q2ns::analysis::anonymous_namespace{q2ns-analysis.cc} Namespace Reference

Functions
qpp::cmat	ToDensityMatrix (const QState &s)
	Convert a supported QState backend to a density matrix.
double	ClampToInterval (double x, double lo, double hi, double tol=1e-10)
	Clamp a scalar metric to a closed interval within numerical tolerance.
Eigen::MatrixXcd	HermitianSqrtPSD (const Eigen::MatrixXcd &A, double negEigTol=1e-12)
	Compute the Hermitian square root of a positive semidefinite matrix.
double	UhlmannFidelity (const Eigen::MatrixXcd &rho, const Eigen::MatrixXcd &sigma, double negEigTol=1e-12)
	Compute Uhlmann fidelity between two density matrices.
double	HermitianTraceNorm (const Eigen::MatrixXcd &A)
	Compute the trace norm of a Hermitian matrix.

Function Documentation

ClampToInterval()

double q2ns::analysis::anonymous_namespace{q2ns-analysis.cc}::ClampToInterval	(	double	x,
		double	lo,
		double	hi,
		double	tol = 1e-10
	)

Clamp a scalar metric to a closed interval within numerical tolerance.

Values slightly outside the target interval due to floating-point roundoff are clamped back to the nearest endpoint. Values outside the tolerance window are returned unchanged.

Parameters

x	Input value.
lo	Lower bound.
hi	Upper bound.
tol	Numerical tolerance for endpoint clamping.

Returns

Clamped value when within tolerance of the interval, otherwise x.

Definition at line 82 of file q2ns-analysis.cc.

References ClampToInterval().

Referenced by ClampToInterval().

Here is the call graph for this function:

Here is the caller graph for this function:

HermitianSqrtPSD()

Eigen::MatrixXcd q2ns::analysis::anonymous_namespace{q2ns-analysis.cc}::HermitianSqrtPSD	(	const Eigen::MatrixXcd &	A,
		double	negEigTol = 1e-12
	)

Compute the Hermitian square root of a positive semidefinite matrix.

Small negative eigenvalues caused by numerical roundoff are clamped to zero.

Parameters

A	Input matrix.
negEigTol	Tolerance for small negative eigenvalues.

Returns

Hermitian square root of A.

Definition at line 103 of file q2ns-analysis.cc.

References q2ns::H, and HermitianSqrtPSD().

Referenced by HermitianSqrtPSD(), and UhlmannFidelity().

Here is the call graph for this function:

Here is the caller graph for this function:

HermitianTraceNorm()

double q2ns::analysis::anonymous_namespace{q2ns-analysis.cc}::HermitianTraceNorm

(

const Eigen::MatrixXcd &

A

)

Compute the trace norm of a Hermitian matrix.

For a Hermitian matrix H, the trace norm is the sum of the absolute values of its eigenvalues.

The input is symmetrized first to suppress tiny anti-Hermitian numerical noise before diagonalization.

Parameters

A	Input matrix.

Returns

Trace norm of A.

Exceptions

std::runtime_error

if the matrix is not square or if eigenvalue decomposition fails.

Definition at line 188 of file q2ns-analysis.cc.

References q2ns::H, and HermitianTraceNorm().

Referenced by HermitianTraceNorm().

Here is the call graph for this function:

Here is the caller graph for this function:

ToDensityMatrix()

qpp::cmat q2ns::analysis::anonymous_namespace{q2ns-analysis.cc}::ToDensityMatrix

(

const QState &

s

)

Convert a supported QState backend to a density matrix.

This helper provides a common density-matrix representation for analysis routines that are naturally expressed in terms of rho, such as purity, entropy, and trace distance.

For ket and stabilizer backends, this may require constructing a dense matrix representation and can therefore be substantially more expensive than backend-native calculations.

Parameters

s	Input state.

Returns

Dense density-matrix representation of s.

Exceptions

std::runtime_error

if the backend is unsupported or if conversion of a stabilizer state requires unavailable backend-specific functionality.

Definition at line 47 of file q2ns-analysis.cc.

References ToDensityMatrix().

Referenced by ToDensityMatrix().

Here is the call graph for this function:

Here is the caller graph for this function:

UhlmannFidelity()

double q2ns::analysis::anonymous_namespace{q2ns-analysis.cc}::UhlmannFidelity	(	const Eigen::MatrixXcd &	rho,
		const Eigen::MatrixXcd &	sigma,
		double	negEigTol = 1e-12
	)

Compute Uhlmann fidelity between two density matrices.

The returned value is F(rho, sigma) = (Tr sqrt(sqrt(rho) sigma sqrt(rho)))^2.

Parameters

rho	First density matrix.
sigma	Second density matrix.
negEigTol	Tolerance for small negative eigenvalues in intermediate PSD checks.

Returns

Fidelity in the range [0.0, 1.0], up to numerical tolerance.

Definition at line 145 of file q2ns-analysis.cc.

References HermitianSqrtPSD(), UhlmannFidelity(), and q2ns::X.

Referenced by UhlmannFidelity().

Here is the call graph for this function:

Here is the caller graph for this function: