{"id":1724,"date":"2023-10-17T10:17:25","date_gmt":"2023-10-17T14:17:25","guid":{"rendered":"https:\/\/blogs.mathworks.com\/matlab\/?p=1724"},"modified":"2024-02-08T11:03:01","modified_gmt":"2024-02-08T16:03:01","slug":"quantum-computing-in-matlab-r2023b-on-the-desktop-and-in-the-cloud","status":"publish","type":"post","link":"https:\/\/blogs.mathworks.com\/matlab\/2023\/10\/17\/quantum-computing-in-matlab-r2023b-on-the-desktop-and-in-the-cloud\/","title":{"rendered":"Quantum computing in MATLAB R2023b: On the desktop and in the cloud"},"content":{"rendered":"
Back in May of this year i attended the <\/span>ISC High Performance Computing conference<\/span><\/a> with a few other colleagues from MathWorks and was astonished at the number of booths related to various quantum computing intitiatives. I had more conversations about quantum computing in those few days than I'd had in years leading up to the event! As such, it seems rather timely that it's now possible to do quantum computing in MATLAB.<\/span><\/div>

Getting started with quantum computing in MATLAB<\/span><\/h2>
The MATLAB Support Package for Quantum Computing is a free add-on developed by MathWorks. There are several ways to install it but my preferred way is via the <\/span>Add-on Explorer<\/span><\/a>. <\/span><\/div>
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Once in Add-on explorer, just search for quantum computing and you'll find it. Another way to get it is <\/span>via its entry on File Exchange<\/span><\/a>. Quantum computing has been available in MATLAB for a while now -- since R2023a but it recently got a few additional updates so now is a good time to dive in. <\/span><\/div>
MATLAB currently supports a flavour of quantum computing called <\/span>gate-based quantum computing<\/span><\/a> at the root of which is a so-called quantum circuit. Let's create and visualise one<\/span><\/div>
gates = [hGate(1);<\/span><\/span><\/div><\/div>
cxGate(1,2);<\/span><\/span><\/div><\/div>
cxGate(1,3)];<\/span><\/span><\/div><\/div>
C = quantumCircuit(gates);<\/span><\/span><\/div><\/div>
plot(C)<\/span><\/span><\/div>
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This is a three-<\/span>qubit<\/span><\/a> circuit with three <\/span>quantum gates<\/span><\/a>. Each horizonal line in the plot represents one of the qubits and the gates are arranged from left to right in the order that they are applied. The first qubit has a <\/span>Hadamard gate<\/span><\/a> applied to it while <\/span>CNOT gates<\/span><\/a> have been applied to the second and third qubits, using the first qubit as the control.<\/span><\/div>
In order to actually run this quantum circuit, you'd need access to a real quantum computer and these are not the sort of thing that one has on their desk! <\/span><\/div>
For now, let's <\/span>simulate<\/span><\/a> this circuit, specifying that each qubit has an inital state of <\/span>|<\/mo>0<\/mn>\u27e9<\/mo><\/mrow><\/math><\/span> (never seen this notation before? It's an example of <\/span>bra-ket notation<\/span><\/a>) . We'll discuss how to run it on a real quantum computer later.<\/span><\/div>
S = simulate(C,<\/span>\"000\"<\/span>)<\/span><\/span><\/div>
S = <\/span><\/div>
QuantumState with properties:\r\n\r\n BasisStates: [8\u00d71 string]\r\n Amplitudes: [8\u00d71 double]\r\n NumQubits: 3\r\n<\/div><\/div><\/div><\/div><\/div><\/div>
Let's express the simulated quantum state as a <\/span>formula<\/span><\/a><\/div>
f = formula(S)<\/span><\/span><\/div>
f = <\/span><\/div>
\"0.70711 * |000> +\r\n 0.70711 * |111>\"\r\n<\/div><\/div><\/div><\/div><\/div><\/div>
There are two possible quantum states in this system but if you were were to actually observe it, you'd only see one. Which one you'd see is a matter of chance which is one of the consequences of quantum mechanics. Let's ask MATLAB for the possible states and the probabilities of seeing each one.<\/span><\/div>
[states,P] = querystates(S)<\/span><\/span><\/div>
states = <\/span>2\u00d71 string<\/span><\/div><\/div>
\"000\"
\"111\"
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P = <\/span>2\u00d71<\/span><\/div><\/div>
0.5000\r\n 0.5000\r\n<\/div>
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Each state has a 50% change of being measured. We can plot this as a histogram but it's not a particularly interesting one<\/span><\/div>
histogram(S)<\/span><\/span><\/div>
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If you actually had that quantum system, you'd not be able to directly measure probabilities. What you'd measure are the states and you'd do it a bunch of times to get an approximation of the probabilities. How do you do that in MATLAB?<\/span><\/div>
% Simulate 50 quantum measurements of the circuit<\/span><\/span><\/div><\/div>
M = randsample(S,100)<\/span><\/span><\/div>
M = <\/span><\/div>
QuantumMeasurement with properties:\r\n\r\n MeasuredStates: [2\u00d71 string]\r\n Counts: [2\u00d71 double]\r\n NumQubits: 3\r\n<\/div><\/div><\/div><\/div><\/div><\/div>
Put the result into a table<\/span><\/div>
simT = table(M.Counts,M.MeasuredStates,VariableNames=[<\/span>\"Counts\"<\/span>,<\/span>\"States\"<\/span>])<\/span><\/span><\/div>
simT = <\/span>2\u00d72 table <\/span><\/div>
 <\/span><\/th>Counts<\/span><\/th>States<\/span><\/th><\/tr><\/thead>
1<\/span><\/th>51<\/span><\/td>\"000\"<\/span><\/td><\/tr>
2<\/span><\/th>49<\/span><\/td>\"111\"<\/span><\/td><\/tr><\/tbody><\/table><\/div><\/div>
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This is roughly what you'd expect if the probability of getting each state is 50%. Anyone expecting exactly 50 Counts for each state should retake probability-101! <\/span><\/div>

Qubits? Gates? Quantum probabilities? What's going on?<\/span><\/h2>
\"824rqv.jpg\"<\/img><\/div>
I've shown you how to create and simulate a quantum circuit in MATLAB but, at this point, you may be wondering what on earth is going on? How does any of this relate to implementing numerical algorithms? This talk of qubits, gates and state probabilities is rather far removed from the variables, if-statements and for-loops that I used when I first studied how to solve problems. As Alice famously said \"Toto, I\u2019ve a feeling we\u2019re not in Kansas anymore\"<\/span><\/div>
Quantum computing is a totally different way of approaching computation that requires rather more explanation than I could fit into a blog post. We've got you covered, however. If you are totally new to the field of quantum computing, just start with this article in the MATLAB documentation: <\/span>Introduction to Quantum Computing<\/span><\/a>. You may also find this MathWorks <\/span>quantum computing cheat sheet<\/span><\/a> useful.<\/div>\r\n
Another article that you may find interesting is this in-depth one from fellow MathWorks blogger Sofia Ma: <\/span>Quantum Computing for Optimizing Investment Portfolios<\/span><\/a><\/div>
An insight that really helped me make my first baby steps into quantum computing is to understand that the states of quantum systems can be represented by vectors while all of the gates have matrix representations. Here are two of them. For more, see <\/span>Types of Quantum Gates<\/span><\/a><\/div>
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or in other words....<\/span><\/div>
\"824r3r.jpg\"<\/img><\/div>
If you have any other favourite sources for learning about quantum computing, let me know in the comments section. <\/span><\/div>

Applications of quantum computing<\/span><\/h2>
Maybe you don't care so much about how to design a quantum algorithm and want to jump straight to potential applications. MathWorks has you covered here as well with a range of algorithms fully implemented in the new framework and available in the documentation. These include<\/span><\/div>