MatlabQAOA

Simulating the quantum approximate optimization algorithm with Matlab

Table of contents

1. Installation
2. Usage

Installation <a name="installation"></a>

Installation requires Matlab version 2018b or newer.

Usage <a name="usage"></a>

The code is executed using the problem.m script file. To get started you begin by specifying the cost Hamiltonian of which you want to find the ground state of as a 1-D array (column vector) with all of its energy eigenvalues. Storing the cost Hamiltonian as a vector is more memory efficient than storing it as a matrix. We can do this since the cost Hamiltonian is diagonal in the computational basis. Next, you choose the number of iterations that you want the QAOA to run, i.e. the variable p. You have the option to specify the angles gamma and beta or simply leave them as empty arrays. If you specify gamma and beta as arrays, the QAOA will use these angles to construct the variational state. Otherwise, if the angles are given by empty arrays the code when executed, will try to find the optimal ones using MATLAB´s GlobalSearch classical optimizer as default. You can change which classical optimizer that you want to use. There are seven ones in total to choose from.

1. GlobalSearch (Default)
2. MultiStart
3. Bayesian
4. BayesianHybridNelderMead
5. NelderMead
6. ParticleSwarm
7. BruteForce

When you run the problem.m script file, it will call on the QAOA algorithm (qaoa.m) file using the qaoa function. This function can have up to six input variables: two are required the rest are optional! The required ones are: 1. The eigenvalues of the cost Hamiltonian cost and 2. The number of iterations p of the QAOA algorithm. The optional ones are 3. The gamma angles; 4. The beta angles; 5. The classical optimizer and 6 potential starting points for the classical optimizer to use. The qaoa function will return the final variational state |γ,β⟩ (using either the given input angles or the best-found angles by the classical optimizer) and the result from the classical optimizer as a struct data type.

A typical example could be

% Eigenvalues of the Cost Hamiltonian given as a column vector for a single spin 1/2 particle
cost = [1;-1];

% Circuit depth
p = 1;
% Angles
gamma = [];
beta = [];
% Classical optimizer
minimizer = 'GlobalSearch';
[final_state,result] = qaoa(cost,p,gamma,beta,minimizer);