qgates 1.0.3

Helper library for quantum matrix math

QGates

created by Austin Poor

A small file with some helper functions and quantum gates represented as numpy matrices.

Requirements

• Python 3
• Numpy

Installation

pip install qgates

Usage

Helper Functions

qgates.tens(a,*b)

Computes the tensor product of two or more numbers, vectors, or matrices.

qgates.matmul(a,*b)

Multiplies two or more vectors, or matrices. Wrapper around the built-in matmul operator.

qgates.state(arr)

Creates a state vector from either an iterable of 1s and 0s (or from an int that will be converted to a state vector based on its binary representation.

qgates.conjugate(v)

Computes the complex conjugate of a number or numpy array.

State Vectors

Basic Qubits

qgates.QB0: Quantum state 0

qgates.QB1: Quantum state 1

qgates.QB00: Quantum state 00

qgates.QB01: Quantum state 01

qgates.QB10: Quantum state 10

qgates.QB11: Quantum state 11

Bell States

qgates.BELL00: Bell state 00

qgates.BELL01: Bell state 01

qgates.BELL10: Bell state 10

qgates.BELL11: Bell state 11

Gate Matrices

qgates.IDEN: 2x2 Identity matrix

[[ 1, 0 ],
 [ 0, 1 ]]

qgates.NOT: 2x2 NOT matrix

[[ 0, 1 ],
 [ 1, 0 ]]

qgates.OR: 2x4 OR matrix

[[ 1, 0, 0, 0 ],
 [ 0, 1, 1, 1 ]]

qgates.AND: 2x4 AND matrix

[[ 1, 1, 1, 0 ],
 [ 0, 0, 0, 1 ]]

qgates.XOR: 2x4 XOR matrix

[[ 1, 0, 0, 1 ],
 [ 0, 1, 1, 0 ]]

qgates.NOR: 2x4 NOR matrix

[[ 0, 1, 1, 1 ],
 [ 1, 0, 0, 0 ]]

qgates.NAND: 2x4 NAND matrix

[[ 0, 0, 0, 1 ],
 [ 1, 1, 1, 0 ]]

qgates.COPY: A 4x2 gate matrix for copying a state vector

[[ 1, 0 ],
 [ 0, 0 ],
 [ 0, 0 ],
 [ 0, 1 ]]

qgates.SWAP: A 4x4 gate matrix for swapping a the middle two positions of a length-4 state vector

[[ 1, 0, 0, 0 ],
 [ 0, 0, 1, 0 ],
 [ 0, 1, 0, 0 ],
 [ 0, 0, 0, 1 ]]

qgates.CNOT: 4x4 Conditional-NOT gate. (Read more here)

[[ 1, 0, 0, 0 ],
 [ 0, 1, 0, 0 ],
 [ 0, 0, 0, 1 ],
 [ 0, 0, 1, 0 ]]

qgates.TOFFOLI: 8x8 Toffoli gate. (Read more here)

[[1, 0, 0, 0, 0, 0, 0, 0],
 [0, 1, 0, 0, 0, 0, 0, 0],
 [0, 0, 1, 0, 0, 0, 0, 0],
 [0, 0, 0, 1, 0, 0, 0, 0],
 [0, 0, 0, 0, 1, 0, 0, 0],
 [0, 0, 0, 0, 0, 1, 0, 0],
 [0, 0, 0, 0, 0, 0, 0, 1],
 [0, 0, 0, 0, 0, 0, 1, 0]]

qgates.HAD: 2x2 Hadamard gate. (Read more here)

[[ 1/√2,  1/√2 ],
 [ 1/√2, -1/√2 ]]