Classical variational simulation of the Quantum Approximate Optimization Algorithm

A key open question in quantum computing is whether quantum algorithms can potentially offer a significant advantage over classical algorithms for tasks of practical interest. Understanding the limits of classical computing in simulating quantum systems is one key route to address this question. In this work we introduce a method to classically simulate quantum circuits consisting of several layers of parametrized gates, a key component of many variational quantum algorithms suitable for near-term quantum computers. The classical simulation approach we adopt is based on a neural-network quantum state parametrization of the many-qubit wave function. As a specific example, we focus on alternating layered ansatz states that are relevant for the Quantum Approximate Optimization Algorithm (QAOA). For the largest circuits simulated, we reach 54 qubits and 20 layers of independent gates (depth) without requiring large-scale computational resources. When available, we compare the obtained states with outputs of exact simulators and find good approximations for both the cost function values and state vectors. For larger number of qubits, our approach can be used to provide accurate simulations of QAOA at previously unexplored regions of its parameter space, and to benchmark the next generation of experiments in the Noisy Intermediate-Scale Quantum (NISQ) era.