Single-Qubit Fidelity Assessment of Quantum Annealing Hardware

Abstract

As a wide variety of quantum computing platforms become available, methods for assessing and comparing the performance of these devices are of increasing interest and importance. Inspired by the success of single-qubit error rate computations for tracking the progress of gate-based quantum computers, this work proposes a Quantum Annealing Single-qubit Assessment (QASA) protocol for quantifying the performance of individual qubits in quantum annealing computers. The proposed protocol scales to large quantum annealers with thousands of qubits and provides unique insights into the distribution of qubit properties within a particular hardware device. The efficacy of the QASA protocol is demonstrated by analyzing the properties of a D-Wave 2000Q system, revealing unanticipated correlations in the qubit performance of that device. A study repeating the QASA protocol at different annealing times highlights how the method can be utilized to understand the impact of annealing parameters on qubit performance. Overall, the proposed QASA protocol provides a useful tool for assessing the performance of current and emerging quantum annealing devices.

High-quality Thermal Gibbs Sampling with Quantum Annealing Hardware

“…In addition to the fundamental impacts of open quantum systems, the D-Wave hardware documentation highlights five other sources of deviations from ideal system operations called integrated control errors (ICE) [44], which include: background susceptibility; flux noise; Digital-to-Analog Conversion quantization; Input/Ouput system effects; and variable scale across qubits. Consequently, it has long been observed that output distributions of the QA hardware produced by D-Wave Systems are reminiscent of a Gibbs distribution of the input Hamiltonian H Ising [13][14][15][16]18] with a hardware-specific effective temperature of β ≈ 10 [17,45]. The prevailing interpretation of the hardware's output distribution is the Freeze Out model, which proposes that the output reflects a quantum Gibbs distribution occurring at an input-dependent point towards the end of the annealing process where some small amount of σ x i remains [46].…”

“…However, these quantum Gibbs distributions are inaccurate when targeting a desired classical Gibbs distribution for sampling applications [6,18,52,53]. The recent insight from [17] is that when this hardware is operated at a low-energy scale (i.e., |J|, |h| ≤ 0.050) it behaves as a thermalized classical Gibbs sampler from H Ising but suffers from a notable amount of distortion from instantaneous noise in the local field parameters, h, on the order of 0.036 [45,54], resulting in so-called noisy Gibbs samples.…”

“…The α values are determined by calculating an optimistic estimate for α max and then scaling this value by the same step sizes that are used for α in . The α max value is calculated by executing the QASA protocol proposed in [45] on each of the relevant spins and taking the average of the spin-by-spin effective temperatures recovered by that protocol. Therefore, the minimum of the range is 0.0 and the maximum is α max .…”

“…Figure 2 explores this point by presenting the α out values that were found for each of the high-quality input configurations considered (i.e., 0.2 ≤ α in ≤ 0.4). Given the prevailing theories of how QA hardware operates [45,46], one expects that increasing the energy scale of the input α in or the annealing time will increase the effective temperature of the output distribution, α out . Indeed, that trend is observed in Figure 2, where the recovered α out values increase monotonically (or nearly so) with both α in and annealing time.…”

“…To further explore a connection between these experimental observations and the spurious couplings observed in the hardware's output (i.e., Figure 5a), we propose an extension of the effective single-qubit quantum model developed in [17] to the three-qubit context. The singlequbit model considered in [17,45] includes a transverse field with an intensity proportional to the input local field parameter, h. This transverse field component was able to reproduce an observed saturation of the output field for large input values. Another important feature proposed in [17] was qubit noise perturbing the input parameters of the model, which explained the spurious couplings in the regime of low input parameters.…”