Creating random Hamiltonian

[TreeratKJ]

What feature should we add?

Context To create a quantum system contains random Hamiltonians with its elements are randomly generated from a normal(Gaussian) distribution (can add another distribution in the future)

Suggested Implementation

1. Create a randomH function in qg.QuantumToolbox.operators with the input parameters: dimension: int - dimension of Hilbert space sparse: bool - if True, return sparse matrix mean: int - mean of the distribution SD: int - standard deviation of the distribution normalise: bool - if True, return normalised matrix symmetric: bool - if True, return symmetry matrix seedNum: int - specify the seed for random function

   • If setting seedNum=None, the function will generate random matrix and we can know the seedNum of the output matrix such that we are able to reproduce this random matrix.
   • If creating new random operator with the same seedNum, it will return the same matrix.

2. Create a randSys class in qg.classes.Qsystem which is using randomH operator Also, we are able to know the seedNum of the randomH operator

Problem

• In qg.classes.Qsystem, it requires dimension, operator, and frequency. But we cannot set the values inside the operator function, so we cannot set seedNum in randomH operator.
• If we randomly choose seedNum in randomH, we can generate a random matrix every time, but cannot reproduce the previous random matrix because we don't know the seedNum

Benefits from this implementation

• Able to generate a quantum system with random Hamiltonian
• Able to use _createTerm to add a random Hamiltonian term to any quantum systems that is currently in QuanGuru, i.e. _qg.QubitcreateTerm(operator=qg.randomH,...).
• This random Hamiltonian system can be used to test the Trotterization performance for a general system

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Branch 234-Creating_random_Hamiltonian created!