Bounding quantum gate error rate based on reported average fidelity

Abstract

Remarkable experimental advances in quantum computing are exemplified by recent announcements of impressive average gate fidelities exceeding 99.9% for single-qubit gates and 99% for two-qubit gates. Although these high numbers engender optimism that fault-tolerant quantum computing is within reach, the connection of average gate fidelity with fault-tolerance requirements is not direct. Here we use reported average gate fidelity to determine an upper bound on the quantum-gate error rate, which is the appropriate metric for assessing progress towards fault-tolerant quantum computation, and we demonstrate that this bound is asymptotically tight for general noise. Although this bound is unlikely to be saturated by experimental noise, we demonstrate using explicit examples that the bound indicates a realistic deviation between the true error rate and the reported average fidelity. We introduce the Pauli distance as a measure of this deviation, and we show that knowledge of the Pauli distance enables tighter estimates of the error rate of quantum gates. lb 0

Gate-error analysis in simulations of quantum computers with transmon qubits

“…Note that we always find η ♦ η Pauli ♦ , so the dominant errors are non-Pauli errors and belong to the "bad" class of errors [33]. Interestingly, there is almost one order of magnitude difference between the actual error rate η ♦ and the optimal bounds η Pauli ♦ and η ub ♦ calculated from the gate fidelity F avg according to Eqs.…”

“…We have found that gate metrics such as the average gate fidelity [9], the diamond distance [10,33], and the unitarity [11] each provide insights into the errors of the implemented gate pulses. Specifically, while the time evolution of the total system is inherently unitary and the errors are systematic, they appear as incoherent non-Pauli errors on the computational subspace.…”

“…Conceptually, these errors originate from entanglement between the computational states and the noncomputational states in the transmons and the resonator. Such errors cause most of the mismatch between the ideal gates and the implemented pulses (see also [7,11,33,[47][48][49]). …”

“…The best known quantum error-correcting codes require η ♦ to be on the order of 1% or less [33]. Evaluating Eq.…”

Quantum error-correction failure distributions: Comparison of coherent and stochastic error models

“…In contrast, for increasing σ in the pulse-area error model, the distribution rises from small P ψ+1 fail , with the most likely values scaling as σ 4 . We conjecture that the heavy tails in the pulse-area error model distribution are an indicator of the strongly negative impact that purely coherent errors can have on QEC [16,17].…”