A local completely-positive, trace-preserving map in Kraus form. More...

#include <QuantumChannel.h>

Collaboration diagram for Simulators::QuantumChannel:

Public Types
using	KrausOperators = std::vector<Matrix>
using	Matrix = Eigen::MatrixXcd

Public Member Functions
	QuantumChannel (KrausOperators krausOperators)
	Construct and validate a CPTP channel from Kraus operators.
Matrix	ChoiMatrix () const
	Choi matrix of the channel: sum_k vec(E_k) vec(E_k)^dagger, with vec() stacking the operator column by column.
const KrausOperators &	GetKrausOperators () const
size_t	GetNumberOfQubits () const
bool	IsApprox (const QuantumChannel &other, double tolerance=1e-12) const
	Compare two channels as MAPS, not as Kraus lists.

Static Public Member Functions
static QuantumChannel	AmplitudeDamping (double gamma)
	\|1> -> \|0> relaxation with probability gamma.
static QuantumChannel	BitFlip (double probability)
	(1-p) rho + p X rho X.
static QuantumChannel	BitPhaseFlip (double probability)
	(1-p) rho + p Y rho Y.
static QuantumChannel	CorrelatedPhaseFlip (double probability)
	(1-p)rho + p (Z (x) Z) rho (Z (x) Z).
static QuantumChannel	CorrelatedPhaseFlip (double probability, double correlation)
	Interpolate between independent phase flips and a fully correlated ZZ phase flip.
static QuantumChannel	Depolarizing (double errorProbability)
	Depolarizing channel in the NoiseModel/QCSim convention: (1-p)rho + p/3 (XrhoX + YrhoY + ZrhoZ).
static QuantumChannel	DepolarizingMixing (double mixingProbability)
	Depolarizing channel in the replacement convention: (1-p)rho + p I/2.
static QuantumChannel	GeneralizedAmplitudeDamping (double gamma, double excitedStatePopulation)
	Finite-temperature amplitude damping.
static QuantumChannel	Pauli (const std::vector< double > &probabilities)
	Arbitrary local Pauli channel.
static QuantumChannel	Pauli (double px, double py, double pz)
	Single-qubit Pauli channel with X, Y and Z error probabilities.
static QuantumChannel	PhaseDamping (double gamma)
	Phase damping with coherence multiplier sqrt(1-gamma).
static QuantumChannel	PhaseFlip (double probability)
	(1-p) rho + p Z rho Z.
static QuantumChannel	ThermalRelaxation (double duration, double t1, double t2, double excitedStatePopulation=0.0)
	Hardware-style thermal relaxation for a duration, T1 and T2.
static QuantumChannel	TwoQubitDepolarizing (double errorProbability)
	Two-qubit depolarizing in the total-Pauli-error convention: identity has probability 1-p and each other Pauli has p/15.
static QuantumChannel	TwoQubitDepolarizingMixing (double mixingProbability)
	Two-qubit replacement depolarizing, fully mixed at probability one.

Detailed Description

A local completely-positive, trace-preserving map in Kraus form.

Matrices use Maestro's gate convention: for a target list {q0, q1}, q0 is the least-significant local basis bit. Thus a product A on q0 and B on q1 is represented by B (x) A.

Definition at line 33 of file QuantumChannel.h.

Member Typedef Documentation

◆ KrausOperators

using Simulators::QuantumChannel::KrausOperators = std::vector<Matrix>

Definition at line 36 of file QuantumChannel.h.

◆ Matrix

using Simulators::QuantumChannel::Matrix = Eigen::MatrixXcd

Definition at line 35 of file QuantumChannel.h.

Constructor & Destructor Documentation

◆ QuantumChannel()

Simulators::QuantumChannel::QuantumChannel ( KrausOperators krausOperators )

inlineexplicit

Construct and validate a CPTP channel from Kraus operators.

Definition at line 39 of file QuantumChannel.h.

Referenced by AmplitudeDamping(), BitFlip(), BitPhaseFlip(), CorrelatedPhaseFlip(), CorrelatedPhaseFlip(), Depolarizing(), DepolarizingMixing(), GeneralizedAmplitudeDamping(), IsApprox(), Pauli(), Pauli(), PhaseDamping(), PhaseFlip(), ThermalRelaxation(), TwoQubitDepolarizing(), and TwoQubitDepolarizingMixing().

Member Function Documentation

◆ AmplitudeDamping()

QuantumChannel Simulators::QuantumChannel::AmplitudeDamping ( double gamma )

inlinestatic

|1> -> |0> relaxation with probability gamma.

Definition at line 194 of file QuantumChannel.h.

References QuantumChannel().

Referenced by Simulators::IState::ApplyAmplitudeDamping().

◆ BitFlip()

QuantumChannel Simulators::QuantumChannel::BitFlip ( double probability )

inlinestatic

(1-p) rho + p X rho X.

Definition at line 91 of file QuantumChannel.h.

References QuantumChannel(), and Pauli().

Referenced by Simulators::IState::ApplyBitFlipNoise().

◆ BitPhaseFlip()

QuantumChannel Simulators::QuantumChannel::BitPhaseFlip ( double probability )

inlinestatic

(1-p) rho + p Y rho Y.

Definition at line 97 of file QuantumChannel.h.

References QuantumChannel(), and Pauli().

Referenced by Simulators::IState::ApplyBitPhaseFlipNoise().

◆ ChoiMatrix()

Matrix Simulators::QuantumChannel::ChoiMatrix ( ) const

inline

Choi matrix of the channel: sum_k vec(E_k) vec(E_k)^dagger, with vec() stacking the operator column by column.

Two channels are the same map if and only if their Choi matrices are equal.

Definition at line 78 of file QuantumChannel.h.

Referenced by IsApprox().

◆ CorrelatedPhaseFlip() [1/2]

QuantumChannel Simulators::QuantumChannel::CorrelatedPhaseFlip ( double probability )

inlinestatic

(1-p)rho + p (Z (x) Z) rho (Z (x) Z).

Definition at line 315 of file QuantumChannel.h.

References QuantumChannel(), and CorrelatedPhaseFlip().

Referenced by Simulators::IState::ApplyCorrelatedPhaseFlipNoise(), Simulators::IState::ApplyCorrelatedPhaseFlipNoise(), and CorrelatedPhaseFlip().

◆ CorrelatedPhaseFlip() [2/2]

QuantumChannel Simulators::QuantumChannel::CorrelatedPhaseFlip	(	double	probability,
		double	correlation )

inlinestatic

Interpolate between independent phase flips and a fully correlated ZZ phase flip.

correlation=0 is E_Z (x) E_Z; correlation=1 applies either II or ZZ.

Definition at line 324 of file QuantumChannel.h.

References QuantumChannel(), and Pauli().

◆ Depolarizing()

QuantumChannel Simulators::QuantumChannel::Depolarizing ( double errorProbability )

inlinestatic

Depolarizing channel in the NoiseModel/QCSim convention: (1-p)rho + p/3 (XrhoX + YrhoY + ZrhoZ).

Definition at line 178 of file QuantumChannel.h.

References QuantumChannel(), and Pauli().

Referenced by Simulators::IState::ApplyDepolarizingNoise(), and DepolarizingMixing().

◆ DepolarizingMixing()

QuantumChannel Simulators::QuantumChannel::DepolarizingMixing ( double mixingProbability )

inlinestatic

Depolarizing channel in the replacement convention: (1-p)rho + p I/2.

Full mixing occurs at p=1.

Definition at line 188 of file QuantumChannel.h.

References QuantumChannel(), and Depolarizing().

Referenced by Simulators::IState::ApplyDepolarizingMixingNoise().

◆ GeneralizedAmplitudeDamping()

QuantumChannel Simulators::QuantumChannel::GeneralizedAmplitudeDamping	(	double	gamma,
		double	excitedStatePopulation )

inlinestatic

Finite-temperature amplitude damping.

excitedStatePopulation is the equilibrium population of |1>.

Definition at line 222 of file QuantumChannel.h.

References QuantumChannel().

Referenced by Simulators::IState::ApplyGeneralizedAmplitudeDamping().

◆ GetKrausOperators()

const KrausOperators & Simulators::QuantumChannel::GetKrausOperators ( ) const

inline

Definition at line 44 of file QuantumChannel.h.

◆ GetNumberOfQubits()

size_t Simulators::QuantumChannel::GetNumberOfQubits ( ) const

inline

Definition at line 45 of file QuantumChannel.h.

◆ IsApprox()

bool Simulators::QuantumChannel::IsApprox	(	const QuantumChannel &	other,
		double	tolerance = 1e-12 ) const

inline

Compare two channels as MAPS, not as Kraus lists.

The Kraus representation is not unique: {E_k} and {sum_j u_kj E_j} for any unitary u describe the same channel, and a channel may legitimately be built with a different number of operators (Pauli(), for instance, drops zero-probability terms, so the operator count depends on the parameter values). Comparing coefficient by coefficient therefore reports physically identical channels as different.

The Choi matrix sum_k vec(E_k) vec(E_k)^dagger is unique to the map, so comparing Choi matrices answers the question actually being asked.

Definition at line 60 of file QuantumChannel.h.

References QuantumChannel(), and ChoiMatrix().

◆ Pauli() [1/2]

QuantumChannel Simulators::QuantumChannel::Pauli ( const std::vector< double > & probabilities )

inlinestatic

Arbitrary local Pauli channel.

The array must contain 4^n probabilities. Base-4 digit i of an array index selects I, X, Y, or Z on targets[i], respectively. For two targets the order is therefore II, XI, YI, ZI, IX, XX, ... , ZZ.

Definition at line 130 of file QuantumChannel.h.

References QuantumChannel().

◆ Pauli() [2/2]

QuantumChannel Simulators::QuantumChannel::Pauli	(	double	px,
		double	py,
		double	pz )

inlinestatic

Single-qubit Pauli channel with X, Y and Z error probabilities.

The identity probability is 1-px-py-pz.

Definition at line 112 of file QuantumChannel.h.

References QuantumChannel(), and Pauli().

Referenced by Simulators::IState::ApplyPauliChannel(), Simulators::IState::ApplyPauliChannel(), BitFlip(), BitPhaseFlip(), CorrelatedPhaseFlip(), Depolarizing(), Pauli(), PhaseFlip(), and TwoQubitDepolarizing().

◆ PhaseDamping()

QuantumChannel Simulators::QuantumChannel::PhaseDamping ( double gamma )

inlinestatic

Phase damping with coherence multiplier sqrt(1-gamma).

This differs from phase flip, whose multiplier is 1-2p.

Definition at line 208 of file QuantumChannel.h.

References QuantumChannel().

Referenced by Simulators::IState::ApplyPhaseDamping().

◆ PhaseFlip()

QuantumChannel Simulators::QuantumChannel::PhaseFlip ( double probability )

inlinestatic

(1-p) rho + p Z rho Z.

Definition at line 103 of file QuantumChannel.h.

References QuantumChannel(), and Pauli().

Referenced by Simulators::IState::ApplyPhaseFlipNoise().

◆ ThermalRelaxation()

QuantumChannel Simulators::QuantumChannel::ThermalRelaxation	(	double	duration,
		double	t1,
		double	t2,
		double	excitedStatePopulation = 0.0 )

inlinestatic

Hardware-style thermal relaxation for a duration, T1 and T2.

Populations relax toward excitedStatePopulation with exp(-duration/T1), while coherences are multiplied by exp(-duration/T2). The physical Markovian constraint T2 <= 2*T1 is enforced. Positive infinity is accepted for either time constant.

Definition at line 250 of file QuantumChannel.h.

References QuantumChannel().

Referenced by Simulators::IState::ApplyThermalRelaxation().

◆ TwoQubitDepolarizing()

QuantumChannel Simulators::QuantumChannel::TwoQubitDepolarizing ( double errorProbability )

inlinestatic

Two-qubit depolarizing in the total-Pauli-error convention: identity has probability 1-p and each other Pauli has p/15.

Definition at line 344 of file QuantumChannel.h.

References QuantumChannel(), and Pauli().

Referenced by Simulators::IState::ApplyTwoQubitDepolarizingNoise(), and TwoQubitDepolarizingMixing().

◆ TwoQubitDepolarizingMixing()

QuantumChannel Simulators::QuantumChannel::TwoQubitDepolarizingMixing ( double mixingProbability )

inlinestatic

Two-qubit replacement depolarizing, fully mixed at probability one.

Definition at line 352 of file QuantumChannel.h.

References QuantumChannel(), and TwoQubitDepolarizing().

Referenced by Simulators::IState::ApplyTwoQubitDepolarizingMixingNoise().

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

QuantumChannel.h

Public Types

Public Member Functions

Static Public Member Functions

Detailed Description

Member Typedef Documentation

◆ KrausOperators

◆ Matrix

Constructor & Destructor Documentation

◆ QuantumChannel()

Member Function Documentation

◆ AmplitudeDamping()

◆ BitFlip()

◆ BitPhaseFlip()

◆ ChoiMatrix()

◆ CorrelatedPhaseFlip() [1/2]

◆ CorrelatedPhaseFlip() [2/2]

◆ Depolarizing()

◆ DepolarizingMixing()

◆ GeneralizedAmplitudeDamping()

◆ GetKrausOperators()

◆ GetNumberOfQubits()

◆ IsApprox()

◆ Pauli() [1/2]

◆ Pauli() [2/2]

◆ PhaseDamping()

◆ PhaseFlip()

◆ ThermalRelaxation()

◆ TwoQubitDepolarizing()

◆ TwoQubitDepolarizingMixing()