How Small-World Interactions Can Lead to Improved Quantum Annealer Designs

Abstract

There are many factors that influence the design of quantum annealing processing units. Here we address the issue of improving quantum annealing processing unit designs from the point of view of the critical behavior of spin glasses. It has been argued [Phys. Rev. X 4, 021008 (2014)] that among the most difficult Ising spin-glass ground-state problems are those related to lattices which exhibit a finite-temperature spin-glass transition. Here, we show that adding small-world couplers between qubits (spins) to the native quasi-planar quantum processing unit graph results in a topology where a disordered Ising system can undergo a finite-temperature spin-glass transition, even when an Ising spin glass on the quasi-planar native graph does not display a transition into a glassy phase at any finite temperature. To ensure that these systems can be engineered with current fabrication techniques, using large-scale Monte Carlo simulations we demonstrate that highly-constrained systems restricted to a few fabrication layers and with fixed coupler angles can also exhibit a finite-temperature spin-glass transition. This indicates that these systems might be mean-field-like, which also means that embedding highly-nonplanar problems might be simplified when compared to the underlying native topology. Our results are illustrated using the quasi-planar Chimera topology currently used in the D-Wave Systems Inc. quantum annealing machines, as well as standard two-dimensional square lattices. The presented approach can be generalized to other topologies.

Synchronously-pumped OPO coherent Ising machine: benchmarking and prospects

“…The importance of embedding overhead sketched here motivates recent efforts to improve the performance of physical annealers with alternate embedding strategies 33 or increased hardware connectivity. [34][35][36] Quantum annealing offers the promise of quantum speedup, but this must be balanced against the overhead required to embed the problem into the annealer's hardware. As we have shown, this embedding overhead can cause exponential slow-down for general Ising problems.…”

A Cost and Power Feasibility Analysis of Quantum Annealing for NextG Cellular Wireless Networks

“…Assumption-Bespoke QA hardware. Qubit connectivity significantly impacts performance, with sparse connectivity negatively affecting dense problem graphs due to problem mapping difficulties [35], but recent advances in QA have bolstered qubit connectivity [18] while further improvement efforts continue [37,45] and so we assume that these efforts will allow QA hardware tailored to the problem of interest. Roadmap.…”

Physics-Inspired Optimization for Quadratic Unconstrained Problems Using a Digital Annealer

“…To the best of our knowledge, the only known case of speedup is a constant speedup for a class of synthetic problems [29] and, so far, there is no evidence of speedup for an industrial application. The hope is that future improvements to the quantum annealer and, in particular, to its currently sparse connectivity and low precision due to analog noise, will demonstrate the power of quantum effects in solving optimization problems [32,33]. With the same goal in mind, researchers have been inspired to push the envelope for such problems on novel hardware, such as the coherent Ising machine [32], as well as on graphics processing units (GPU) [27,28] and application-specific CMOS hardware [34,35].…”