Fermionic Adaptive Sampling Theory for Variational Quantum Eigensolvers

Abstract

Quantum chemistry has been identified as one of the most promising areas where quantum computing can have a tremendous impact. For current Noisy Intermediate-Scale Quantum (NISQ) devices, one of the best available methods to prepare approximate wave functions on quantum computers is the Adaptive Derivative-Assembled Pseudo-Trotter Ansatz Variational Quantum Eigensolver (ADAPT-VQE). However, ADAPT-VQE suffers from a significant measurement overhead when estimating the importance of operators in the wave function. In this work, we propose Fermionic Adaptive Sampling Theory VQE (FAST-VQE), a method for selecting operators based on importance metrics solely derived from the populations of Slater determinants in the wave function. Thus, our method mitigates measurement overheads for ADAPT-VQE as it is only dependent on the populations of Slater determinants which can simply be determined by measurements in the computational basis. We introduce two heuristic importance metrics, one based on Selected Configuration Interaction with perturbation theory and one based on approximate gradients. In state vector and finite shot simulations, FAST-VQE using the heuristic metric based on approximate gradients converges at the same rate or faster than ADAPT-VQE and requires dramatically fewer shots.

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Cited by in corpus (5)

• ADAPT-QSCI: Adaptive Construction of an Input State for Quantum-Selected Configuration Interaction
• Reducing the Resources Required by ADAPT-VQE Using Coupled Exchange Operators and Improved Subroutines
• Understanding and mitigating noise in molecular quantum linear response for spectroscopic properties on quantum computers
• Calculating the energy profile of an enzymatic reaction on a quantum computer
• Shot-Efficient ADAPT-VQE via Reused Pauli Measurements and Variance-Based Shot Allocation