org.mathIT.quantum.stabilizer

Class GraphRegister

java.lang.Object

org.mathIT.quantum.stabilizer.GraphRegister

public class GraphRegister
extends Object

This class represents the states of a quantum register consisting of stabilizer states. Internally, the quantum computations are performed by the graph state formalism in which each qubit is represented by a vertex and entanglement of two qubits by an edge connecting their corresponding vertices.

For a detailed description of the graphic state formalism and its algorithms see the article

S. Anders, H. J. Briegel: 'Fast simulation of Stabilizer Circuits using a Graph States Formalism', Phys. Rev. A 73, 022334 (2006) DOI: 10.1103/PhysRevA.73.022334 (Preprint: quant-ph/0504117)

This class is based essentially on the C++ program graphsim.cpp, version 0.10 from 2005/01/27 written by Simon Anders, downloadable under http://homepage.uibk.ac.at/~c705213/work/graphsim.html

Version:

1.0

Author:

Andreas de Vries

Constructor Summary

Constructors

Constructor and Description
GraphRegister(int size) Creates a register of n qubits, initialized to the state |0>.

Method Summary

Modifier and Type	Method and Description
void	bitFlip(int v) Applies a bitflip gate, i.e., a Pauli X, on vertex v.
void	cNOT(int vc, int vt) Performs a controlled NOT gate between the vertices vc (control) and vt (target).
void	cPhase(int v1, int v2) Does a conditional phase gate c-S between the two qubits.
boolean	equals(Object o) Compares the specified object with this local Clifford operator.
Register	getRegister() Returns the quantum register (in state vecor representation) represented by this graph register.
void	hadamard(int v) Apply a Hadamard gate on vertex v.
int	hashCode() Returns the hash code for this graph register state.
void	inverseSGate(int v) Applies an inverse S gate on vertex v.
int	measure(int v) Measures qubit v with the Pauli Z gate as basis operator and returns the measured value.
int	measure(int v, LocalCliffordOperator basis) Measures qubit v in the specified basis operator and returns the measured value.
void	phaseFlip(int v) Apply a phase flip gate (i.e. a Pauli-Z) on vertex v.
void	phaseRot(int v) Apply a phase gate S on qubit v.
void	sGate(int v) Applies an S gate, or "phase gate", on vertex v.
String	toString() Returns a string representation of this register.
void	xPauli(int v) Applies a Pauli-X, or "bit flip", on vertex v.
void	yPauli(int v) Applies a Pauli-Y on vertex v.
void	zPauli(int v) Applies a Pauli-Z, or "phase flip", on vertex v.

Methods inherited from class java.lang.Object

clone, finalize, getClass, notify, notifyAll, wait, wait, wait

Constructor Detail

GraphRegister

public GraphRegister(int size)

Creates a register of n qubits, initialized to the state |0>. A register of size n enables a total of q = 2ⁿ quantum states as the computational basis.

Parameters:

size - the number of qubits this register consists of

Method Detail

getRegister

public Register getRegister()

Returns the quantum register (in state vecor representation) represented by this graph register.

Returns:

the register state represented by this graph register state

hadamard

public void hadamard(int v)

Apply a Hadamard gate on vertex v.

Parameters:

v - the qubit on which the gate is to be applied (in an n qubit register, v = 0, 1, ..., n - 1)

xPauli

public void xPauli(int v)

Applies a Pauli-X, or "bit flip", on vertex v.

Parameters:

v - the qubit on which the gate is to be applied (in an n qubit register, v = 0, 1, ..., n - 1)

See Also:

bitFlip(int)

yPauli

public void yPauli(int v)

Applies a Pauli-Y on vertex v.

Parameters:

v - the qubit on which the gate is to be applied (in an n qubit register, v = 0, 1, ..., n - 1)

zPauli

public void zPauli(int v)

Applies a Pauli-Z, or "phase flip", on vertex v.

Parameters:

v - the qubit on which the gate is to be applied (in an n qubit register, v = 0, 1, ..., n - 1)

See Also:

phaseFlip(int)

sGate

public void sGate(int v)

Applies an S gate, or "phase gate", on vertex v.

Parameters:

v - the qubit on which the gate is to be applied (in an n qubit register, v = 0, 1, ..., n - 1)

inverseSGate

public void inverseSGate(int v)

Applies an inverse S gate on vertex v.

Parameters:

v - the qubit on which the gate is to be applied (in an n qubit register, v = 0, 1, ..., n - 1)

See Also:

sGate(int)

bitFlip

public void bitFlip(int v)

Applies a bitflip gate, i.e., a Pauli X, on vertex v.

Parameters:

v - the qubit on which the gate is to be applied (in an n qubit register, v = 0, 1, ..., n - 1)

See Also:

xPauli(int)

phaseFlip

public void phaseFlip(int v)

Apply a phase flip gate (i.e. a Pauli-Z) on vertex v.

Parameters:

v - the qubit on which the gate is to be applied (in an n qubit register, v = 0, 1, ..., n - 1)

phaseRot

public void phaseRot(int v)

Apply a phase gate S on qubit v. Phase gate, or phase rotation, means the gate S = |0><0| + i |1><1|.

Parameters:

v - the qubit on which the gate is to be applied (in an n qubit register, v = 0, 1, ..., n - 1)

cPhase

public void cPhase(int v1,
                   int v2)

Does a conditional phase gate c-S between the two qubits.

Parameters:

v1 - the control qubit (in an n qubit register, v1 = 0, 1, ..., n - 1

v2 - the target qubit (in an n qubit register, v2 = 0, 1, ..., n - 1

cNOT

public void cNOT(int vc,
                 int vt)

Performs a controlled NOT gate between the vertices vc (control) and vt (target).

Parameters:

vc - the control qubit (in an n qubit register, vc = 0, 1, ..., n - 1)

vt - the target qubit (in an n qubit register, vc = 0, 1, ..., n - 1)

measure

public int measure(int v)

Measures qubit v with the Pauli Z gate as basis operator and returns the measured value.

Parameters:

v - the measured qubit (in an n qubit register, v = 0, 1, ..., n - 1)

Returns:

the measured value

measure

public int measure(int v,
                   LocalCliffordOperator basis)

Measures qubit v in the specified basis operator and returns the measured value. The measurement basis must be a Pauli operator, i.e., has to be equal to either X, Y, or Z.

Parameters:

v - the measured qubit (in an n qubit register, v = 0, 1, ..., n - 1)

basis - the Pauli gate which serves as measurement basis

Returns:

the qubit value as measured in the specified basis

equals

public boolean equals(Object o)

Compares the specified object with this local Clifford operator. The method returns true if and only if the specified object represents a graph register state which is the same than this register.

Overrides:

equals in class Object

Parameters:

o - the specified reference with which to compare

Returns:

true if and only if the specified object is the same graph register state than this operator

hashCode

public int hashCode()

Returns the hash code for this graph register state.

Overrides:

hashCode in class Object

Returns:

the hash code for this graph register state

toString

public String toString()

Returns a string representation of this register. It prints its vertices, each one representing a qubit and being shown with its associated vertex operator and its vacancy list, i.e., the list of its neighbor vertices represnting those qubits which are entangled.

Overrides:

toString in class Object

Returns:

a string representation of this register