Simulating a quantum computer in classical computer

Quantum Simulator? Quantum Computing?

We heard a lot about quantum computers and what happens when one is build. We have several algorithms that can run on this computer and it will "shift" with cryptography. However, can we simulate a quantum computer? Can I run quantum algorithms already? 

The simple answer is: yes, for both questions.

Yes, the simulation is possible. However, that does not mean that we can break the crypto. The simulators that are available to use have several restrictions. Such as:

• Number of operations;
• Size of circuit;
• Number of qubits that is possible to use;

Simulators, Special languages and etc...

IBM Q Experience

IBM developed "IBM Q experience" where you can design your circuit and run. The circuit will run on their computers and when it is ready, i.e., when your computation finish you will receive an email. In addition of the simulator, IBM added a nice introduction about quantum algorithms.

Limitations

The problem with the IBM Q  is that it just allows you to use 16 qubits as a member of the community or 17 qubits for commercial use. Also, if you use the community edition sometimes you could be "stuck" in the queue. The reason is that with the community edition you share the "quantum simulator" with the other users and it cannot run more than a certain number of circuits. 

Microsoft Liquid

Microsoft is in the running of "quantum simulators", in fact, they developed their own language for quantum simulation, they created Liquid.  It is "cross-platform", i.e., you can run in Windows, Mac OS or Linux. However, if you decide to use in your Linux distro, you will need to download Mono and then run an executable compiled for Windows. 

The good side of "The Language Integrated Quantum Operations Simulator" is that it is based in "F#" and it came with a lot of examples such as "Quantum Teleportation", "Shor's Algorithm" and others algorithms. 

In fact, the paper Quantum Resource Estimates for Computing Elliptic Curve Discrete Logarithms uses liquid to implement an attack on ECC even with the following limitations. 

Limitations

Liquid allow you to use just 23 qubits. However, the paper before used more than this amount, the reason (when I asked on github) was that the authors are from Microsoft and they can use as much as they need. 

LibQuantum

The libquantum is a library written in C that you can extend and use to create your circuit. It is considerably fast and easy to use. The good side of this library is that you can use as many as qubits you want, the only problem is that if you use a big amount of qubits your "program" will be very slow and it will use a big quantity of memory. 

When I am running tests, I am using this library. I am going to create a small tutorial to use this library. I am assuming that the reader/user is on linux distribution and has a little bit of knowledge of C. First step is to download the library: www.libquantum.de

After, downloading, compile the library and install the library in your system so you will be able to use it. 

First, let's create a register and do some operations:

In the code, we first create a quatum register with initial value in 0 and with 2 qubits. After, we print the content of the register, in this example it will be "0" and finally we do some operations with the register. We perform a simple "CNOT" gate but because the value of the register is "|00>" nothing will change. If we change the value in the 4th line from 0 to 1, in the end we will have a register with "|11>".

The library provides other operations such as: Toffoli, Sigma X, Sigma Y, Sigma Z, phase scale, phase kick and hadamard. 

In the code below we are going to have a more "complex" circuit:

Now, we initialize the quantum register with the value "|10>" and perform first a Hadamard transform to put the qubit 0 in superposition and after we aply a cnot gate with the value from qubit at position 1 to the target qubit at position 0. In the end, we are going to have a composed state as:

0.707107 +0.000000i|3> (5.000000e-01) (|11>)

 0.707107 +0.000000i|0> (5.000000e-01) (|00>)

The library came with more examples that you can compile and run by yourself. I hope that you like this quick tutorial how to simulate quantum computers in classical computers.