QuantumMob/Q3mini | Paclet Repository

Quantum Information Systems

Q3 provides various tools and utilities for symbolic and numerical calculations to simulate quantum computation and quantum information processing.

Here listed are frequently used functions for each subject. The subjects are arranged in parallel with the chapters in the

Quantum Workbook (2022)

For basic usages of Q3 in the context of quantum computation and quantum information, see tutorial document "

Quantum Information Systems with Q3

The Postulates of Quantum Mechanics

Ket

— Represents a vector in the computational basis.

Bra

— The Hermitian conjugate of

Ket

Basis

— Gives the computational basis of the Hilbert space associated with a system of qubits.

Dyad

— Represents a dyadic product two state vectors.

Measurement

— Represents a measurement of Pauli operators (including tensor products of single-qubit Pauli operators).

MeasurementOdds

— Analyses the probabilities for possible outcomes and post-measurement states of a measurement of Pauli operators.

SchmidtDecomposition

— Gives the Schmidt decomposition of a pure state of a composite system.

PartialTrace

— Takes the partial trace of a pure or mixed state or a linear operator.

VonNeumannEntropy

— Gives the von Neumann entropy of a subsystem.

Multiply

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MultiplyExp

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Matrix

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ExpressionFor

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Elaborate

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Garner

Quantum Computation: Overview

QuantumCircuit

— Represents a quantum circuit model of quantum computation.

Rotation

— Represents a single-qubit rotation gate.

Phase

— A relative phase sift on a single qubit.

ControlledGate

— The controlled-unitary gate (including a multi-control unitary gate).

CNOT

— The CNOT gate (including a multi-control and/or multi-target NOT gate).

— The controlled-Z gate (including a multi-control and/or multi-target gate).

SWAP

— The SWAP gates.

Toffoli

— The Toffoli gate on three qubits.

Fredkin

— The Fredkin gate on three qubits.

Oracle

— Represents a quantum oracle.

Hadamard

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Quadrant

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Octant

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EulerRotation

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Deutsch

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QFT

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Matrix

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ExpressionFor

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Elaborate

Quantum Computation: Models

MultiplyExp

— The exponential function of an operator.

ProperSystem

— Returns both the eigenvalues and eigenstates of an operator in an analytic expression (not a matrix).

ProperVectors

— Returns the eigenstates of an operator in an analytic expression (not a matrix).

ProperValues

— Returns the eigenvalues of an operator in an analytic expression (not a matrix).

GraphState

— Constructs a graph state corresponding to a graph.

Measurement

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MeasurementOdds

Quantum Algorithms

QuantumCircuit

— Represents a quantum circuit model of quantum computation.

Rotation

— Represents a single-qubit rotation gate.

Phase

— A relative phase sift on a single qubit.

ControlledGate

— The controlled-unitary gate (including a multi-control unitary gate).

CNOT

— The CNOT gate (including a multi-control and/or multi-target NOT gate).

— The controlled-Z gate (including a multi-control and/or multi-target gate).

SWAP

— The SWAP gates.

Toffoli

— The Toffoli gate on three qubits.

Fredkin

— The Fredkin gate on three qubits.

Oracle

— Represents a quantum oracle.

Hadamard

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Quadrant

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Octant

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EulerRotation

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Deutsch

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QFT

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Matrix

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ExpressionFor

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Elaborate

Quantum Noise and Decoherence

Supermap

— Represents a supermap, a linear map from ℒ() to ℒ().

ChoiMatrix

— Returns the Choi matrix of a supermap.

LindbladSupermap

— Represents the generator of a Lindblad equation (i.e. a quantum master equation).

LindbladSolve

— Solves a Lindblad equation.

HilbertSchmidtNorm

— Returns the Hilbert-Schmidt norm (or Frobenius norm) of a (pure or mixed) state.

HilbertSchmidtDistance

— Returns the Hilbert-Schmidt distance between two of a (pure or mixed) state.

TraceNorm

— Returns the trace norm of a (pure or mixed) state.

TraceDistance

— Returns the trace distance between two (pure or mixed) state.

Fidelity

— Returns the fidelity between two (pure or mixed) state.

LindbladConvert

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DampingOperator

Quantum Error-Correction Codes

PauliGroup

— Represents the Pauli group on a system of

qubits.

CliffordGroup

— Represents the Clifford group on a system of

qubits.

GottesmanVector

— Returns the binary vector corresponding to a Pauli operator.

FromGottesmanVector

— Returns the Pauli operator corresponding to a binary vector.

GottesmanDot

— The symplectic product of Gottesman vectors and matrices of Gottesman vectors.

GottesmanSplit

— Returns the X- and Z-part of a Gottesman vector or a set of Gottesman vectors.

GottesmanMerge

— Combines the X- and Z-part to construct a full Gottesman vector or a set of full Gottesman vectors.

GottesmanMatrix

— Returns the binary symplectic matrix corresponding to a Clifford operator.

FromGottesmanMatrix

— Returns the Clifford operator corresponding to a binary symplectic matrix.

GroupOrder

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GroupElements

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GroupGenerators

Quantum Information Theory

HilbertSchmidtNorm

— Returns the Hilbert-Schmidt norm (or Frobenius norm) of a (pure or mixed) state.

HilbertSchmidtDistance

— Returns the Hilbert-Schmidt distance between two of a (pure or mixed) state.

TraceNorm

— Returns the trace norm of a (pure or mixed) state.

TraceDistance

— Returns the trace distance between two (pure or mixed) state.

Fidelity

— Returns the fidelity between two (pure or mixed) state.

ShannonEntropy

— Returns the Shannon entropy of a probability distribution.

VonNeumannEntropy

— Returns the von Neumann entropy of a density operator.

PartialTrace

— Takes the partial trace of a linear operator (or a pure-state vector) over a subsystem.

PartialTranspose

— Takes the partial transposition of a linear operator over a subsystem.

LogarithmicNegativity

— Returns the logarithmic negativity (an entanglement measure) of a mixed state.

TechNotes

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Quantum Information Systems with Q3

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The Postulates of Quantum Mechanics

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Quantum Computation: Overview

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Quantum Algorithms

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Quantum Noise and Decoherence

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Quantum Error-Correction Codes

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Quantum Information Theory

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Quick Quantum Computing with Q3

RelatedGuides

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Clifford Quantum Circuits

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Fermionic Quantum Computation

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Quantum Many-Body Systems

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Quantum Spin Systems

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Q3: Symbolic Quantum Simulation

RelatedLinks

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Mahn-Soo Choi (2022)

, A Quantum Computation Workbook (Springer).