Noise dynamics of quantum annealers: estimating the effective noise using idle qubits

Abstract

Quantum annealing is a type of analog computation that aims to use quantum mechanical fluctuations to search for optimal solutions of QUBO (quadratic unconstrained binary optimization) or, equivalently, Ising problems. Since NP-hard problems can in general be mapped to Ising and QUBO formulations, the quantum annealing paradigm has the potential to help solve various NP-hard problems. Current quantum annealers, such as those manufactured by D-Wave Systems, Inc., have various practical limitations including the size (number of qubits) of the problem that can be solved, the qubit connectivity, and sources of error from the environment or system calibration which can reduce the quality of the solutions. Typically, for an arbitrary problem instance, the corresponding QUBO (or Ising) structure will not natively embed onto the available qubit architecture on the quantum chip. Thus, in these cases, a minor embedding of the problem structure onto the device is necessary. However, minor embeddings on these devices do not always make use of the full sparse chip hardware graph, and a large portion of the available qubits stay unused during quantum annealing. In this work, we embed a disjoint random QUBO on the unused parts of the chip alongside the QUBO to be solved, which acts as an indicator of the solution quality of the device over time. Using experiments on three different D-Wave quantum annealers, we demonstrate that (i) long term trends in solution quality exist on the D-Wave device, and (ii) the unused qubits can be used to measure the current level of noise of the quantum system.

Analysis of a Programmable Quantum Annealer as a Random Number Generator

“…This is what is observed in this D-Wave quantum annealer data. This is not unexpected, especially given the observed trends over time on multiple D-Wave quantum annealers [27]. However, it is important to note that this type of biased random sampling is very likely to occur with other Noisy Intermediate Scale Quantum (NISQ) computers [63].…”

“…the order of the bits will not be changed by some other entropy source. This time series representation of the data is especially important since it has been shown that there are long term trends that can be observed in current D-Wave quantum annealing processors [27]. Additionally, the exact ordering of the bits within each anneal (e.g.…”

“…The primary reason that modern quantum annealers are not perfect random number generators is because there are a large number of sources of error and bias in the computation, for example the spin bath polarization effect [24,25] can cause sequential anneal-readout cycles to have self correlations (in time), and programmed coefficients (even if they are 0) have slightly different effective weights on the hardware [26]. Furthermore, it has been shown that modern D-Wave quantum annealers have a measurable performance change over time [27,28]. There have also been cross-qubit correlations observed on a D-Wave 2000Q chip [29,30].…”

Posiform planting: generating QUBO instances for benchmarking

“…We observe that the results for DW_2000Q_6 in Figure 1 show periodic variations of the measured GSP. This is because the annealing time measurements in increments of 100 µs were made several weeks apart from the measurements made for all other annealing times in increments of 10 µs, and previous studies (Pelofske et al, 2023) have shown that there are longterm variations (in solution quality) of the computations carried out on current D-Wave quantum annealing devices. Therefore, the variations that have a periodicity of 100 µs are due to variance of the noise profile of the device, rather than variations that are a function of the annealing time.…”

“…The D-Wave quantum annealers have been evaluated for sampling a large number of different types of problems, typically focusing on combinatorial optimization problems or Hamiltonian dynamics (Boixo et al, 2013(Boixo et al, , 2014(Boixo et al, , 2016Lanting et al, 2014;Venturelli et al, 2015;Harris et al, 2018;King et al, 2021King et al, , 2022King et al, , 2023Tasseff et al, 2022). D-Wave quantum annealing devices offer on the scale of hundreds to thousands of qubits, but are still subject to connectivity constraints, control errors, and noise from the environment (Pearson et al, 2019;Lanting et al, 2020;Nelson et al, 2021;Zaborniak and de Sousa, 2021;Grant and Humble, 2022;Pelofske et al, 2023). To map a QUBO Q of Equation (1) directly on the hardware chip of a quantum annealer, its connectivity structure should be consistent with the connectivity structure of the quantum device.…”