The current generation of experimental quantum annealers can shed light on the effects of noise and thermalization present in superconducting quantum circuits. Recent advances in this technology allow for direct probing of intermediate dynamics during the annealing process. By pausing the annealing over spans ranging from micro- to milliseconds and allowing the system to equilibrate, the authors identify several regimes of interest, characterized by the time scales of the dominant processes. It is shown that alternative annealing schedules inspired by physics may prove a fruitful avenue for designing more efficient solvers for optimization problems in quantum computing.
The current generation of experimental quantum annealers can shed light on the effects of noise and thermalization present in superconducting quantum circuits. Recent advances in this technology allow for direct probing of intermediate dynamics during the annealing process. By pausing the annealing over spans ranging from micro- to milliseconds and allowing the system to equilibrate, the authors identify several regimes of interest, characterized by the time scales of the dominant processes. It is shown that alternative annealing schedules inspired by physics may prove a fruitful avenue for designing more efficient solvers for optimization problems in quantum computing.
Recent research has shown that alternative annealing schedules provide the means for improving performance in modern quantum annealing devices. One such type of schedule is forward annealing with a pause, in which there is a period of time when system evolution is paused. While the results from using this type of schedule have been promising, effectively using a pause is not a trivial task. One challenge associated with introducing a pause into the schedule is determining the point in the anneal at which the pause will start. Additionally, tuning the schedule in real-time requires a significant amount of time. A second challenge is that while a pause may increase the number of correct solutions returned from the annealer, the time-to-solution, a standard metric for measuring performance in quantum annealing, will not necessarily be improved. We propose a method for constructing annealing schedules containing a pause that avoids the costly process of determining the optimal pause location in an online manner. We also evaluate our method on the subset sum problem, a problem of practical significance, and show that our method is able to achieve a 70% reduction in time-to-solution from a standard schedule containing no pause.
Annealing schedule control provides opportunities to better understand the manner and mechanisms by which putative quantum annealers operate. By appropriately modifying the annealing schedule to include a pause (keeping the Hamiltonian fixed) for a period of time, we show that it is possible to more directly probe the dissipative dynamics of the system at intermediate points along the anneal and examine thermal relaxation rates, for example, by observing the repopulation of the ground state after the minimum spectral gap. We provide a detailed comparison of experiments from a D-Wave device, simulations of the quantum adiabatic master equation, and a classical analogue of quantum annealing, spin-vector Monte Carlo, and we observe qualitative agreement, showing that the characteristic increase in success probability when pausing is not a uniquely quantum phenomena. We find that the relaxation in our system is dominated by a single timescale, which allows us to give a simple condition for when we can expect pausing to improve the time to solution, the relevant metric for classical optimization. Finally, we also explore in simulation the role of temperature whilst pausing as a means to better distinguish quantum and classical models of quantum annealers.
Prior work showed the efficacy of pausing midanneal: such a pause improved the probability of success by orders of magnitude in a class of native problem instances and improved the time to solution in a class of embedded problem instances. A physics-based picture provides qualitative suggestions for where pausing midanneal is effective, for the interplay between annealing schedule parameters and other annealing properties and parameters such as embedding size and strength of the ferromagnetic coupling ∣JF∣, and for the conditions under which pausing can improve the time to solution. Here, through demonstrations on an updated annealing architecture that has higher connectivity than previous annealers, and on multiple embedded problem classes, we are able to confirm various aspects of this picture. We demonstrate the robustness of the optimal pause parameters across platforms and problem classes, explore how to set ∣JF∣ to optimize performance in different scenarios, and provide empirical evidence that short pauses trump longer overall annealing times in time to solution. We also identify the number of different coefficients in a problem as a predictor of problem hardness, and explore its interplay with the optimal ∣JF∣ and embedding size. Based on these results we are able to present qualitative guidelines for parameter setting in quantum annealers.
In the noisy intermediate-scale quantum (NISQ) era, annealing-based computing is emerging as a new type of high-performance computing (HPC) technology for solving computationally intractable combinatorial optimization problems (COPs). Inspired by thermal annealing in metallurgy, the cost function of a COP is encoded in an energy function (Hamiltonian), with its lowest energy state being searched using an annealer and finally transformed to the global or global approximate optimal solution to a target problem. We address the key technology underlying annealing-based methods along with an experimental study with a commercial digital annealer (DA). We hope to shed light on how industries could benefit from this emerging computing technology to explore the challenges and opportunities in the quantum computing age.
Abstract : Quantum annealing is a general strategy for solving difficult optimization problems with the aid of quantum adiabatic evolution [1, 2]. Both analytical and numerical evidence suggests that under idealized, closed system conditions, quantum annealing can outperform classical thermalization-based algorithms such as simulated annealing [3, 4]. Do engineered quantum annealing devices effectively perform classical thermalization when coupled to a decohering thermal environment? To address this we establish, using superconducting flux qubits with programmable spin-spin couplings, an experimental signature which is consistent with quantum annealing, and at the same time inconsistent with classical thermalization, in spite of a decoherence timescale which is orders of magnitude shorter than the adiabatic evolution time. This suggests that programmable quantum devices, scalable with current superconducting technology, implement quantum annealing with a surprising robustness against noise and imperfections.
Quantum devices are affected by intrinsic and environmental noises. An in-depth characterization of noise effects is essential for exploiting noisy quantum computing. To this end, we studied the energy dissipative behavior of a quantum annealer via experiments and numerical simulations. Our investigation adopts a recently proposed technique that interpolates between pure quantum dynamics and pure thermodynamics. Experiments were conducted on a quantum annealer with an anneal pause function, which inserts a thermal relaxation period into the annealing schedule by pausing the transverse field, which is a source of quantum fluctuation. After investigating the special Hamiltonian that characterizes the quantum thermodynamics of the system, we then observed enhancement of thermodynamic signature depending on the anneal pause parameter. The time development of the state vector, observed in the open quantum simulation, provides rich information for investigating phenomena beyond energy-gap analysis. We identified a special eigenstate bridges ground states far-separated in Hilbert space and the transfer probabilities from one ground state to another. This finding can improve the sampling uniformity by reducing the sampling bias in finding the classical ground states in the quantum annealer. Our study does not only characterize the open quantum phenomenon of the specific Hamiltonian but also demonstrates the usefulness of the method in investigating noisy quantum devices.