# [−][src]Crate q1tsim

A simple, efficient, quantum computer simulator.

# Overview

q1tsim is a simulator library for a quantum computer, written in Rust. Its goal is to be an easy to use, efficient simulator for the development and testing of quantum algorithms.

# Features

• Easy implementation and simulation of quantum circuits
• Supports the creation of arbitrary quantum gates
• Most common quantum gates already included
• Measurement in `X`, `Y`, or `Z` basis
• Possibility of measurement without affecting the quantum state
• Creation of histograms of measurement results over multiple runs
• Operations conditional on classical values
• Export of circuits to Open QASM and c-QASM for running your programs on other computers or simulators
• Export of circuits to LaTeX, for drawing pictures of your circuit

# Usage

To use q1tsim in your Rust application, add the following to your `Cargo.toml` file:

``````[dependencies]
q1tsim = "0.3"
``````

As an example, here is a 3-qubit quantum Fourier transform of the |000⟩ quantum state:

```use q1tsim::circuit::Circuit;
use q1tsim::gates::{CS, CT, Swap};

fn main()
{
// The number of times this circuit is evaluated
let nr_runs = 8192;

// Create a quantum circuit with 3 quantum bits and 3 classical (measurement)
// bits. The circuit starts by default with all quantum bits in the |0⟩
// state, so in this case |000⟩.
let mut circuit = Circuit::new(3, 3);

// Set up a 3-qubit quantum Fourier transform
// There is no predefined method on Circuit that implements a controlled
// `S` or `T` gate, so we use the `add_gate()` method for those.
circuit.h(2);
circuit.h(1);
circuit.h(0);

// Measure all quantum bits in the Pauli `Z` basis
circuit.measure_all(&[0, 1, 2]);

// Actually calculate the resulting quantum state, and perform the
// measurements, averaging over `nr_runs` runs.
circuit.execute(nr_runs);

// And print the results.
let hist = circuit.histogram_string().unwrap();
for (bits, count) in hist.iter()
{
println!("{}: {}", bits, count);
}
}```

The result should be a more or less equal distribution over the eight possible states (000, 001, ..., 111).

# Creating a circuit

Struct Circuit is the main structure used in creating a quantum program. The basic layout of a program to create a quantum circuit, execute it, and collect the results, is as follows:

```use q1tsim::circuit::Circuit;

// Create a new circuit with `nr_qbits` quantum bits and `nr_cbits`
// classical bits
let nr_qbits = 2;
let nr_cbits = 2;
let mut circuit = Circuit::new(nr_qbits, nr_cbits);

// Add operations on the circuit. In this case, a Hadamard transform on the
// first bit, followwed by a CNOT gate with the first bit as control and
// the second bit as target.
circuit.h(0);
circuit.cx(0, 1);

// Add a measurement of the resulting quantum state. This measures the first
// qbit into classical bit 0, and the second qbit into classical bit 1.
circuit.measure_all(&[0, 1]);

// Now execute the circuit, averaging measurements over `nr_runs` runs
// of the circuit.
let nr_runs = 1024;
circuit.execute(nr_runs);

// And finally collect the results. The `histogram_vec()` method returns a
// vector with at each index `i` the number if times the measurement returned
// `i` in the classical register.
let hist = circuit.histogram_vec();```

Since version 0.3, many of the methods on `Circuit` will return a `Result`, possibly containing an error code (e.g. if invalid bit numbers are used). Checking the result of each modification of the circuit quickly becomes tedious, so the circuit macro was added that can make multiple method calls and immediately returns on the first error encountered (or returns `Ok(())` if all calls were successful). With this, the previous program can be written as

```let nr_qbits = 2;
let nr_cbits = 2;
let mut circuit = circuit!(nr_qbits, nr_cbits, {
h(0);
cx(0, 1);
measure_all(&[0, 1]);
}).expect("Failed to build circuit");

let nr_runs = 1024;
circuit.execute(nr_runs);
let hist = circuit.histogram_vec();```

# Custom gates

Using the Circuit::add_gate() method, arbitrary gates can be added to a circuit. You can define your own custom gates by implementing the Gate trait. To implement this trait, the type should implement at least the description(), nr_affected_bits(), and matrix() methods. The `description()` method should return a short textual identifier or label for the gate, while `nr_affected_bits()` returns the number of qubits on which the gate operates. The `matrix()` method should return a matrix of size `2``n``×2``n`, where `n` is the number of affected bits, that describes the unitary transformation that the gate implements. An example of a simple custom gate that rotates the `|01⟩` and `|10⟩` components of a pair of qubits, is given below:

```use ndarray::array;
use q1tsim::ExportGate;

#[derive(ExportGate)]
struct Mix
{
alpha: f64
}

impl q1tsim::gates::Gate for Mix
{
fn description(&self) -> &str { "M" }
fn nr_affected_bits(&self) -> usize { 2 }
fn matrix(&self) -> q1tsim::cmatrix::CMatrix
{
let o = q1tsim::cmatrix::COMPLEX_ONE;
let z = q1tsim::cmatrix::COMPLEX_ZERO;
let c = self.alpha.cos() * o;
let s = self.alpha.sin() * o;
array![
[o, z,  z, z],
[z, c, -s, z],
[z, s,  c, z],
[z, z,  z, o]
]
}
}```

Types implementing the `Gate` trait may optionally also implement the apply() family of methods if a more optimal implementation than simply multiplying by its associated matrix can be found.

# Exporting gates and circuits

The discerning reader may have notices the `#[derive(ExportGate)]` statement on the custom gate in the listing above. This makes the type use the default implementations of the export functions for a gate. Currently, there are three traits for exporting a gate:

• OpenQasm for exporting a gate to OpenQasm code.
• CQasm for exporting a gate to c-Qasm code.
• Latex for exporting a gate to LaTeX.

You can use the default implementation for each of these traits by deriving them, e.g.

```use q1tsim::OpenQasm;
use q1tsim::gates::Gate;

#[derive(OpenQasm)]
struct MySpecialGate {}

impl Gate for MySpecialGate {
/* ... */
}```

The default implementations for OpenQasm and CQasm simply return an error, since there is no way 1 to know how to encode a custom gate in these formats. The default implementation for the LaTeX export simply draws a rectangular box with the gate description inside. As seen before, if you want to use default definitions for all export traits, derive from `ExportGate`.

Note that to use a gate type in a circuit, it must be exportable, so an implementation for the export traits must be defined for your custom type, either through deriving or by providing your own implementation.

1. No reasonable way at least. Technically, we could take the matrix for the gate, decompose it into primitive gates, and export the corresponding code.

## Modules

 circuit cmatrix error export gates permutation qustate

## Macros

 assert_complex_matrix_eq assert_complex_vector_eq circuit circuit_method_check declare_controlled declare_controlled_cost declare_controlled_impl declare_controlled_impl_gate declare_controlled_latex declare_controlled_qasm declare_controlled_type