Degeneracy, degree, and heavy tails in quantum annealing

King, Andrew D.; Hoskinson, Emile; Lanting, T.; Andriyash, Evgeny; Amin, M. H. S.

doi:10.1103/physreva.93.052320

Cited by 29 publications

(34 citation statements)

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“…, which generalises equation (9) to spins. We restate that this choice of local Lindblad operators does not lead to thermalisation in the steady state, as for this purpose nonlocal terms would be required.…”

Section: ( )mentioning

confidence: 94%

“…Together with the progress in implementing quantum gates and concatenating them, i.e. by realising standard circuit computation [4], recently, adiabatic quantum computation (AQC) [5] and quantum annealing [6] have received a tremendous boost thanks to the experiments performed with D-wave machines [7][8][9][10]. The strategy underlying adiabatic quantum computation [5,6] is based on the fact that any quantum algorithm can be formulated in terms of identifying the global minimum (ground state) of a given function (Hamiltonian) over a set of many local minima.…”

Section: Introductionmentioning

confidence: 99%

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Dissipation in adiabatic quantum computers: lessons from an exactly solvable model

et al. 2017

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We introduce and study the adiabatic dynamics of free-fermion models subject to a local Lindblad bath and in the presence of a time-dependent Hamiltonian. The merit of these models is that they can be solved exactly, and will help us to study the interplay between nonadiabatic transitions and dissipation in many-body quantum systems. After the adiabatic evolution, we evaluate the excess energy (the average value of the Hamiltonian) as a measure of the deviation from reaching the final target ground state. We compute the excess energy in a variety of different situations, where the nature of the bath and the Hamiltonian is modified. We find robust evidence of the fact that an optimal working time for the quantum annealing protocol emerges as a result of the competition between the nonadiabatic effects and the dissipative processes. We compare these results with the matrix-productoperator simulations of an Ising system and show that the phenomenology we found also applies for this more realistic case.

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Section: ( )mentioning

confidence: 94%

Section: Introductionmentioning

confidence: 99%

Dissipation in adiabatic quantum computers: lessons from an exactly solvable model

et al. 2017

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“…T is called the annealing time and the functions A and B determine the annealing schedule (for details on D-Wave's schedule, see Refs. [3] and [28]).…”

Section: 1 Quantum Annealingmentioning

confidence: 98%

A hybrid quantum-classical paradigm to mitigate embedding costs in quantum annealing

Abbott

Calude

Dinneen

et al. 2019

Int. J. Quantum Inform.

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Despite rapid recent progress towards the development of quantum computers capable of providing computational advantages over classical computers, it seems likely that such computers will, initially at least, be required to run in a hybrid quantum-classical regime. This realisation has led to interest in hybrid quantum-classical algorithms allowing, for example, quantum computers to solve large problems despite having very limited numbers of qubits. Here we propose a hybrid paradigm for quantum annealers with the goal of mitigating a different limitation of such devices: the need to embed problem instances within the (often highly restricted) connectivity graph of the annealer. This embedding process can be costly to perform and may destroy any computational speedup. In order to solve many practical problems, it is moreover necessary to perform many, often related, such embeddings. We will show how, for such problems, a raw speedup that is negated by the embedding time can nonetheless be exploited to give a real speedup. As a proof-of-concept example we present an in-depth case study of a simple problem based on the maximum weight independent set problem. Although we do not observe a quantum speedup experimentally, the advantage of the hybrid approach is robustly verified, showing how a potential quantum speedup may be exploited and encouraging further efforts to apply the approach to problems of more practical interest.Quantum computation has the potential to revolutionise computer science, and as a consequence has, since its inception, received a great deal of attention from theorists and experimentalists alike. Although much progress has been made through the concerted efforts of the community, we are still some distance from being able to build sufficiently large-scale universal quantum computers to realise this potential [1,2].More recently, however, significant progress has been made in the development of special-purpose quantum computers. This has been driven by the realisation that, by dropping the requirement of being able to efficiently simulate arbitrary computations and relaxing some of the constraints that make large-scale universal quantum computing difficult (e.g., the ability to apply gates to arbitrary pairs of, possibly non-adjacent, qubits), such devices can be more easily engineered and scaled. The expectation is that with this approach one may be able to exploit some of the capabilities of quantum computation-even if its full abilities are for now beyond our reach-to obtain lesser, but nevertheless practical, advantages in practical applications. Quantum annealers, which solve particular optimisation problems, exemplify this approach, and significant progress has been made in recent years towards engineering moderately large-scale such devices [3,4]. This approach has been pursued particularly zealously by D-Wave, who have developed quantum annealers with upwards of 2000 qubits (e.g., the D-Wave 2000Q™ machine [5]), and are thus of sufficient size to tackle problems for which their performanc...

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“…A spin in a classical state is said to be free or floppy if flipping the spin results in another classical state that is degenerate. Floppy qubits, and associated degeneracies, have been implicated in perturbative anticrossings 4,6,8 .…”

Section: B Connecting Perturbative Anticrossings and Degeneracymentioning

confidence: 99%

“…Previously available quantum annealing systems have allowed only uniform QA, in which each qubit is initialized with the same transverse-field driver Hamiltonian and all qubits are annealed in unison. In this case smallgap perturbative anticrossings can arise in unfavorably structured inputs, even those that are not particularly hard for classical solvers [4][5][6] .…”

Section: Introductionmentioning

confidence: 99%

Experimental demonstration of perturbative anticrossing mitigation using nonuniform driver Hamiltonians

et al. 2017

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Perturbative anticrossings have long been identified as a potential computational bottleneck for quantum annealing. This bottleneck can appear, for example, when a uniform transverse driver Hamiltonian is applied to each qubit. Previous theoretical research sought to alleviate such anticrossings by adjusting the transverse driver Hamiltonians on individual qubits according to a perturbative approximation. Here we apply this principle to a physical implementation of quantum annealing in a D-Wave 2000Q system. We use samples from the quantum annealing hardware and per-qubit anneal offsets to produce nonuniform driver Hamiltonians. On small instances with severe perturbative anticrossings, our algorithm yields an increase in minimum eigengaps, ground state success probabilities, and escape rates from metastable valleys. We also demonstrate that the same approach can mitigate biased sampling of degenerate ground states.

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Degeneracy, degree, and heavy tails in quantum annealing

Cited by 29 publications

References 50 publications

Dissipation in adiabatic quantum computers: lessons from an exactly solvable model

Dissipation in adiabatic quantum computers: lessons from an exactly solvable model

A hybrid quantum-classical paradigm to mitigate embedding costs in quantum annealing

Experimental demonstration of perturbative anticrossing mitigation using nonuniform driver Hamiltonians

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