Robust resource-efficient quantum variational ansatz through evolutionary algorithm

Abstract

Variational quantum algorithms (VQAs) are promising methods to demonstrate quantum advantage on near-term devices as the required resources are divided between a quantum simulator and a classical optimizer. As such, designing a VQA which is resource-efficient and robust against noise is a key factor to achieve potential advantage with the existing noisy quantum simulators. It turns out that a fixed VQA circuit design, such as the widely-used hardware efficient ansatz, is not necessarily robust against imperfections. In this work, we propose a genome-length-adjustable evolutionary algorithm to design a robust VQA circuit that is optimized over variations of both circuit ansatz and gate parameters, without any prior assumptions on circuit structure or depth. Remarkably, our method not only generates a noise-effect-minimized circuit with shallow depth, but also accelerates the classical optimization by substantially reducing the number of parameters. In this regard, the optimized circuit is far more resource-efficient with respect to both quantum and classical resources. As applications, based on two typical error models in VQA, we apply our method to calculating the ground energy of the hydrogen molecule and the Heisenberg model. Simulations suggest that compared with conventional hardware efficient ansatz, our circuit-structure-tunable method can generate circuits apparently more robust against both coherent and incoherent noise, and hence more likely to be implemented on near-term devices.

Symmetry enhanced variational quantum spin eigensolver

“…The VQE has been extensively applied to quantum chemistry problems [16,[48][49][50] and experimentally realized on superconducting [16,49,55,56] and ion trap [1,10,57] quantum simulators. Several attempts have been made to enhance the VQE performance, including: minimizing the number of required measurements [58][59][60][61][62][63], improving the initialization [52,64,65], speeding up the classical optimization [66][67][68] and designing better circuits [69][70][71][72][73][74]. Several important phenomena in physics, such as topological phases [75], are described by the knowledge of a few low-energy eigenstates and not just the ground state.…”