Two quantum Ising algorithms for the shortest-vector problem

Joseph, David; Callison, Adam; Ling, Cong; Mintert, Florian

doi:10.1103/physreva.103.032433

Cited by 16 publications

(20 citation statements)

References 39 publications

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“…Quantum annealing is an approach to quantum computing where optimization and other problems are mapped such that their solutions correspond to the ground and low energy states of a Hamiltonian, and quantum fluctuations are used to solve the problem. Small proof-of-concept experiments have been performed based on a variety of real problems, with applications as diverse as cryptography [1], design of radar waveforms [2], protein folding [3], air traffic control [4], scheduling [5][6][7], and hydrology [8]. To the best of our knowledge, no scaling advantage has been observed on these devices for optimization, although recent work suggests one may be present for quantum simulation [9].…”

Section: Introductionmentioning

confidence: 99%

Experimental test of search range in quantum annealing

Chancellor

Kendon

2021

Phys. Rev. A

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Section: Introductionmentioning

confidence: 99%

Experimental test of search range in quantum annealing

Chancellor

Kendon

2021

Phys. Rev. A

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“…However, this does not tell the whole story, as currently available annealing hardware only has linear and quadratic interactions available. It is not necessarily true that the interactions between two binary variables can be written only in terms of these types of interactions; in fact, except for special cases such as objective functions involving multiplication of variables [30], [35], it is not going to be true. This can be rectified by engineering effective higher order interactions [27], [28], but each of these will require at least one auxiliary variable to engineer (although if this variable instantiated as a physical qubit, it may have less stringent requirements than the one used for computation [28]).…”

Section: B Binary Encodingmentioning

confidence: 99%

Performance of Domain-Wall Encoding for Quantum Annealing

Chen

Stollenwerk

Chancellor

2021

IEEE Trans. Quantum Eng.

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In this article, we experimentally test the performance of the recently proposed domain-wall encoding of discrete variables Chancellor, 2019, on Ising model flux qubit quantum annealers. We compare this encoding with the traditional one-hot methods and find that they outperform the one-hot encoding for three different problems at different sizes of both the problem and the variables. From these results, we conclude that the domain-wall encoding yields superior performance against a variety of metrics furthermore; we do not find a single metric by which one hot performs better. We even find that a 2000Q quantum annealer with a drastically less connected hardware graph but using the domain-wall encoding can outperform the next-generation Advantage processor if that processor uses one-hot encoding.

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“…We restrict ourselves to the question of encoding general interactions, in other words encodings which can assign arbitrary energies based on the value of the two variables. This is an important restriction, since binary encoding is known to be efficient for specific interactions, for example in the case of the shortest vector problem [33].…”

Section: A Efficiency Of Domain-wall Techniquementioning

confidence: 99%

Understanding domain-wall encoding theoretically and experimentally

Berwald¹,

Chancellor²,

Dridi³

2021

Preprint

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We analyze the performance of encoding pairwise interactions of higher-than-binary discrete variables (these models are sometimes referred to as discrete quadratic models) into binary variables based on domain walls on one dimensional Ising chains. We discuss how this is relevant to quantum annealing, but also many gate model algorithms such as VQE and QAOA. We theoretically show that for problems of practical interest for quantum computing and assuming only quadratic interactions are available between the binary variables, it is not possible to have a more efficient general encoding in terms of number of binary variables per discrete variable. We furthermore use a D-Wave Advantage 1.1 flux qubit quantum annealing computer to show that the dynamics effectively freeze later for a domain-wall encoding compared to a traditional one-hot encoding. This second result could help explain the dramatic performance improvement of domain wall over one hot which has been seen in a recent experiment on D-Wave hardware. This is an important result because usually problem encoding and the underlying physics are considered separately, our work suggests that considering them together may be a more useful paradigm. We argue that this experimental result is also likely to carry over to a number of other settings, we discuss how this has implications for gate-model and quantum-inspired algorithms.

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Two quantum Ising algorithms for the shortest-vector problem

Cited by 16 publications

References 39 publications

Experimental test of search range in quantum annealing

Experimental test of search range in quantum annealing

Performance of Domain-Wall Encoding for Quantum Annealing

Understanding domain-wall encoding theoretically and experimentally

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