How to Write a Simulator for Quantum Circuits from Scratch: A Tutorial

In this lecture note, the authors provide an introductory tutorial on simulating quantum circuits on a personal laptop using Javascript, without the requirement of installing any packages or libraries. In particular, the main focus of the lecture note is not to compete in functionalities with existing full-featured frameworks, but rather focus on the implementation of the underlying algorithms in building a quantum circuit simulator. The lecture note includes a self-contained section on the basic operations and conventions that are used in quantum mechanics and quantum computation, which is beneficial for people who have minimal or zero background in these areas. The authors also emphasize on the time complexity of various algorithms used to perform quantum circuit computations.

The targeted audience of this lecture note is software engineers with minimal exposure to quantum computing. However, it will also be beneficial to readers who have a solid background in quantum mechanics but with minimal programming experience. To better accommodate a broader range of backgrounds, I suggest to including the following details to the lecture note:

1. The console output of the code that represents the quantum circuit in Figure 1:

n = 3; // number of qubits $\psi$ = $( | 0 \rangle^ {\otimes {\rm n}} )$; // initialization $\psi$ = qubitWiseMultiply(n,Hadamard,1,$\psi$); $\psi$ = qubitWiseMultiply(n,PauliX,2,$\psi$); $\psi$ = qubitWiseMultiply(n,PauliX,0,$\psi$,[[1,true]]); $\psi$ = qubitWiseMultiply(n,PauliZ,0,$\psi$); $\psi$ = qubitWiseMultiply(n,PauliX,2,$\psi$,[[1,true]]);

and Figure 4 respectively:

n = 3; // number of qubits $\psi$ = $( | 0 \rangle^ {\otimes {\rm n}} )$; // initialization $\psi$ = qubitWiseMultiply(n,Hadamard,0,$\psi$); $\psi$ = applySwap(n,0,2,$\psi$); $\psi$ = qubitWiseMultiply(n,PauliX,1,$\psi$,[[2,false]]); $\psi$ = qubitWiseMultiply(n,PauliX,0,$\psi$,[[1,true]]); $\psi$ = qubitWiseMultiply(n,PauliY,0,$\psi$); $\psi$ = applySwap(n,1,2,$\psi$,[[0,true]]); $\psi$ = qubitWiseMultiply(n,PauliZ,1,$\psi$);

1. Include a section or appendix on the code structure of the index.html file, outlining the main Javascript classes (Util, Complex, CMatrix, Sim) and how users can call functions and view results of console output. This will be helpful for physics learners who like to verify the behavior of the quantum circuit simulator and explore various gate applications.

2. (Optional) Include 1 or 2 consistency checks with existing frameworks, such as IBM Quantum Composer or Quirk. The authors are welcome to include images of their own frontend webpage design for illustration purposes.

I recommend the manuscript to be published in SciPost Physics Lecture Notes after revision.

Pleaser refer to report.

Ask for minor revision