As quantum computing field is starting to reach the realm of advantage over classical algorithms, simulating quantum circuits becomes increasingly challenging as we design and evaluate more complex quantum algorithms. In this context, tensor networks, which have become a standard method for simulations in various areas of physics, from many-body quantum physics to quantum gravity, offer a natural approach. Despite the availability of efficient tools for physics simulations, simulating quantum circuits presents unique challenges, which I address in this work, specifically using the Quantum Approximate Optimization Algorithm as an example. The main results of this work span several steps of the problem. For the step of creating a tensor network, I demonstrate that applying the diagonal representation of quantum gates leads to a complexity reduction in tensor network contraction by one to four orders of magnitude. For large-scale contraction of tensor networks, I propose a step-dependent parallelization approach which performs slicing of partially contracted tensor network. Finally, I study tensor network contractions on GPU and propose an algorithm of contraction which uses both CPU and GPU to reduce GPU overhead. In our benchmarks, this algorithm reduces time to solution from 6 seconds to 1.5-2 seconds.
Danylo Lykov (Fri,) studied this question.