Abstract

Current quantum computers are limited to small numbers of noisy qubits with low decoherence times. Hybrid quantum-classical algorithms have been devised to make the most of these noisy intermediate scale quantum (NISQ) devices. One of the most popular is the Variational Quantum Eigensolver (VQE) [1] which is based around the classical optimization of a quantum cost function. This method has found applications in finding the ground state for chemical systems. In this context, the unitary coupled cluster (UCC) [2] ansatz has resurfaced as a convenient parametrisation, due to its relatively well-behaved energy landscape, and particle-number and spin preserving properties. However, the circuits required to encode UCC on a quantum computer are often too deep to be implemented on current machines. One way to reduce the size of these circuits is to decrease the number of parameters in the ansatz. Quantum Monte Carlo (QMC) methods have been shown to be efficient at sampling the most important contributions to a wavefunction first and therefore show promise as screening approaches for more complicated methods. Therefore, we present a stochastic implementation of UCC in the coupled cluster Monte Carlo (CCMC) framework [3]. The results from this approach are shown to be in good agreement with conventional UCC and then the method is used to screen cluster amplitudes for use in UCC -based VQE calculation. We obtain highly accurate results for a series of small molecules and show that significant reductions in quantum resources can be achieved in a systematically improvable way [4].

References

1. A. Peruzzo, J. McClean, P. Shadbolt, M.-H. Yung, X.-Q. Zhou, P. J. Love, A. Aspuru-Guzik and J. L. O’Brien, Nat. Commun., 2014, 5, 1

2. R. J. Bartlett, S. Kucharski and J. Noga, Chem. Phys. Lett, 1989, 155, 133

3. M.-A. Filip and A. J. W. Thom, J. Chem. Phys., 2020, 153, 214106

4. M.-A. Filip, N. Fitzpatrick, D. Muñoz Ramo and A. J. W. Thom, 2021, arXiv:2108.10912