Quantum algorithms for generator coordinate methods
- URL: http://arxiv.org/abs/2212.09205v1
- Date: Mon, 19 Dec 2022 01:22:19 GMT
- Title: Quantum algorithms for generator coordinate methods
- Authors: Muqing Zheng, Bo Peng, Nathan Wiebe, Ang Li, Xiu Yang, Karol Kowalski
- Abstract summary: This paper discusses quantum algorithms for the generator coordinate method (GCM) that can be used to benchmark molecular systems.
We illustrate the performance of the quantum algorithm for constructing a discretized form of the Hill-Wheeler equation for ground and excited state energies.
- Score: 12.744157326232749
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: This paper discusses quantum algorithms for the generator coordinate method
(GCM) that can be used to benchmark molecular systems. The GCM formalism
defined by exponential operators with exponents defined through generators of
the Fermionic U(N) Lie algebra (Thouless theorem) offers a possibility of
probing large sub-spaces using low-depth quantum circuits. In the present
studies, we illustrate the performance of the quantum algorithm for
constructing a discretized form of the Hill-Wheeler equation for ground and
excited state energies. We also generalize the standard GCM formulation to
multi-product extension that when collective paths are properly probed, can
systematically introduce higher rank effects and provide elementary mechanisms
for symmetry purification when generator states break the spatial or spin
symmetries. The GCM quantum algorithms also can be viewed as an alternative to
existing variational quantum eigensolvers, where multi-step classical
optimization algorithms are replaced by a single-step procedure for solving the
Hill-Wheeler eigenvalue problem.
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