Recently the question of whether the D-Wave processors exhibit large-scale quantum behavior or can be described by a classical model has attracted significant interest. In this work we address this question by studying a 503-qubit D-Wave Two device in the ``black box'' model i.e., by studying its input-output behavior. Our work generalizes an approach introduced in Boixo et al. [Nat. Commun. 4, 2067 (2013)] and uses groups of up to 20 qubits to realize a transverse Ising model evolution with a ground-state degeneracy whose distribution acts as a sensitive probe that distinguishes classical and quantum models for the D-Wave device. Our findings rule out all classical models proposed to date for the device and provide evidence that an open-system quantum dynamical description of the device that starts from a quantized energy level structure is well justified, even in the presence of relevant thermal excitations and a small value of the ratio of the single-qubit decoherence time to the annealing time.
Recently the question of whether the D-Wave processors exhibit large-scale quantum behavior or can be described by a classical model has attracted significant interest. In this work we address this question by studying a 503-qubit D-Wave Two device in the ``black box'' model i.e., by studying its input-output behavior. Our work generalizes an approach introduced in Boixo et al. [Nat. Commun. 4, 2067 (2013)] and uses groups of up to 20 qubits to realize a transverse Ising model evolution with a ground-state degeneracy whose distribution acts as a sensitive probe that distinguishes classical and quantum models for the D-Wave device. Our findings rule out all classical models proposed to date for the device and provide evidence that an open-system quantum dynamical description of the device that starts from a quantized energy level structure is well justified, even in the presence of relevant thermal excitations and a small value of the ratio of the single-qubit decoherence time to the annealing time.
A recent experiment [T. Lanting et al., Phys. Rev. X 4, 021041 (2014)] claimed to provide evidence of up to eight-qubit entanglement in a D-Wave quantum annealing device. However, entanglement was measured using qubit tunneling spectroscopy, a technique that provides indirect access to the state of the system at intermediate times during the anneal by performing measurements at the end of the anneal with a probe qubit. In addition, an underlying assumption was that the quantum transverse-field Ising Hamiltonian, whose ground states are already highly entangled, is an appropriate model of the device and not some other (possibly classical) model. This begs the question of whether alternative classical or semiclassical models would be equally effective at predicting the observed spectrum and thermal state populations. To check this, we consider a recently proposed classical rotor model with classical Monte Carlo updates, which has been successfully employed in describing features of earlier experiments involving the device. We also consider simulated quantum annealing with quantum Monte Carlo updates, an algorithm that samples from the instantaneous Gibbs state of the device Hamiltonian. Finally, we use the quantum adiabatic master equation, which cannot be efficiently simulated classically and which has previously been used to successfully capture the open-system quantum dynamics of the device. We find that only the master equation is able to reproduce the features of the tunneling spectroscopy experiment, while both the classical rotor model and simulated quantum annealing fail to reproduce the experimental results. We argue that this bolsters the evidence for the reported entanglement.
Motivated by recent experiments in which specific thermal properties of complex many-body systems were successfully reproduced on a commercially available quantum annealer, we examine the extent to which quantum annealing hardware can reliably sample from the thermal state in a specific basis associated with a target quantum Hamiltonian. We address this question by studying the diagonal thermal properties of the canonical one-dimensional transverse-field Ising model on a D-Wave 2000Q quantum annealing processor. We find that the quantum processor fails to produce the correct expectation values predicted by Quantum Monte Carlo. Comparing to master equation simulations, we find that this discrepancy is best explained by how the measurements at finite transverse fields are enacted on the device. Specifically, measurements at finite transverse field require the system to be quenched from the target Hamiltonian to a Hamiltonian with negligible transverse field, and this quench is too slow. The limitations imposed by such hardware make it an unlikely candidate for thermal sampling, and it remains an open question what thermal expectation values can be robustly estimated in general for arbitrary quantum many-body systems.
Recent tests performed on the D-Wave Two quantum annealer have revealed no clear evidence of speedup over conventional silicon-based technologies. Here we present results from classical parallel-tempering Monte Carlo simulations combined with isoenergetic cluster moves of the archetypal benchmark problem---an Ising spin glass---on the native chip topology. Using realistic uncorrelated noise models for the D-Wave Two quantum annealer, we study the best-case resilience, i.e., the probability that the ground-state configuration is not affected by random fields and random-bond fluctuations found on the chip. We thus compute classical upper-bound success probabilities for different types of disorder used in the benchmarks and predict that an increase in the number of qubits will require either error correction schemes or a drastic reduction of the intrinsic noise found in these devices. We restrict this study to the exact ground state, however, the approach can be trivially extended to the inclusion of excited states if the success metric is relaxed. We outline strategies to develop robust, as well as hard benchmarks for quantum annealing devices, as well as any other (black box) computing paradigm affected by noise.
Demonstrating genuine many-body quantum coherence in large-scale quantum processors remains a central challenge for near-term quantum technologies. Recent experiments on D-Wave quantum annealers have investigated quenches of Ising chains and observed defect densities that show Kibble-Zurek scaling, consistent with coherent quantum dynamics. However, identical scaling can arise from classical or thermal processes. Here we propose the use of many-body coherent oscillations (MBCO) as a diagnostic for the identification of system-wide coherence in analog quantum simulators. Solving the time-dependent Schrodinger equation, we show that quenches of a staggered one-dimensional Ising chain across a quantum critical point produce oscillatory signatures in defect observables. We implement this model on the D-Wave Advantage quantum annealer. Using fast-anneal protocols, we find that, although defect densities follow Kibble-Zurek scaling, the expected oscillatory behavior is absent. We demonstrate that static disorder associated with individual qubits is not likely responsible for the absence of MBCO. Modest modifications to annealing schedules can dramatically enhance oscillation visibility. This work gives a general roadmap for the search for quantum coherence in noisy, large-scale quantum platforms.
The observation of an unequivocal quantum speedup remains an elusive objective for quantum computing. The D-Wave quantum annealing processors have been at the forefront of experimental attempts to address this goal, given their relatively large numbers of qubits and programmability. A complete determination of the optimal time-to-solution (TTS) using these processors has not been possible to date, preventing definitive conclusions about the presence of a scaling advantage. The main technical obstacle has been the inability to verify an optimal annealing time within the available range. Here we overcome this obstacle and present a class of problem instances for which we observe an optimal annealing time using a D-Wave 2000Q processor over a range spanning up to more than 2000 qubits. This allows us to perform an optimal TTS benchmarking analysis and perform a comparison to several classical algorithms, including simulated annealing, spin-vector Monte Carlo, and discrete-time simulated quantum annealing. We establish the first example of a scaling advantage for an experimental quantum annealer over classical simulated annealing: we find that the D-Wave device exhibits certifiably better scaling than simulated annealing, with 95% confidence, over the range of problem sizes that we can test. However, we do not find evidence for a quantum speedup: simulated quantum annealing exhibits the best scaling by a significant margin. Our construction of instance classes with verifiably optimal annealing times opens up the possibility of generating many new such classes, paving the way for further definitive assessments of scaling advantages using current and future quantum annealing devices.
Quantum annealers are emerging as programmable, dynamical experimental platforms for probing strongly correlated spin systems. Yet key thermal assumptions, chiefly a Gibbs-distributed output ensemble, remain unverified in the large-scale regime. Here, we experimentally and quantitatively assess Gibbs sampling fidelity across system sizes spanning over three orders of magnitude. We explore a wide parameter space of coupling strengths, system sizes, annealing times, and D-wave hardware architectures. We find that the naively assumed scaling law for the effective temperature requires a non-negligible, coupling-independent offset that is robust across machines and parameter regimes, quantifying residual non-thermal effects that still conform to an effective Gibbs description. These non-idealities are further reflected in a systematic discrepancy between the physical temperature inferred from the sampled ensemble and the nominal cryogenic temperature of the device. Our results systematically assess the viability of quantum annealers as experimental platforms for probing classical thermodynamics, correct previous assumptions, and provide a physically grounded thermometry framework to benchmark these machines for future thermodynamic experiments.