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Bulletin of the American Physical Society

Coherent oscillations in diabatic quantum annealing schedules

Robbyn Trappen, Xi Dai, Daniel Tennant, Denis Melanson, Muhammet Ali Yurtalan, Rui Q. Yang, Rabindra Nath Das, David K. Kim, Alexander J. Melville, Bethany M. Niedzielski, William D. Oliver, Jonilyn Yoder, Steven J. Weber, Andrew J. Kerman, Joseph Gibson, Jeffrey A. Grover, Steven Dissler, James I. Basham, S P Novikov, Tameem Albash, Evgeny Mozgunov, Mostafa Khezri, Huo Chen, Daniel A. Lidar, Adrian Lupaşcu

Published Mar 15, 2021• 0 citations
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We formulate and analyze a double-slit proposal for quantum annealing, which involves observing the probability of finding a two-level system (TLS) undergoing evolution from a transverse to a longitudinal field in the ground state at the final time tf. We demonstrate that for annealing schedules involving two consecutive diabatic transitions, an interference effect is generated akin to a double-slit experiment. The observation of oscillations in the ground state probability as a function of tf (before the adiabatic limit sets in) then constitutes a sensitive test of coherence between energy eigenstates. This is further illustrated by analyzing the effect of coupling the TLS to a thermal bath: increasing either the bath temperature or the coupling strength results in a damping of these oscillations. The theoretical tools we introduce significantly simplify the analysis of the generalized Landau-Zener problem. Furthermore, our analysis connects quantum annealing algorithms exhibiting speedups via the mechanism of coherent diabatic transitions to near-term experiments with quantum annealing hardware.
Diabatic quantum annealing with variationally optimized schedules can exhibit exponential speedups over conventional adiabatic quantum annealing, as was demonstrated numerically for a frustrated Ising ring model by C{ô}t{é} et al. Here we identify Landau-Zener-St{ü}ckelberg interference as the underlying mechanism for this speedup, and based on this insight we propose a variational schedule ansatz with far fewer parameters. This simplified ansatz allows us to show analytically that the classical optimization of the schedule parameters can be done in polynomial time and discuss conditions when we expect this type of mechanism to provide speedups over adiabatic annealing. Furthermore, we provide an analytical argument that coherence is an essential resource for this mechanism, which we verify numerically. We perform extensive numerical tests of the proposed ansatz and observe substantial improvements over adiabatic annealing and competitive performance in particularly challenging problem instances, including a well-studied MAXCUT instance commonly used for benchmarking. Our work shows that explicitly leveraging physical mechanisms can lead to more effective designs of variational annealing algorithms.
Abstract We formulate and analyze a double-slit proposal for quantum annealing, which involves observing the probability of finding a two-level system (TLS) undergoing evolution from a transverse to a longitudinal field in the ground state at the final time tf. We demonstrate that for annealing schedules involving two consecutive diabatic transitions, an interference effect is generated akin to a double-slit experiment. The observation of oscillations in the ground state probability as a function of tf (before the adiabatic limit sets in) then constitutes a sensitive test of coherence between energy eigenstates. This is further illustrated by analyzing the effect of coupling the TLS to a thermal bath: increasing either the bath temperature or the coupling strength results in a damping of these oscillations. The theoretical tools we introduce significantly simplify the analysis of the generalized Landau-Zener problem. Furthermore, our analysis connects quantum annealing algorithms exhibiting speedups via the mechanism of coherent diabatic transitions to near-term experiments with quantum annealing hardware.