VQE Method: A Short Survey and Recent Developments

2021/03/15 by Dmitry A. Fedorov, Bo Peng, Fedorov, Dmitry A. +5 · 31 citations
Computer Science · Physics and Astronomy · #FOS: Physical sciences #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Physics (quant-ph) #Quantum-Dot Cellular Automata #quant-ph

paper · pdf · doi:10.48550/arxiv.2103.08505

openalex publication_date 2021/03/15 · arxiv created 2021/08/30 · arxiv updated 2021/09/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The variational quantum eigensolver (VQE) is a method that uses a hybrid quantum-classical computational approach to find eigenvalues and eigenvalues of a Hamiltonian. VQE has been proposed as an alternative to fully quantum algorithms such as quantum phase estimation because fully quantum algorithms require quantum hardware that will not be accessible in the near future. VQE has been successfully applied to solve the electronic Schrödinger equation for a variety of small molecules. However, the scalability of this method is limited by two factors: the complexity of the quantum circuits and the complexity of the classical optimization problem. Both of these factors are affected by choice of the variational ansatz used to represent the trial wave function. Hence, the construction of efficacious ansatz is an active area of research. Put another way, modern quantum computers are not capable of executing deep quantum circuits produced by using currently available ansatze for problems that map onto more than several qubits. In this review, we present recent developments in the field of designing effective ansatzes that fall into two categories -- chemistry inspired and hardware efficient -- that produce quantum circuits that are easier to run on modern hardware. We discuss the shortfalls of ansatzes originally formulated for VQE simulations, how they are addressed in more sophisticated methods, and the potential ways for further improvements.

Citations

• A Fast Learning Algorithm for Deep Belief Nets
• Simulating physics with computers
• Tapering off qubits to simulate fermionic Hamiltonians
• Quantum Computing in the NISQ era and beyond
• Ground-state energy estimation of the water molecule on a trapped ion quantum computer
• Fault Tolerant Quantum Computation with Constant Error
• Quantum Filter Diagonalization: Quantum Eigendecomposition without Full Quantum Phase Estimation
• How will quantum computers provide an industrially relevant computational advantage in quantum chemistry?
• Toward Trainability of Quantum Neural Networks

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• Slice-Wise Initial State Optimization to Improve Cost and Accuracy of the VQE on Lattice Models
• Scalable parallel simulation of quantum circuits on CPU and GPU systems
• Quantum Computation of the Electronic Structure of Some Prototype Solids
• Multi-QIDA method for VQE state preparation in molecular systems
• BenchRL-QAS: Benchmarking reinforcement learning algorithms for quantum architecture search
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• Accelerating Parameter Initialization in Quantum Chemical Simulations via LSTM-FC-VQE
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