Variational quantum chemistry requires gate-error probabilities below the fault-tolerance threshold

Dalton, Kieran; K., Long, Christopher; Yordanov, Yordan S.; Smith, Charles G.; Barnes, C. H. W.; Mertig, Normann; Arvidsson-Shukur, David R. M.

doi:10.48550/arxiv.2211.04505

Cited by 1 publication

(2 citation statements)

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“…[72,105]), and assuming the ground state can be prepared perfectly with a depth of d = n = 100, already an error rate of p e ≈ 10 −7 is required. This is an error rate several orders of magnitude lower than what can currently be achieved and also several orders of magnitude below known error thresholds for fault-tolerant quantum computation [64,65]. The data for the performance of CVQE on 20 sites under noise (Fig.…”

Section: B Noisy Resultsmentioning

confidence: 80%

“…Using this relation, we estimate that to obtain the kagome HAFM ground state on a system of a hundred sites with a fidelity of 99.9%, error rates as low as p e = 10 −7 may be needed. This is several orders of magnitude below known error thresholds for fault-tolerant quantum computation [64,65]. This makes the high-fidelity preparation of ground states of systems with on the order of a hundred sites unlikely on noisy hardware.…”

Section: B Summary Of Numerical Resultsmentioning

confidence: 95%

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Variational quantum eigensolver for the Heisenberg antiferromagnet on the kagome lattice

Kattemölle

Wezel

2022

Phys. Rev. B

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Establishing the nature of the ground state of the Heisenberg antiferromagnet (HAFM) on the kagome lattice is well-known to be a prohibitively difficult problem for classical computers. Here, we give a detailed proposal for a variational quantum eigensolver (VQE) intending to solve this physical problem on a quantum computer. At the same time, this VQE constitutes an explicit experimental proposal for showing a useful quantum advantage on noisy intermediate-scale quantum devices because of its natural hardware compatibility. We classically emulate noiseless and noisy quantum computers with either 2D-grid or all-to-all connectivity and simulate patches of the kagome HAFM of up to 20 sites. In the noiseless case, the ground-state energy, as found by the VQE, approaches the true ground-state energy exponentially as a function of the circuit depth. Furthermore, VQEs for the HAFM on any graph can inherently perform their quantum computations in a decoherence-free subspace that protects against collective longitudinal and collective transversal noise, adding to the noise resilience of these algorithms. Nevertheless, the extent of the effects of other noise types suggests the need for error mitigation and performance targets alternative to high-fidelity ground-state preparation, even for essentially hardware-native VQEs.

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