Adaptive variational preparation of the Fermi-Hubbard eigenstates

Abstract

Approximating the ground states of strongly interacting electron systems in quantum chemistry and condensed matter physics is expected to be one of the earliest applications of quantum computers. In this paper, we prepare highly accurate ground states of the Fermi-Hubbard model for small grids up to 6 sites (12 qubits) by using an interpretable, adaptive variational quantum eigensolver(VQE) called ADAPT-VQE. In contrast with non-adaptive VQE, this algorithm builds a system-specific ansatz by adding an optimal gate built from one-body or two-body fermionic operators at each step. We show this adaptive method outperforms the non-adaptive counterpart in terms of fewer variational parameters, short gate depth, and scaling with the system size. The fidelity and energy of the prepared state appear to improve asymptotically with ansatz depth. We also demonstrate the application of adaptive variational methods by preparing excited states and Green functions using a proposed ADAPT-SSVQE algorithm. Lower depth, asymptotic convergence, noise tolerance of a variational approach, and a highly controllable, system-specific ansatz make the adaptive variational methods particularly well-suited for NISQ devices.

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Cited by in corpus (5)

• Classical Pre-optimization Approach for ADAPT-VQE: Maximizing the Potential of High-Performance Computing Resources to Improve Quantum Simulation of Chemical Applications
• A Quantum Annealing Protocol to Solve the Nuclear Shell Model
• Efficient Fermi-Hubbard model ground-state preparation by coupling to a classical reservoir in the instantaneous-response limit
• Gradient Scalability and Taylor Surrogation of Quantum Cost Landscapes
• An occupation number quantum subspace expansion approach to compute the single-particle Green function: an opportunity for noise filtering