Combinatorial optimization by simulating adiabatic bifurcations in nonlinear Hamiltonian systems

Goto, Hayato; Tatsumura, Kosuke; Dixon, A. R.

doi:10.1126/sciadv.aav2372

Cited by 302 publications

(262 citation statements)

References 51 publications

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“…This reassuring conclusion is reached here using the simplest possible error suppression and correction scheme [25], so that much room for improvement remains for more advanced methods. We expect our results to apply broadly, certainly beyond the D-Wave devices to other quantum [32][33][34] and semiclassical annealing implementations [35,36], and to other forms of analog quantum computing [37].…”

Section: Introductionmentioning

confidence: 85%

Analog errors in quantum annealing: doom and hope

et al. 2019

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Quantum annealing has the potential to provide a speedup over classical algorithms in solving optimization problems. Just as for any other quantum device, suppressing Hamiltonian control errors will be necessary before quantum annealers can achieve speedups. Such analog control errors are known to lead to J-chaos, wherein the probability of obtaining the optimal solution, encoded as the ground state of the intended Hamiltonian, varies widely depending on the control error.Here, we show that J-chaos causes a catastrophic failure of quantum annealing, in that the scaling of the time-to-solution metric becomes worse than that of a deterministic (exhaustive) classical solver. We demonstrate this empirically using random Ising spin glass problems run on the two latest generations of the D-Wave quantum annealers. We then proceed to show that this doomsday scenario can be mitigated using a simple error suppression and correction scheme known as quantum annealing correction (QAC). By using QAC, the time-to-solution scaling of the same D-Wave devices is improved to below that of the classical upper bound, thus restoring hope in the speedup prospects of quantum annealing.

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Section: Introductionmentioning

confidence: 85%

Analog errors in quantum annealing: doom and hope

et al. 2019

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“…Herein quantum annealer as an Ising machine is used for the black-box optimization algorithm. In the future, the application domain of our algorithm will expand to even larger problems as next-generation quantum annealers or other Ising machines equipped with many bits [70][71][72][73][74][75][76] become available. As demonstrated by our experiments, the hard computational barrier (e.g., candidate selection) in automated materials discovery can be partly resolved with the help of an Ising machine.…”

Section: Discussion and Summarymentioning

confidence: 99%

Designing metamaterials with quantum annealing and factorization machines

Kitai

Guo

et al. 2020

Phys. Rev. Research

123

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Automated materials design with machine learning is increasingly common in recent years. Theoretically, it is characterized as black-box optimization in the space of candidate materials. Since the difficulty of this problem grows exponentially in the number of variables, designing complex materials is often beyond the ability of classical algorithms. We show how quantum annealing can be incorporated into automated materials discovery and conduct a proof-of-principle study on designing complex thermofunctional metamaterials. Our algorithm consists of three parts: regression for a target property by factorization machine, selection of candidate metamaterial based on the regression results, and simulation of the metamaterial property. To accelerate the selection part, we rely on the D-Wave 2000Q quantum annealer. Our method is used to design complex structures of wavelength selective radiators showing much better concordance with the thermal atmospheric transparency window in comparison to existing human-designed alternatives.

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“…Quantum annealing devices were argued to be superior to classical annealing due to the availability of quantum effects such as superposition and tunneling (23,24). This inspired several quantum and classical devices, including the D-Wave quantum annealer (25)(26)(27), the coherent Ising machine (28,29), the recently-introduced Fujitsu-led application-specific CMOS-based digital annealer (30), and even more recently, the Toshiba simulated bifurcation algorithm (31). In Table 1, we give an overview of these optimization annealing machines and their characteristics.…”

Section: + ⋯mentioning

confidence: 99%

“…We expect that the kinetics of the problem, as well as imperfections in the settings of the molecular computer, will result in trapping in local minima for particular experiments, requiring the repetition of the computation to sample from the low-energy states of the problem. The alternative approaches mentioned earlier, namely simulated annealing, quantum annealing, and the Toshiba simulated bifurcation algorithm, share this challenge (30,31).…”

Section: Description and Requirementsmentioning

confidence: 99%

A Molecular Computing Approach to Solving Optimization Problems via Programmable Microdroplet Arrays

Guo¹,

Friederich²,

Cao³

et al. 2019

Preprint

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The search for novel forms of computing that show advantages as alternatives to the dominant von-Neuman model-based computing is important as it will enable different classes of problems to be solved. By using droplets and room-temperature processes, molecular computing is a promising research direction with potential biocompatibility and cost advantages. In this work, we present a new approach for computation using a network of chemical reactions taking place within an array of spatially localized droplets whose contents represent bits of information. Combinatorial optimization problems are mapped to an Ising Hamiltonian and encoded in the form of intra- and inter- droplet interactions. The problem is solved by initiating the chemical reactions within the droplets and allowing the system to reach a steady-state; in effect, we are annealing the effective spin system to its ground state. We propose two implementations of the idea, which we ordered in terms of increasing complexity. First, we introduce a hybrid classical-molecular computer where droplet properties are measured and fed into a classical computer. Based on the given optimization problem, the classical computer then directs further reactions via optical or electrochemical inputs. A simulated model of the hybrid classical-molecular computer is used to solve boolean satisfiability and a lattice protein model. Second, we propose architectures for purely molecular computers that rely on pre-programmed nearest-neighbour inter-droplet communication via energy or mass transfer.

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Combinatorial optimization by simulating adiabatic bifurcations in nonlinear Hamiltonian systems

Cited by 302 publications

References 51 publications

Analog errors in quantum annealing: doom and hope

Analog errors in quantum annealing: doom and hope

Designing metamaterials with quantum annealing and factorization machines

A Molecular Computing Approach to Solving Optimization Problems via Programmable Microdroplet Arrays

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