Quantum Gates

Gates are used to manipulate quantum registers and to implement quantum algorithms.

Built In Gates

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

use qcgpu::State;

let mut state = State::new(5, 0);

state.h(0); // Applies the hadamard (`h`) gate to the 0th qubit

h can be replaced with any of the following:

The hadmard 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 control1 = 0, control1 = 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

use qcgpu::gates::{h};
use qcgpu::State;

let mut state = State::new(5, 0);
state.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

use qcgpu::gates::{x};
use qcgpu::State;

let mut state = State::new(5, 0);
state.apply_controlled_gate(x(), 0, 1);

User Defined Gates

Gates in QCGPU are represented by the Gate struct, available through qcgpu::Gate.

It is defined as follows:

extern crate num_complex;
use num_complex::Complex32;

struct Gate {
    a: Complex32,
    b: Complex32,
    c: Complex32,
    d: Complex32,
}

To create your own gate, you will need to add the num_complex crate to your dependencies.

A gate is created as follows:

let x = Gate {
    Gate {
        a: Complex32::new(0.0, 0.0),
        b: Complex32::new(1.0, 0.0),
        c: Complex32::new(1.0, 0.0),
        d: Complex32::new(0.0, 0.0),
    }
}

This corresponds to the matrix

\[x = \begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix}\]

This can be applied using the same long hand method as above:

let mut state = State::new(1, 0);
state.apply_gate(x, 0);

gates.md 2.2 KB Histórico Raw

Quantum Gates

Built In Gates

User Defined Gates

gates.md 2.2 KB

Histórico Raw