Layer VQE: A Variational Approach for Combinatorial Optimization on Noisy Quantum Computers

Abstract

Combinatorial optimization on near-term quantum devices is a promising path to demonstrating quantum advantage. However, the capabilities of these devices are constrained by high noise levels and limited error mitigation. In this paper, we propose an iterative Layer VQE (L-VQE) approach, inspired by the Variational Quantum Eigensolver (VQE). We present a large-scale numerical study, simulating circuits with up to 40 qubits and 352 parameters, that demonstrates the potential of the proposed approach. We evaluate quantum optimization heuristics on the problem of detecting multiple communities in networks, for which we introduce a novel qubit-frugal formulation. We numerically compare L-VQE with QAOA and demonstrate that QAOA achieves lower approximation ratios while requiring significantly deeper circuits. We show that L-VQE is more robust to sampling noise and has a higher chance of finding the solution as compared with standard VQE approaches. Our simulation results show that L-VQE performs well under realistic hardware noise.

A Structured Survey of Quantum Computing for the Financial Industry

“…Amongst the most widely used algorithms for this type of procedure are the Variational Quantum Eigensolver (VQE) [56] and the Quantum Approximate Optimization Algorithm (QAOA) [57]. Both of these algorithms are classicalquantum hybrid algorithms, i.e., they combine the use of a classical computer with a (smaller) quantum computer which can further improve the applicability of these algorithms on current quantum computing devices [58].…”

A Convergence Theory for Over-parameterized Variational Quantum Eigensolvers

“…Commonly studied VQAs include Quantum Neural Networks (QNNs) [13] used to perform classification tasks in machine learning, and Variational Quantum Eigensolvers (VQEs) that are used to find the ground state of a given Hamiltonian from physics or chemistry [26]. Variational Quantum Eigensolvers have gained particular interest: with applications to quantum chemistry [6], or to combinatorial optimization [12,22]. The quantum systems used in VQEs are challenging to classically simulate so there is a promising possibility of quantum computational advantages for these important applications.…”

Quantum agents in the Gym: a variational quantum algorithm for deep Q-learning

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