQ));
00187     int i, j;
00188     for (i=0; i<NQ; i++) {
00189         if (counter[i]!=mu_counter[i]) { //locate place from which to update
00190             if (i==0) { //base case
00191                 //mu_cell[i] = mu_array[0];
00192                 //mu_cell[0] = gsl_matrix_complex_alloc(2, 2);
00193                 gsl_matrix_complex_memcpy(mu_cell[0], mu_array[counter[i]]);
00194                 i++;
00195             }
00196             for (j=i; j<NQ; j++) { //update the rest of elements
00197                 //gsl_matrix_complex_free(mu_cell[i]);
00198                 //printf("mu_tensor, j=%d and i=%d, counter[j]=%d \n", j, i, counter[j]);
00199                 //mu_cell[j] = gsl_matrix_complex_alloc((mu_cell[j-1]->size1)*2, (mu_cell[j-1]->size2)*2);
00200                 kron(mu_cell[j-1], mu_array[counter[j]], mu_cell[j]);
00201             }
00202             break; // done updating
00203         }
00204     }
00205 }

Variable Documentation

double N

Specifies the simulated number of times an experiment is performed.

Specifies the simulated number of times an experiment is performed, i.e. the number of times projection measurements were taken.

Definition at line 457 of file header.h.

Referenced by fill_tangle_entropy_plane(), find_N(), init(), my_df(), my_f(), my_fdf(), and states_1_to_10().


Defines
#define	CUT_ITER 1
	Boolean to stop iteration if MLE function starts to decrease by some very small amount.
#define	DATA "/home/max/Desktop/2/"
	Output location for the matrices produced by the program.
#define	DO_MLE 1
	Boolean to specify whether MLE should be performed.
#define	EPS 0.05
	Experimental State Error value.
#define	KEEP_GOING 1
	Boolean to cutoff MLE based on MAX_FIDELITY.
#define	MAX_FIDELITY 0.90
	Max fidelity cutoff point. If fidelity is over this value, simulations stops.
#define	MAXCHAR 512
	Defines the numerical value of a character - do not alter.
#define	MAXITER 100
	Maximum number of iterations of MLE function, an integer.
#define	MILLION 1000000
	Defines the numerical value of one million - do not alter.
#define	NQ 2
	Number of Qubits.
#define	NUMTRIALS 1
	Number of times tomography is repeated.
#define	STATE 5
	Main control which selects what kind of tomography will be perfomred.
#define	VERBOSE 1
	Boolean extra verboseness level toggle.
#define	WRITE_DENSITY 1
	Boolean toggle for density matrices to be written to disc.
Functions
double	abs_val (gsl_vector *vec)
	Returns absolute value (length) of vector vec.
void	base_4_rep_inc (int counter[], int n)
	Input array has base-4 rep of n-1, it's incremented to n.
double	concurrence (gsl_matrix_complex *matrix)
	Returns concurrence of the input density matrix.
void	display_matrix (gsl_matrix_complex *data)
	Prints complex matrix to screen.
void	display_matrix_real (gsl_matrix *data)
	Prints real matrix to screen.
void	display_vector_real (gsl_vector *data)
	Prints real-valued vector to screen.
double	entropy_linear (gsl_matrix_complex *matrix)
	Returns entropy of the input complex-valued density matrix.
double	fidelity (gsl_matrix_complex m1, gsl_matrix_complex m2)
	Returns fidelity between two density matrices m1 and m2.
int	Fwrite (const void ptr, size_t size, size_t nmemb, FILE stream)
	Wrapper function for fwrite to handle return codes.
void	gsl_vector_add_element (gsl_vector *vector, double element)
	Adds element as last element in vector, after re-allocating size of vector.
void	kron (gsl_matrix_complex a, gsl_matrix_complex b, gsl_matrix_complex *c)
	Performs tensor product on matrices A and B storing the output into pre-allocated matrix C.
void	make_T (const gsl_vector t, gsl_matrix_complex T)
	Seeds in values from vector t into Cholesky lower-diagonal matrix T, like described in the paper.
void	matrix_complex_random_init (gsl_matrix_complex *random)
	Fills a pre-allocated matrix with random values sampled from U(-1,1).
void	mu_tensor (gsl_matrix_complex mu_cell[], gsl_matrix_complex mu_array[], int mu_counter[], int counter[])
	Shortcut algorithm for tensoring on additional mu matrices to save computation time.
void	outer_product (gsl_vector_complex a, gsl_matrix_complex outp)
	Performs outer product \|a><a\| into pre-allocated output matrix.
void	PSI_matrix (gsl_matrix_complex *psi, double theta)
	Adjusts the density matrix psi to fall on the Werner state line by using the paramter theta, which is delta in the paper.
void	random_density_matrix (gsl_matrix_complex *density_random)
	Creates a random density matrix out of a pre-allocated complex matrix.
int	read_vector_real (char fname, gsl_vector data)
	Reads in real valued vector into data from ASCII file fname.
void	rho_MEMS (gsl_matrix_complex *rho_mems, double gamma)
	Density matrix rho_mems fall on MEMS line by varying parameter gamma, as described in the paper.
void	sig_tensor (gsl_matrix_complex sigma_cell[], gsl_matrix_complex sig_array[], int mu_counter[], int counter[])
	Shortcut algorithm for tensoring on additional sigma matrices to save computation time, see mu_tensor function description.
void	sqrtm (gsl_matrix_complex *matrix)
	Computes square root of complex matrix, stores output in originally pre-allocated matrix.
gsl_complex	trace (gsl_matrix_complex *m)
	Computes trace of a complex matrix and returns a complex number.
void	W_state (gsl_matrix_complex *density)
	Creates a W state density matrix.
int	write_data (char name, gsl_matrix_complex data)
	Writes complex matrix data into ASCII file specified by name, standard return codes for write.
int	write_matrix_real (char name, gsl_matrix data)
	Writes real matrix data into ASCII file name.
int	write_vector_real (char name, gsl_vector data)
	Writes real vector into ASCII file specified by name char string.
Variables
gsl_matrix_complex *	mu_array [4]
	Stores the Stokes measurement basis matrices.
gsl_matrix_complex *	mu_cell [NQ]
	Stores tensored mu matrices to compute the projection operators for >1 qubits, as described in the paper.
double	N
	Specifies the simulated number of times an experiment is performed.
gsl_complex	one
	Computational constant.
gsl_matrix_complex *	ones
	Matrix full of ones.
gsl_matrix_complex *	sig_array [4]
	Stores the 4 Pauli matrices.
gsl_matrix_complex *	sigma_cell [NQ]
	Stores tensored sigma matrices to compute the Pauli operators for >1 qubits, as described in the paper.
double	theta_handle
	Used to adjust the tangle value.
double	Werner_handle
	State handle used to adjust the Werner state.
gsl_complex	zero
	Computational constant.