Net Class Reference

Net class. More...

#include <Net.h>

Inheritance diagram for Net:

List of all members.


Public Types
typedef std::complex< double >	cdouble
typedef std::map< icoord, std::list< knot * >, icoord_cmp >	nettype
Public Member Functions
void	generate_net (int max_length)
	Internal helper for generating nets.
void	add (Matrix< cdouble > &U, char *word, int l)
	Add the knot (Matrix,word,length) to the net.
icoord	coordinate (const Matrix< cdouble > &U, int rounding=-1)
	Storage for the net.
	Net (double tw)
	Initialize a Net with a given tile width.
	Net (const char *file)
	Load a previously generated Net from a file.
	~Net (void)
	DESTROY!
void	generate (char labels, cdouble *basis, int n, int max_length)
	Generate the net.
void	generate (char labels[], cdouble basis[][4], int n, int max_length)
	As above, but taking constant size arrays as arguments for convenience.
int	load (const char *file)
	Load a net saved from a file.
void	save (const char *file)
	Save the generated net into a file.
knot *	nearest (const Matrix< cdouble > &U)
	Return the nearest knot to U.
std::string	nearest_string (const Matrix< cdouble > &U)
	Return the closest approximating string to U in SU(2).
Matrix< cdouble >	evaluate (const std::string &s)
	Evaluate an instruction string and return the resulting Matrix.
std::string	invert (const std::string &s)
	Invert an instruction string (same as taking its adjoint).
int	searched (void)
	Return the total number of knots seached last approximation.
int	size (void)
	Number of points in the net.
knot	solovay_kitaev (const Matrix< cdouble > &U, int depth)
	...
Public Attributes
std::list< knot * >	knots
	Storage was chosen somewhat arbitrarily as a list<knot*>.
double	tilewidth
	Precision of this net.
int	G
	Number of intervals the coordinate axes are divided into.
Matrix< cdouble > *	gate_set
	The 'instruction set' of matrices.
int	N
	Size of the instruction set.
char *	gate_labels
	Labels for each of the matrices above.
int *	gate_orders
	The order of each gate.
int *	gate_inverses
	Index of each gate's inverse.
int	search_count
	Maps a label to its corresponding index in the above (very oversized).
char	label_indices [512]
nettype	su2net
Friends
std::ostream &	operator<< (std::ostream &out, const Net &N)
	Output operator.
Classes
struct	icoord
	Integer coordinates for an SU(2) matrix in 4D space. More...
struct	icoord_cmp
	Comparison operator for the 4D integer coordinates. More...
struct	knot
	A 'knot' is a mildly amusing term for a point in a Net. More...

Detailed Description

Net class.

The purpose of a Net is to generate and store instruction sequences from a given instruction set, and to provide a means for obtaining the nearest instruction sequence to a given U in SU(2).

A net is initially constructed by specifying a tile width. The coordinate space for SU(2) is divided up into tiles, so that when we want to look up an approximation to a given U we need only search the tile that it is in.

When generating a Net, the tile coordinate for each instruction sequence is determined. There are 16 corners to this tile, and the instruction sequence is associated with each corner. When given a operator U to be approximated we find the closest corner, and search through all the instruction sequences associated with that corner.

To generate a Net, we require an instruction set specified as a 2D array containing the instruction gates, and an array of chars containing the labels we want to denote these matrices by.

Examples:: example.cpp.

Member Typedef Documentation

typedef std::complex<double> Net::cdouble

Reimplemented in PyNet.

typedef std::map<icoord, std::list<knot*> , icoord_cmp> Net::nettype

Constructor & Destructor Documentation

Net::Net ( double tw )

Initialize a Net with a given tile width.

Net::Net ( const char * file )

Load a previously generated Net from a file.

Net::~Net ( void )

DESTROY!

Member Function Documentation

void Net::add ( Matrix< cdouble > & U,

char * word,

int l

)

Add the knot (Matrix,word,length) to the net.

Net::icoord Net::coordinate ( const Matrix< cdouble > & U,

int rounding = -1

)

Storage for the net.
The matrix U lies in a 4D tile bounded by 16 coordinates. If the optional 'corner' paramemter is given it specifies which of these 16 coordinates to return. Otherwise it returns the nearest.

Matrix< cdouble > Net::evaluate ( const std::string & s )

Evaluate an instruction string and return the resulting Matrix.

void Net::generate ( char labels[],

cdouble basis[][4],

int n,

int max_length

) [inline]

As above, but taking constant size arrays as arguments for convenience.

void Net::generate ( char * labels,

cdouble ** basis,

int n,

int max_length

)

Generate the net.
This function takes an array of n chars which denote the labels to be used for the net (upper case only). For each label[i] there is a cdouble vector basis[i] which is the corresponding matrix elements as u₀₀, u₀₁, u₁₀, u₁₁. max_length is the maximum length of the instruction sequences we wish to generate.

void Net::generate_net ( int max_length )

Internal helper for generating nets.

string Net::invert ( const std::string & s )

Invert an instruction string (same as taking its adjoint).

int Net::load ( const char * file )

Load a net saved from a file.

Net::knot * Net::nearest ( const Matrix< cdouble > & U )

Return the nearest knot to U.

std::string Net::nearest_string ( const Matrix< cdouble > & U ) [inline]

Return the closest approximating string to U in SU(2).

void Net::save ( const char * file )

Save the generated net into a file.

int Net::searched ( void ) [inline]

Return the total number of knots seached last approximation.

int Net::size ( void ) [inline]

Number of points in the net.

Net::knot Net::solovay_kitaev ( const Matrix< cdouble > & U,

int depth

)

...

Friends And Related Function Documentation

std::ostream& operator<< ( std::ostream & out,

const Net & N

) [friend]

Output operator.
Prints some terse information about the gate set

Member Data Documentation

int Net::G

Number of intervals the coordinate axes are divided into.

int* Net::gate_inverses

Index of each gate's inverse.

char* Net::gate_labels

Labels for each of the matrices above.

int* Net::gate_orders

The order of each gate.

Matrix<cdouble>* Net::gate_set

The 'instruction set' of matrices.

std::list<knot*> Net::knots

Storage was chosen somewhat arbitrarily as a list<knot*>.

char Net::label_indices[512]

int Net::N

Size of the instruction set.

int Net::search_count

Maps a label to its corresponding index in the above (very oversized).

nettype Net::su2net

double Net::tilewidth

Precision of this net.

The documentation for this class was generated from the following files:

include/Net.h
src/Net.cpp

Generated on Sun Jul 10 21:57:14 2005 by

1.4.1

Net Class Reference

Public Types

Public Member Functions

Public Attributes