2021/02/28 by Stuart M. Harwood, Dimitar Trenev, Spencer T. Stober +5 · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Adiabatic process #Algorithm #Applied mathematics #Computer science #Eigenvalues and eigenvectors #Hamiltonian (control theory) #Mathematical optimization #Mathematics #Neural Networks and Reservoir Computing #Parameterized complexity #Physics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum algorithm #Quantum circuit #Quantum computer #Quantum error correction #Quantum mechanics #quant-ph
paper · pdf · doi:10.1145/3479197
published as ACM Transactions on Quantum Computing, Volume 3 (1), 2022 · 21 pages, 5 figures
arxiv created 2021/08/16 · openalex publication_date 2022/01/14 · arxiv updated 2022/02/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The variational quantum eigensolver (VQE) is a hybrid quantum-classical algorithm for finding the minimum eigenvalue of a Hamiltonian that involves the optimization of a parameterized quantum circuit. Since the resulting optimization problem is in general nonconvex, the method can converge to suboptimal parameter values that do not yield the minimum eigenvalue. In this work, we address this shortcoming by adopting the concept of variational adiabatic quantum computing (VAQC) as a procedure to improve VQE. In VAQC, the ground state of a continuously parameterized Hamiltonian is approximated via a parameterized quantum circuit. We discuss some basic theory of VAQC to motivate the development of a hybrid quantum-classical homotopy continuation method. The proposed method has parallels with a predictor-corrector method for numerical integration of differential equations. While there are theoretical limitations to the procedure, we see in practice that VAQC can successfully find good initial circuit parameters to initialize VQE. We demonstrate this with two examples from quantum chemistry. Through these examples, we provide empirical evidence that VAQC, combined with other techniques (an adaptive termination criteria for the classical optimizer and a variance-based resampling method for the expectation evaluation), can provide more accurate solutions than “plain” VQE, for the same amount of effort.