Family of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mo>[</mml:mo><mml:mo>[</mml:mo><mml:mrow><mml:mn>6</mml:mn><mml:mi>k</mml:mi><mml:mo>,</mml:mo><mml:mn>2</mml:mn><mml:mi>k</mml:mi><mml:mo>,</mml:mo><mml:mn>2</mml:mn></mml:mrow><mml:mo>]</mml:mo><mml:mo>]</mml:mo></mml:mrow></mml:math>codes for practical and scalable adiabatic quantum computation

Ganti, Anand; Onunkwo, Uzoma; Young, Kevin

doi:10.1103/physreva.89.042313

Cited by 22 publications

(24 citation statements)

References 14 publications

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“…Interest in quantum annealing has piqued in recent years since com mercial processors comprising hundreds of programmable superconducting flux qubits have become available to the research community [10,11], and a lively debate has erupted concerning their quantumness [12][13][14][15][16][17][18][19] and the possibility of observing a quantum speedup [20][21][22], for which there exists theoretical evidence via specific examples [4,5,23], While error mitigation strategies for quantum annealing and, more generally, adiabatic quantum computing have been proposed [24][25][26][27][28][29][30][31][32][33] and implemented [34], much less is known compared to the relatively mature state of quantum error correction in the circuit model [1,35]. In particular, an accuracy threshold theorem [36][37][38] for fault-tolerant quantum annealing remains elusive, in spite of some degree of inherent robustness of adiabatic quantum computation to thermal excitations and control errors [39][40][41].…”

Section: Introductionmentioning

confidence: 99%

Quantum annealing correction for random Ising problems

2015

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We demonstrate that the performance of a quantum annealer on hard random Ising optimization problems can be substantially improved using quantum annealing correction (QAC). Our error correction strategy is tailored to the D-Wave Two device. We find that QAC provides a statistically significant enhancement in the performance of the device over a classical repetition code, improving as a function of problem size as well as hardness. Moreover, QAC provides a mechanism for overcoming the precision limit of the device, in addition to correcting calibration errors. Performance is robust even to missing qubits. We present evidence for a constructive role played by quantum effects in our experiments by contrasting the experimental results with the predictions of a classical model of the device. Our work demonstrates the importance of error correction in appropriately determining the performance of quantum annealers.Comment: 17 pages, 14 figures. v2: updated to published versio

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Section: Introductionmentioning

confidence: 99%

Quantum annealing correction for random Ising problems

2015

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“…V B), it is still clear that no useful AQC can take place: the ground state of H S (t) will, in general, be a coherent superposition of the complete set of eigenstates of the {A α } operators, and we have demonstrated that this superposition decays on multiple timescales, varying from the single-qubit dephasing time T to N times this timescale. Thus, to be able to perform useful AQC in the SCL under the independent decoherence model, one must invoke some form of error correction, suppression, or avoidance [42,[60][61][62][63][64][65][66][67][68].…”

Section: Independent Decoherencementioning

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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“…Therefore, any scalable quantum annealing architecture will require quantum error correction [25]. Unfortunately, theoretical progress in quantum error correction for adiabatic quantum computing and quantum annealing has not enjoyed the same success as that of other quantum computing paradigms, in spite of recent advances [26][27][28][29][30]. Physical constraints, such as locality of the interaction terms in the Hamiltonian [31,32], and a nogo theorem constraining what can be achieved with commuting two-local interactions [33], remain stubborn hurdles.…”

Section: Introductionmentioning

confidence: 99%

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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Family of[[6k,2k,2]]codes for practical and scalable adiabatic quantum computation

Cited by 22 publications

References 14 publications

Quantum annealing correction for random Ising problems

Quantum annealing correction for random Ising problems

Decoherence in adiabatic quantum computation

Performance of two different quantum annealing correction codes

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