Resources on hybrid quantum-classical algorithms applied to combinatorial optimization problems

Question

I am doing a thesis on "Metaheuristics and Quantum Computing", and was wondering if anyone could recommend some papers/pages to read talking about hybrid quantum/classical computing.

(My idea is to get quantum population, evaluate through classical function and then considering the classical evaluation, change the original state of qubits to get new quantum sample, and so on and so forth.)

Answer 1

So for hybrid quantum-classical algorithms, I suggest looking at :

• The Quantum Approximate Optimization Algorithm
• Variational hybrid quantum-classical algorithms that include the so famous Variational Quantum Eigensolver applied for Max-Cut problems
• PennyLane which helps you in developping hybrid computation for optimization problems and Machine Learning. They give a list of references for hybrid computation in their references like the Practical optimization for hybrid quantum-classical algorithms.

List is non exhaustive of course.

Answer 2

Pedro! I assume you are familiar to Grover's algorithm. Therefore, I suggest to read carefully these two papers below:

1) Tight bounds on quantum searching (BBHT): it's a very broad Grover's algorithm analysis;

2) A quantum algorithm for finding the minimum (DH): this is the first Grover's algorithm application to optimization problems and we call DH (authors' name);

My first steps in quantum computing were in optimization problems. I think the papers below are a very good start:

3) Grover’s quantum algorithm applied to global optimization (BBW): an adaptation of Grover's to optimization and it uses DH at the framework;

4) Using modifications to grover’s search algorithm for quantum global optimization: a modification of BBW;

5) A hybrid method for quantum global optimization

6) A new hybrid classical-quantum algorithm for continuous global optimization problems: this last paper was produced at my research group at LNCC (Brazil) and you search several minimums with classical routines and the algorithm escapes with Grover.