Finding spin glass ground states using quantum walks
TLDR
This work investigates the performance of continuous-time quantum walks as a tool for finding spin glass ground states, a problem that serves as a useful model for realistic optimization problems and uncover significant ways in which solving spin glass problems differs from applying quantum walks to the search problem.Abstract:
Quantum computation using continuous-time evolution under a natural hardware Hamiltonian is a promising near- and mid-term direction toward powerful quantum computing hardware. We investigate the performance of continuous-time quantum walks as a tool for finding spin glass ground states, a problem that serves as a useful model for realistic optimization problems. By performing detailed numerics, we uncover significant ways in which solving spin glass problems differs from applying quantum walks to the search problem. Importantly, unlike for the search problem, parameters such as the hopping rate of the quantum walk do not need to be set precisely for the spin glass ground state problem. Heuristic values of the hopping rate determined from the energy scales in the problem Hamiltonian are sufficient for obtaining a better quantum advantage than for search. We uncover two general mechanisms that provide the quantum advantage: matching the driver Hamiltonian to the encoding in the problem Hamiltonian, and an energy redistribution principle that ensures a quantum walk will find a lower energy state in a short timescale. This makes it practical to use quantum walks for solving hard problems, and opens the door for a range of applications on suitable quantum hardware.read more
Citations
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Prospects for Quantum Enhancement with Diabatic Quantum Annealing
E. J. Crosson,Daniel A. Lidar +1 more
TL;DR: Diabatic quantum annealing is argued for as the most promising route to quantum enhancement within this framework on the basis that improved coherence times and control capabilities will enable the near-term exploration of several heuristic quantum optimization algorithms that have been introduced in the literature.
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Optimality of spatial search via continuous-time quantum walks
TL;DR: This work derives general expressions, depending on the spectral properties of the Hamiltonian driving the walk, that predict the performance of this quantum search algorithm provided certain spectral conditions are fulfilled and shows the optimality of quantum search for certain graphs with very small spectral gaps, such as graphs that can be efficiently partitions into clusters.
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Quantum speedup of branch-and-bound algorithms
TL;DR: A quantum algorithm that can accelerate classical branch-and-bound algorithms near-quadratically in a very general setting and it is shown that the quantum algorithm can find exact ground states for most instances of the Sherrington-Kirkpatrick model in time $O(2^{0.226n})$, which is substantially more efficient than Grover's algorithm.
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An energetic perspective on rapid quenches in quantum annealing
TL;DR: In this paper, the energy expectation value of different elements of the Hamiltonian was analyzed, and it was shown that monotonic quenches, where the strength of the problem Hamiltonian is consistently increased relative to fluctuation (driver) terms, will yield a better result on average than random guessing.
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Two quantum Ising algorithms for the shortest-vector problem
TL;DR: Two quantum algorithms are proposed to solve the shortest-vector problem, which could play an important role in designing new cryptosystems for the postquantum era.
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