LocalCliffordOperator

java.lang.Object
- org.mathIT.quantum.stabilizer.LocalCliffordOperator

```
public class LocalCliffordOperator
extends Object
```
An operator in the local Clifford group C₁. The 24 local Clifford operators form a multiplicative group C₁, the multiplication in the Clifford group is not commutative. A local Clifford operator is a stabilizer if and only if it is in the Pauli group P₁ = { ±I, ±iI, ±X, ±iX, ±Y, ±iY, ±Z, ±iZ }.

Version:

1.0

Author:

Andreas de Vries

Field Summary

Fields
Modifier and Type	Field and Description
`static LocalCliffordOperator`	`H` The Hadamard operator acting on a single qubit.
`static LocalCliffordOperator`	`I` The identity operator acting on a single qubit.
`static LocalCliffordOperator`	`S` The pi/4 phase rotation operator acting on a single qubit.
`static LocalCliffordOperator`	`S_H` The Hermitian conjugate of the pi/4 phase rotation acting on a single qubit.
`static LocalCliffordOperator`	`smiX` The Sqrt(-iX) operator acting on a single qubit.
`static LocalCliffordOperator`	`smiY` The Sqrt(-iY) operator acting on a single qubit.
`static LocalCliffordOperator`	`smiZ` The Sqrt(-iZ) operator acting on a single qubit.
`static LocalCliffordOperator`	`spiX` The Sqrt(+iX) operator acting on a single qubit.
`static LocalCliffordOperator`	`spiY` The Sqrt(+iY) operator acting on a single qubit.
`static LocalCliffordOperator`	`spiZ` The Sqrt(+iZ) operator acting on a single qubit.
`static LocalCliffordOperator`	`X` The Pauli-X operator acting on a single qubit.
`static LocalCliffordOperator`	`Y` The Pauli-Y operator acting on a single qubit.
`static LocalCliffordOperator`	`Z` The Pauli-Z operator acting on a single qubit.

Constructor Summary

Constructors
Constructor and Description
`LocalCliffordOperator(int code)` Constructor, takes an integer in 0..23.
`LocalCliffordOperator(int signsymb, int permsymb)` constructor, takes a sign symbol in 0..3 (for I, X, Y, Z) and a permutation symbol 0..5 (for A, B, ..., F).

Method Summary

All Methods Instance Methods Concrete Methods
Modifier and Type	Method and Description
`LocalCliffordOperator`	`adjoint()` Returns the Hermitian adjoint of this operator.
`int`	`conjugate(LocalCliffordOperator trans)` Replaces this operator by the conjugation trans · `this` · trans^† and returns a phase, either +1 if trans is a stabilizer, or -1.
`boolean`	`equals(LocalCliffordOperator operator)` Checks whether this LC operator is equal to the specified operator.
`boolean`	`equals(Object o)` Compares the specified object with this local Clifford operator.
`double[][][]`	`getMatrix()` Returns this local Clifford operator as an array representing a 2x2 matrix of complex numbers.
`String`	`getName()` Returns the name of this local Clifford operator.
`int`	`hashCode()` Returns the hash code for this local Clifford operator.
`boolean`	`isDiagonal()` Returns whether this operator is represented by a diagonal matrix.
`boolean`	`isXY()` Returns whether this operator is the Pauli-X gate or the Pauli-Y.
`LocalCliffordOperator`	`multiply(LocalCliffordOperator operator)` Muliplies this operator with the specified local Clifford operator.
`String`	`toString()` Returns this operator as a string representation of the 2x2 matrix representing it.

Methods inherited from class java.lang.Object
clone, finalize, getClass, notify, notifyAll, wait, wait, wait

- Field Detail
  - I
```
public static final LocalCliffordOperator I
```
    The identity operator acting on a single qubit.
  - X
```
public static final LocalCliffordOperator X
```
    The Pauli-X operator acting on a single qubit.
  - Y
```
public static final LocalCliffordOperator Y
```
    The Pauli-Y operator acting on a single qubit.
  - Z
```
public static final LocalCliffordOperator Z
```
    The Pauli-Z operator acting on a single qubit.
  - H
```
public static final LocalCliffordOperator H
```
    The Hadamard operator acting on a single qubit.
  - spiZ
```
public static final LocalCliffordOperator spiZ
```
    The Sqrt(+iZ) operator acting on a single qubit.
  - smiZ
```
public static final LocalCliffordOperator smiZ
```
    The Sqrt(-iZ) operator acting on a single qubit.
  - spiY
```
public static final LocalCliffordOperator spiY
```
    The Sqrt(+iY) operator acting on a single qubit.
  - smiY
```
public static final LocalCliffordOperator smiY
```
    The Sqrt(-iY) operator acting on a single qubit.
  - spiX
```
public static final LocalCliffordOperator spiX
```
    The Sqrt(+iX) operator acting on a single qubit.
  - smiX
```
public static final LocalCliffordOperator smiX
```
    The Sqrt(-iX) operator acting on a single qubit.
  - S
```
public static final LocalCliffordOperator S
```
    The pi/4 phase rotation operator acting on a single qubit.
  - S_H
```
public static final LocalCliffordOperator S_H
```
    The Hermitian conjugate of the pi/4 phase rotation acting on a single qubit.
- Constructor Detail
  - LocalCliffordOperator
```
public LocalCliffordOperator(int code)
```
    Constructor, takes an integer in 0..23.
    
    Parameters:
    
    code - the code of this operator
  - LocalCliffordOperator
```
public LocalCliffordOperator(int signsymb,
                             int permsymb)
```
    constructor, takes a sign symbol in 0..3 (for I, X, Y, Z) and a permutation symbol 0..5 (for A, B, ..., F).
    
    Parameters:
    
    signsymb - the sign symbol of this operator
    
    permsymb - the permutation symbol of this operator
- Method Detail
  - getName
```
public String getName()
```
    Returns the name of this local Clifford operator. For instance, "YC" for Hadamard=Y^C.
```
  code  |  0  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
  -------------------------------------------------------------------------------
  name  | IA XA YA ZA IB XB YB ZB IC XC YC ZC ID XD YD ZD IE XE YE ZE IF XF YF ZF
  usual |  I  X  Y  Z        S           H                         HS
  
```
    Returns:
    
    the name of this local Clifford operator
  - conjugate
```
public int conjugate(LocalCliffordOperator trans)
```
    Replaces this operator by the conjugation trans · this · trans^† and returns a phase, either +1 if trans is a stabilizer, or -1. A local Clifford operator is a stabilizer if and only if it is in the Pauli group P₁.
    
    Parameters:
    
    trans - the operator which conjugates this operator
    
    Returns:
    
    +1 if trans is a stabilizer -1 otherwise
    
    Throws:
    
    IllegalArgumentException - if this gate is not a Pauli gate
  - adjoint
```
public LocalCliffordOperator adjoint()
```
    Returns the Hermitian adjoint of this operator.
    
    Returns:
    
    the Hermitian adjoint of this operator.
  - isXY
```
public boolean isXY()
```
    Returns whether this operator is the Pauli-X gate or the Pauli-Y.
    
    Returns:
    
    true if this operator is X or Y
  - isDiagonal
```
public boolean isDiagonal()
```
    Returns whether this operator is represented by a diagonal matrix. This means that it is an operator diagonal in the computational basis.
    
    Returns:
    
    true if this operator is represented by a diagonal matrix
  - getMatrix
```
public double[][][] getMatrix()
```
    Returns this local Clifford operator as an array representing a 2x2 matrix of complex numbers. The indices are organized as follows:
```
    matrix[row][column][real/imaginary part]
  
```
    with the index ranges matrix[0..1][0..1][0..1].
    Returns:
    
    this local Clifford operator in a 2x2 complex matrix representation
  - multiply
```
public LocalCliffordOperator multiply(LocalCliffordOperator operator)
```
    Muliplies this operator with the specified local Clifford operator. The local Clifford operators form a multiplicative group C₁, the Clifford group. The multiplication in the Clifford group is not commutative.
    
    Parameters:
    
    operator - the operator to be multiplied from the right
    
    Returns:
    
    the product this · operator
  - equals
```
public boolean equals(LocalCliffordOperator operator)
```
    Checks whether this LC operator is equal to the specified operator.
    
    Parameters:
    
    operator - the local Clifford operator to be compared with this operator
    
    Returns:
    
    true if and only if both operators are equal
  - toString
```
public String toString()
```
    Returns this operator as a string representation of the 2x2 matrix representing it.
    
    Overrides:
    
    toString in class Object
    
    Returns:
    
    the 2x2 matrix representing this operator
  - equals
```
public boolean equals(Object o)
```
    Compares the specified object with this local Clifford operator.
    
    Overrides:
    
    equals in class Object
    
    Returns:
    
    true if and only if the specified object represents the same local Clifford operator than this operator
  - hashCode
```
public int hashCode()
```
    Returns the hash code for this local Clifford operator.
    
    Overrides:
    
    hashCode in class Object
    
    Returns:
    
    the hash code for this local Clifford operator

Class LocalCliffordOperator

Field Summary

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Field Detail

I

X

Y

Z

H

spiZ

smiZ

spiY

smiY

spiX

smiX

S

S_H

Constructor Detail

LocalCliffordOperator

LocalCliffordOperator

Method Detail

getName

conjugate

adjoint

isXY

isDiagonal

getMatrix

multiply

equals

toString

equals

hashCode