Density-Oriented Quantum Simulator using Block-Encoding Variational Eigensolvers

This paper presents the methods and initial results about a reconfigurable density-oriented quantum simulator, using a new block-encoding variational quantum eigensolver (BE-VQE), which is well suited to new materials and drug discovery. We first propose a modification to the traditional Variational Quantum Eigensolver (VQE), which uses block-encoded matrices instead of Pauli stings in situations where the Pauli decomposition is not readily available, or the Hamiltonian is not unitary. This process can reduce the number of quantum circuits to be executed when evaluating an operator's expectation value, but may lead to a longer operation time, which could be constrained by the quantum decoherence. The procedure to estimate the expectation value of a Hamiltonian operator (or its matrix representation) using block-encodings is discussed in the paper. Then, we use the expectation values in a block-encoding-based VQE and apply the solver to the Kohn-Sham Density Functional Theory (KS-DFT) formulation in a 3-dimensional discretized grid space. Also, several case studies are presented to illustrate the design and implementation options (including a variational quantum deflation - VQD algorithm) with different Hamiltonian formations and demonstrate the potential capabilities of the reconfigurable quantum simulator. Finally, the paper is concluded and a plan for future work is identified.

I. Introduction

Discovery and testing of new drugs, materials, structures and systems are not only time-consuming, but also highly expensive. Traditionally, simulation has been widely used to facilitate the research as a low-cost computational tool. Classical computing was highly effective in the past to solve simulation problems but is facing challenges due to the complexity of large simulated systems and increasing computational demands of sophisticated numerical methods. Emerging quantum computers show great promise in solving linear systems of equations and molecular-level simulation efficiently as compared to classical computers. Recent advances in quantum algorithms, such as the variational quantum eigensolver (VQE), etc., promise to offer potentially exponential speedup over classical counterparts and can be implemented on near-term quantum computers [1].