Quantum annealing correction for random Ising problems

Pudenz, Kristen L.; Albash, Tameem; Lidar, Daniel A.

doi:10.1103/physreva.91.042302

Cited by 95 publications

(135 citation statements)

References 53 publications

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“…In order to quantify the performance of the QAC scheme, we also test two classical strategies and one additional quantum strategy [40][41][42].…”

Section: Benchmarking Using Antiferromagnetic Chainsmentioning

confidence: 99%

“…Work on the first generation D-Wave 1 (DW1) "Rainier" and second generation D-Wave 2 (DW2) "Vesuvius" processors has already demonstrated that error correction can substantially benefit quantum annealing [40][41][42]. Namely, it was shown that even a relatively simple quantum repetition code incorporating energy penalty terms and a decoding procedure, can significantly improve the success probability of finding ground states, as well as overcome precision issues in the specification of the Ising Hamiltonian.…”

Section: Introductionmentioning

confidence: 99%

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Performance of two different quantum annealing correction codes

Mishra

Albash

Lidar

2015

Quantum Inf Process

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Quantum annealing is a promising approach for solving optimization problems, but like all other quantum information processing methods, it requires error correction to ensure scalability. In this work we experimentally compare two quantum annealing correction codes in the setting of antiferromagnetic chains, using two different quantum annealing processors. The lower temperature processor gives rise to higher success probabilities. The two codes differ in a number of interesting and important ways, but both require four physical qubits per encoded qubit. We find significant performance differences, which we explain in terms of the effective energy boost provided by the respective redundantly encoded logical operators of the two codes. The code with the higher energy boost results in improved performance, at the expense of a lower degree encoded graph. Therefore, we find that there exists an important tradeoff between encoded connectivity and performance for quantum annealing correction codes.

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“…In order to quantify the performance of the QAC scheme, we also test two classical strategies and one additional quantum strategy [40][41][42].…”

Section: Benchmarking Using Antiferromagnetic Chainsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Performance of two different quantum annealing correction codes

Mishra

Albash

Lidar

2015

Quantum Inf Process

Self Cite

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“…For such flux qubits, the T 2 time can at present range from tens of nanoseconds to a few hundred nanoseconds [21,22], yet the computation lasts on the order of microseconds to milliseconds. If the qubits have all decohered long before the computation is over, how can this be reconciled with evidence that the D-Wave devices perform quantum annealing [23][24][25][26][27][28][29][30][31][32]? In essence, the answer boils down to two key points:…”

Section: Introductionmentioning

confidence: 99%

Decoherence in adiabatic quantum computation

2015

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Recent experiments with increasingly larger numbers of qubits have sparked renewed interest in adiabatic quantum computation, and in particular quantum annealing. A central question that is repeatedly asked is whether quantum features of the evolution can survive over the long time-scales used for quantum annealing relative to standard measures of the decoherence time. We reconsider the role of decoherence in adiabatic quantum computation and quantum annealing using the adiabatic quantum master equation formalism. We restrict ourselves to the weak-coupling and singular-coupling limits, which correspond to decoherence in the energy eigenbasis and in the computational basis, respectively. We demonstrate that decoherence in the instantaneous energy eigenbasis does not necessarily detrimentally affect adiabatic quantum computation, and in particular that a short single-qubit T2 time need not imply adverse consequences for the success of the quantum adiabatic algorithm. We further demonstrate that boundary cancellation methods, designed to improve the fidelity of adiabatic quantum computing in the closed system setting, remain beneficial in the open system setting. To address the high computational cost of master equation simulations, we also demonstrate that a quantum Monte Carlo algorithm that explicitly accounts for a thermal bosonic bath can be used to interpolate between classical and quantum annealing. Our study highlights and clarifies the significantly different role played by decoherence in the adiabatic and circuit models of quantum computing.

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“…This scaling is not an inherent part of the quantum isomer search algorithm. Increasing the problem size decreases the probability of finding a successful answer due to annealing error and imperfect hardware [48]. It is not surprising that more runs are needed for larger molecules, especially when the quadratic scaling of parameters and the limited connectivity of the D-Wave 2000Q's chimera graph are taken into account.…”

Section: Discussionmentioning

confidence: 99%

Quantum isomer search

et al. 2020

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Isomer search or molecule enumeration refers to the problem of finding all the isomers for a given molecule. Many classical search methods have been developed in order to tackle this problem. However, the availability of quantum computing architectures has given us the opportunity to address this problem with new (quantum) techniques. This paper describes a quantum isomer search procedure for determining all the structural isomers of alkanes. We first formulate the structural isomer search problem as a quadratic unconstrained binary optimization (QUBO) problem. The QUBO formulation is for general use on either annealing or gate-based quantum computers. We use the D-Wave quantum annealer to enumerate all structural isomers of all alkanes with fewer carbon atoms (n < 10) than Decane (C 10 H 22 ). The number of isomer solutions increases with the number of carbon atoms. We find that the sampling time needed to identify all solutions scales linearly with the number of carbon atoms in the alkane. We probe the problem further by employing reverse annealing as well as a perturbed QUBO Hamiltonian and find that the combination of these two methods significantly reduces the number of samples required to find all isomers.

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Quantum annealing correction for random Ising problems

Cited by 95 publications

References 53 publications

Performance of two different quantum annealing correction codes

Performance of two different quantum annealing correction codes

Decoherence in adiabatic quantum computation

Quantum isomer search

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