Adiabatic Optimization and Quantum Annealing

Jeremy Côté, Frédéric Sauvage, Martín Larocca +3 more

Abstract Quantum annealing (QA) is a continuous-time heuristic quantum algorithm for solving or approximately solving classical optimization problems. The algorithm uses a schedule to interpolate between a driver Hamiltonian with an easy-to-prepare ground state and a problem Hamiltonian whose ground state encodes solutions to an optimization problem. The standard implementation relies on the evolution being adiabatic: keeping the system in the instantaneous ground state with high probability and requiring a time scale inversely related to the minimum energy gap between the instantaneous ground and excited states. However, adiabatic evolution can lead to evolution times that scale exponentially with the system size, even for computationally simple problems. Here, we study whether non-adiabatic evolutions with optimized annealing schedules can bypass this exponential slowdown for one such class of problems called the frustrated ring model. For sufficiently optimized annealing schedules and system sizes of up to 39 qubits, we provide numerical evidence that we can avoid the exponential slowdown. Our work highlights the potential of highly-controllable QA to circumvent bottlenecks associated with the standard implementation of QA.

Arnab Das, Bikas K. Chakrabarti

Elizabeth Crosson, Mingkai Deng

We analyze the performance of simulated quantum annealing (SQA) on an optimization problem for which simulated classical annealing (SA) is provably inefficient because of a high energy barrier. We present evidence that SQA can pass through this barrier to find the global minimum efficiently. This demonstrates the potential for SQA to inherit some of the advantages of quantum annealing (QA), since this problem has been previously shown to be efficiently solvable by quantum adiabatic optimization.

Das, Arnab, Chakrabarti, Bikas

Lucas T. Brady, Wim van Dam

Quantum annealing is guaranteed to find the ground state of optimization problems provided it operates in the adiabatic limit. Recent work [S. Muthukrishnan et al., Phys. Rev. X 6, 031010 (2016)] has found that for some barrier tunneling problems, quantum annealing can be run much faster than is adiabatically required. Specifically, an $n$-qubit optimization problem was presented for which a nonadiabatic, or diabatic, annealing algorithm requires only a constant run time, while an adiabatic annealing algorithm requires a run-time polynomial in $n$. Here we show that this nonadiabatic speedup is the direct result of a specific symmetry in the studied problem. In the more general case, no such nonadiabatic speedup occurs and we show why the special case achieves this speedup compared to the general case. We also prove that the adiabatic annealing algorithm has a necessary and sufficient run time that is quadratically better than the standard quantum adiabatic condition suggests. We conclude with an observation about the required precision in timing for the diabatic algorithm.

Bastien Chopard B, Marco Tomassini