J.P. Locquet, J. Perret, et al.
SPIE Optical Science, Engineering, and Instrumentation 1998
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.
J.P. Locquet, J. Perret, et al.
SPIE Optical Science, Engineering, and Instrumentation 1998
Fan Jing Meng, Ying Huang, et al.
ICEBE 2007
B.K. Boguraev, Mary S. Neff
HICSS 2000
Yvonne Anne Pignolet, Stefan Schmid, et al.
Discrete Mathematics and Theoretical Computer Science