Quantum Gates¶

Built-In Gates¶

There are a number of gates built into QCGPU. They can all be applied the same way:

import qcgpu

register = qcgpu.State(2)

state.h(0) # Applies the Hadamard (H) gate to the first qubit.
state.x(1) # Applies a pauli-x (NOT) gate to the second qubit.

h and x can be replaced with any of the following:

• The Hadamard gate: h - state.h(0)
• The S gate: s - state.s(0)
• The T gate: t - state.t(0)
• The Pauli-X / NOT gate: x - state.x(0)
• The Pauli-Y gate: y - state.y(0)
• The Pauli-Z gate: z - state.z(0)
• The CNOT gate: cx - state.cx(0, 1) # CNOT with control = 0, target = 1
• The SWAP gate: swap - state.swap(0,1) # Swaps the 0th and 1st qubit
• The Toffoli gate: toffoli - state.toffoli(0, 1, 2) # Toffoli with controls = (0, 1), target = 2

These are all shorthand methods for the application of arbitrary gates. For example, the application of a Hadamard gate above is shorthand for

import qcgpu

h = qcgpu.gate.h()

register = qcgpu.State(5)
register.apply_gate(h, 0)

You can also use any of the gates as controlled gates. For example, the application of the CNOT gate above is shorthand for

import qcgpu

x = qcgpu.gate.x()

register = qcgpu.State(5)
register.apply_controlled_gate(x, 0, 1)

Applying A Gate To A Whole Register¶

There is a convenience method to apply a gate to every qubit in the register. The following applies a Hadamard gate to the whole register,

import qcgpu

h = qcgpu.gate.h()

register = qcgpu.State(5)
register.apply_all(h)

User Defined Gates¶

Gates in QCGPU are represented by the qcgpu.Gate class.

The only gates that can be defined by the user are single qubit gates.

The process of creating a gate is

import qcgpu
import numpy as np

gate_matrix = np.array([
    [1, 0],
    [0, np.exp(1j * np.pi / 4)]
])

gate = qcgpu.Gate(gate_matrix)

The input to the Gate constructor is checked to be a 2x2 unitary matrix.

This newly created gate can then be applied the long hand way,

import qcgpu

register = qcgpu.State(2)
register.apply_gate(gate, 0)