Classical variational simulation of the Quantum Approximate Optimization Algorithm

A key open question in quantum computing is whether quantum algorithms can offer significant advantage over classical algorithms for tasks of practical interest. Probing classical computing limits in simulating quantum systems is one important route to address this question. We introduce a method to classically simulate quantum circuits made of several layers of parameterized gates, a key component of variational algorithms suitable for near-term quantum computers. Our approach is based on a neural-network parameterization of the many-qubit wave function, focusing on states relevant for the Quantum Approximate Optimization Algorithm (QAOA). We reach 54 qubits and QAOA depth of 4 without requiring large-scale computational resources. When possible, we compare obtained states with outputs of exact simulators and find good approximations for cost function values and state vectors. For larger qubit counts, our approach provides accurate QAOA simulations at previously unexplored regions of its parameter space, and to benchmark the next generation of experiments in the Noisy Intermediate-Scale Quantum era. (arXiv:2009.01760)