Base namespace for the Tomographer project. More...

Namespaces
	Logger
	Tomographer's Logging Framework

	MAT
	Utilities and helpers for reading MATLAB .mat files.

	MHRWTasks
	Definitions for running multiple random walks.

	MultiProc
	Definitions for multi-processing classes and helpers.

	SolveCLyap
	Definitions for solving the Complex Lyapunov Equation.

	SphCoords

	Tools
	Various useful tools.

Classes
struct	AveragedHistogram
	Combines several histograms (with same parameters) into an averaged histogram. More...

class	BinningAnalysis
	Simple binning analysis for determining error bars. More...

struct	BinningAnalysisParams
	Group template parameters for BinningAnalysis. More...

class	DMStateSpaceLLHMHWalker
	A random walk in the density matrix space of a Hilbert state space of a quantum system. More...

class	FidelityToRefCalculator
	Calculate the fidelity to a reference state for each sample. More...

struct	IndepMeasTomoProblem
	Stores data for a tomography problem with independent measurements. More...

struct	MatrQ
	Defines the data types for a particular problem setting. More...

struct	MatrQBase
	Basic definitions for MatrQ. More...

struct	MatrQBaseDimStore
	Helper intermediate class for MatrQ. More...

struct	MatrQBaseDimStore< Derived, false >
	Specialization of MatrQBaseDimStore<Derived,has_fixed_dim> for dynamic sized types. More...

class	MHRandomWalk
	A Metropolis-Hastings Random Walk. More...

struct	MHRWStatsCollectorStatus
	Template, specializable class to get status reports from stats collectors. More...

struct	MHRWStatsCollectorStatus< MultipleMHRWStatsCollectors< Args... > >
	Provide status reporting for a MultipleMHRWStatsCollectors. More...

struct	MHRWStatsCollectorStatus< ValueHistogramMHRWStatsCollector< ValueCalculator_, LoggerType_, HistogramType_ > >
	Provide status reporting for a ValueHistogramMHRWStatsCollector. More...

struct	MHRWStatsCollectorStatus< ValueHistogramWithBinningMHRWStatsCollector< Params_, LoggerType_ > >
	Provide status reporting for a ValueHistogramWithBinningMHRWStatsCollector. More...

class	MultipleMHRWStatsCollectors
	A simple MHRWStatsCollector interface which combines several stats collectors. More...

class	ObservableValueCalculator
	Calculate expectation value of an observable for each sample. More...

class	ParamRhoA
	Parameterization of density matrices in su(N) generators. More...

class	PurifDistToRefCalculator
	Calculate the "purified distance" to a reference state for each sample. More...

struct	RandomWalkBase
	Base class performing an abstract random walk. More...

class	TrDistToRefCalculator
	Calculate the trace distance to a reference state for each sample. More...

struct	UniformBinsHistogram
	Stores a histogram. More...

struct	UniformBinsHistogramWithErrorBars
	Stores a histogram along with error bars. More...

class	ValueHistogramMHRWStatsCollector
	A StatsCollector which builds a histogram of values calculated with a ValueCalculator for each data sample point. More...

class	ValueHistogramWithBinningMHRWStatsCollector
	Collect a histogram of values from a MH random walk, with binning analysis. More...

struct	ValueHistogramWithBinningMHRWStatsCollectorParams
	Traits-like class for ValueHistogramWithBinningMHRWStatsCollector. More...

Typedefs
typedef MatrQ< Eigen::Dynamic, Eigen::Dynamic, double, int >	DefaultMatrQ
	Data types for all arguments set at run-time. More...

typedef MatrQ< 2, 6, double, int >	QubitPaulisMatrQ
	Data types for Pauli measurements on a single qubit. More...

Enumerations
enum

Functions
template<typename HistogramType >
void	histogram_pretty_print (std::ostream &str, const HistogramType &histogram, int max_width=0)
	pretty-print the given histogram. More...

template<typename HistogramType >
std::string	histogram_pretty_print (const HistogramType &histogram, int max_width=0)
	Utility to display histograms for humans. More...

template<typename HistogramType >
int	histogram_short_bar (std::ostream &str, const HistogramType &histogram, bool log_scale=true, int max_width=0)
	Format the histogram as a one-line bar. More...

template<typename HistogramType >
std::string	histogram_short_bar (const HistogramType &histogram, bool log_scale=true, int max_width=0)
	Format the histogram as a one-line bar. More...

template<typename ValueType , typename Derived , typename Derived2 >
ValueType	fidelity (const Eigen::MatrixBase< Derived > &rho, const Eigen::MatrixBase< Derived2 > &sigma)
	Fidelity between two density matrices. More...

template<typename ValueType , typename Der1 , typename Der2 >
ValueType	fidelity_T (const Eigen::MatrixBase< Der1 > &T1, const Eigen::MatrixBase< Der2 > &T2)
	Fidelity between two quantum states given by their T Parameterization. More...

template<bool OnlyLowerTri = false, typename Derived1 = Eigen::MatrixXd, typename Derived2 = Eigen::MatrixXd>
void	param_x_to_herm (Eigen::MatrixBase< Derived1 > &Herm, const Eigen::DenseBase< Derived2 > &x)
	Get the Hermitian matrix parameterized by the "X-parameter" vector `x`. More...

template<typename Derived1 , typename Derived2 >
void	param_herm_to_x (Eigen::DenseBase< Derived1 > &x, const Eigen::MatrixBase< Derived2 > &Herm)
	Get the X-parameterization corresponding to a given hermitian matrix. More...

template<typename DerU , typename Rng , typename Log >
void	random_unitary (Eigen::MatrixBase< DerU > &U, Rng &rng, Log &logger)
	Generate a Haar-distributed random unitary. More...

template<typename Der1 , typename Rng >
void	random_unitary (Eigen::MatrixBase< Der1 > &U, Rng &rng)
	Overload of random_unitary(U, rng, logger) which discards all logging messages.

template<typename Der , typename Rng , typename RndDist , typename... IndexTypes>
auto	dense_random (Rng &rng, RndDist &rnddist, IndexTypes...sizes) -> const Eigen::CwiseNullaryOp< tomo_internal::random_generator< Rng, RndDist, typename Eigen::internal::traits< Der >::Scalar >, Der >
	a matrix populated with random entries using C++'s `random` framework More...

template<typename Der , typename IndexType >
auto	can_basis_vec (IndexType k, IndexType size) -> const Eigen::CwiseNullaryOp< tomo_internal::can_basis_vec_generator< typename Eigen::internal::traits< Der >::Scalar, IndexType >, Der >
	Expression for the k-th canonical basis vector of given dimension. More...

template<typename Der , typename IndexType >
auto	can_basis_vec (IndexType k, IndexType j, IndexType rows, IndexType cols) -> const Eigen::CwiseNullaryOp< tomo_internal::can_basis_vec_generator< typename Eigen::internal::traits< Der >::Scalar, IndexType >, Der >
	Expression for the (k,j)-th canonical basis matrix of given dimension. More...

template<typename Der , typename... IndexTypes>
auto	powers_of_two (IndexTypes...sizes) -> const Eigen::CwiseNullaryOp< tomo_internal::powers_of_two_generator< typename Eigen::internal::traits< Der >::Scalar >, Der >
	Expression for a 1-D expression of powers of two. More...

template<int RowFactorCTime, int ColFactorCTime, typename Derived , typename std::enable_if<(RowFactorCTime==Eigen::Dynamic\|\|ColFactorCTime==Eigen::Dynamic), bool >::type dummy = true>
auto	replicated (const Eigen::DenseBase< Derived > &x, int row_factor, int col_factor) -> const Eigen::Replicate< Derived, Eigen::Dynamic, Eigen::Dynamic >
	Replicate a Eigen Dense object; same call for compile-time & run-time dimensions. More...

Detailed Description

Base namespace for the Tomographer project.

This namespace contains the public API for the Tomographer project template library.

Typedef Documentation

typedef MatrQ<Eigen::Dynamic, Eigen::Dynamic, double, int> Tomographer::DefaultMatrQ

Data types for all arguments set at run-time.

In this convenience typedef the dimension and the maximum number of POVM effects are set at runtime.

You might incur a (very?) slight performance loss due to dynamic memory allocation each time a vector or matrix type is instantiated.

Definition at line 364 of file matrq.h.

typedef MatrQ<2,6,double,int> Tomographer::QubitPaulisMatrQ

Data types for Pauli measurements on a single qubit.

Convenience typedef for the data types corresponding to 6 POVM effects on a 2-level quantum system.

Definition at line 371 of file matrq.h.

Enumeration Type Documentation

anonymous enum

Enumerator
MHUseFnValue	Provides the MH function value at each point (see Role of UseFnSyntaxType)
MHUseFnLogValue	Provides the logarithm MH function value at each point (see Role of UseFnSyntaxType)
MHUseFnRelativeValue	Provides directly the ratio of the function values for two consecutive points of the MH random walk (see Role of UseFnSyntaxType)

Definition at line 153 of file mhrw.h.

Function Documentation

template<typename Der , typename IndexType >

auto Tomographer::can_basis_vec	(	IndexType	k,
		IndexType	size
	)		-> const Eigen::CwiseNullaryOp< tomo_internal::can_basis_vec_generator<typename Eigen::internal::traits<Der>::Scalar, IndexType>, Der >

inline

Expression for the k-th canonical basis vector of given dimension.

Definition at line 271 of file util.h.

template<typename Der , typename IndexType >

auto Tomographer::can_basis_vec	(	IndexType	k,
		IndexType	j,
		IndexType	rows,
		IndexType	cols
	)		-> const Eigen::CwiseNullaryOp< tomo_internal::can_basis_vec_generator<typename Eigen::internal::traits<Der>::Scalar, IndexType>, Der >

inline

Expression for the (k,j)-th canonical basis matrix of given dimension.

This is a matrix of zeros except for the entry (k,j) which is one.

Definition at line 289 of file util.h.

template<typename Der , typename Rng , typename RndDist , typename... IndexTypes>

auto Tomographer::dense_random	(	Rng &	rng,
		RndDist &	rnddist,
		IndexTypes...	sizes
	)		-> const Eigen::CwiseNullaryOp< tomo_internal::random_generator<Rng, RndDist, typename Eigen::internal::traits<Der>::Scalar>, Der >

inline

a matrix populated with random entries using C++'s random framework

Parameters

rng	the `std::random` generator, such as a `std::mt19937` instance
rnddist	the `std::random` distribution to sample from, such as a `std::normal_distribution` instance
sizes	either no parameter, one parameter or two parameters specifying the sizes of the dense object to return.

Definition at line 215 of file util.h.

template<typename ValueType , typename Derived , typename Derived2 >

ValueType Tomographer::fidelity	(	const Eigen::MatrixBase< Derived > &	rho,
		const Eigen::MatrixBase< Derived2 > &	sigma
	)

inline

Fidelity between two density matrices.

Calculates \( F(\rho,\sigma) = \left\Vert\sigma^{1/2}\rho^{1/2}\right\Vert_1 \).

Note: This is the Nielsen & Chuang fidelity, sometimes also called "root fidelity."

Definition at line 52 of file dist.h.

template<typename ValueType , typename Der1 , typename Der2 >

ValueType Tomographer::fidelity_T	(	const Eigen::MatrixBase< Der1 > &	T1,
		const Eigen::MatrixBase< Der2 > &	T2
	)

inline

Fidelity between two quantum states given by their T Parameterization.

The \( T \) -parameterization of \( \rho \) is a matrix \( T \) which satisfies

\[ \rho = T T^\dagger . \]

This function calculates the same fidelity function as fidelity(), but accepts the T Parameterization of the quantum states instead. The formula used by this function acts directly on the \( T \) 's:

\[ F(T_1 T_1^\dagger, T_2 T_2^\dagger) = \left\Vert\rho^{1/2}\sigma^{1/2}\right\Vert_1 = \left\Vert T_1^\dagger T_2\right\Vert_1 . \]

Note: This is the Nielsen & Chuang fidelity, sometimes also called "root fidelity."

Definition at line 79 of file dist.h.

template<typename HistogramType >

void Tomographer::histogram_pretty_print	(	std::ostream &	str,
		const HistogramType &	histogram,
		int	max_width = `0`
	)

inline

pretty-print the given histogram.

This overload dumps the pretty print into the ostream str.

If max_width <= 0, then the screen width (or default width) minus the given amount in absolute value is used. The negative amount is useful if your line is already occupied by some content.

Definition at line 1026 of file histogram.h.

template<typename HistogramType >

std::string Tomographer::histogram_pretty_print	(	const HistogramType &	histogram,
		int	max_width = `0`
	)

inline

Utility to display histograms for humans.

This version of the function returns a formatted std::string.

If max_width <= 0, then the screen width (or default width) minus the given amount in absolute value is used. The negative amount is useful if your line is already occupied by some content.

Definition at line 1048 of file histogram.h.

template<typename HistogramType >

int Tomographer::histogram_short_bar	(	std::ostream &	str,
		const HistogramType &	histogram,
		bool	log_scale = `true`,
		int	max_width = `0`
	)

inline

Format the histogram as a one-line bar.

Produces a one-line visual representation of the histogram. The histogram is printed in the given std::ostream.

There's no final newline.

If max_width <= 0, then the screen width (or default width) minus the given amount in absolute value is used. The negative amount is useful if your line is already occupied by some content.

Returns: The number of characters which are still left to fill a line with maximal width. More precisely, the maximum width is first determined from max_width and/or from the COLUMNS environment variable. Then histogram is formatted into a bar which fits in this width. The difference between the maximum width and the histogram length is returned.

Definition at line 1073 of file histogram.h.

template<typename HistogramType >

std::string Tomographer::histogram_short_bar	(	const HistogramType &	histogram,
		bool	log_scale = `true`,
		int	max_width = `0`
	)

inline

Format the histogram as a one-line bar.

Produces a one-line visual representation of the histogram. Returns a std::string.

There's no final newline.

If max_width <= 0, then the screen width (or default width) minus the given amount in absolute value is used. The negative amount is useful if your line is already occupied by some content.

Definition at line 1101 of file histogram.h.

template<typename Derived1 , typename Derived2 >

void Tomographer::param_herm_to_x	(	Eigen::DenseBase< Derived1 > &	x,
		const Eigen::MatrixBase< Derived2 > &	Herm
	)

inline

Get the X-parameterization corresponding to a given hermitian matrix.

Note: This function only accesses lower triangular part of Herm.

Todo:: Currently, we can't pass an expression as second parameter here. So use Eigen::Ref instead to allow for that, too...

Definition at line 93 of file param_herm_x.h.

template<bool OnlyLowerTri = false, typename Derived1 = Eigen::MatrixXd, typename Derived2 = Eigen::MatrixXd>

void Tomographer::param_x_to_herm	(	Eigen::MatrixBase< Derived1 > &	Herm,
		const Eigen::DenseBase< Derived2 > &	x
	)

inline

Get the Hermitian matrix parameterized by the "X-parameter" vector x.

This calculates the hermitian matrix which is parameterized by x. See X Parameterization.

Definition at line 53 of file param_herm_x.h.

template<typename Der , typename... IndexTypes>

auto Tomographer::powers_of_two ( IndexTypes... sizes ) -> const Eigen::CwiseNullaryOp< tomo_internal::powers_of_two_generator<typename Eigen::internal::traits<Der>::Scalar>, Der >

inline

Expression for a 1-D expression of powers of two.

An Eigen template expression yielding powers of two as a column vector. The \( i\) -th item is \( 2^i \).

Parameters

sizes You may either specify the length of the vector (1 parameter), or the size of a column matrix (2 parameters, the second being equal to one).

Definition at line 357 of file util.h.

template<typename DerU , typename Rng , typename Log >

void Tomographer::random_unitary	(	Eigen::MatrixBase< DerU > &	U,
		Rng &	rng,
		Log &	logger
	)

inline

Generate a Haar-distributed random unitary.

Parameters

U	reference to an Eigen type (already sized to a square matrix)
rng	a std::random random number generator (such as std::mt19937)
logger	a reference to a logger (Logging and Loggers) where we can log what we're doing.

Definition at line 60 of file random_unitary.h.

template<int RowFactorCTime, int ColFactorCTime, typename Derived , typename std::enable_if<(RowFactorCTime==Eigen::Dynamic||ColFactorCTime==Eigen::Dynamic), bool >::type dummy = true>

auto Tomographer::replicated	(	const Eigen::DenseBase< Derived > &	x,
		int	row_factor,
		int	col_factor
	)		-> const Eigen::Replicate<Derived, Eigen::Dynamic, Eigen::Dynamic>

inline

Replicate a Eigen Dense object; same call for compile-time & run-time dimensions.

See replicated<RowFactorCTime, ColFactorCTime, Derived, dummy>

Allow our libraries to use the same syntax, for example

Eigen::Matrix<...> m_replicated = replicated<1,ColFactorAtCompileTime>(matrix, 1, col_factor);

for replicating a matrix for which one might, or might not, know the factor at compile time.

The corresponding factor template parameter should be either Eigen::Dynamic or a fixed value. If a fixed value is given, you need to specify the same value in the runtime argument (done as an eigen_assert() check, i.e. this is compiled out if -DNDEBUG is used)

This is the implementation for fixed RowFactorCTime and ColFactorCTime.

Definition at line 394 of file util.h.

Namespaces

Classes

Typedefs

Enumerations

Functions

Detailed Description

Typedef Documentation

Enumeration Type Documentation

Function Documentation