Power of Pausing: Advancing Understanding of Thermalization in Experimental Quantum Annealers

Abstract

We investigate alternative annealing schedules on the current generation of quantum annealing hardware (the D-Wave 2000Q), which includes the use of forward and reverse annealing with an intermediate pause. This work provides new insights into the inner workings of these devices (and quantum devices in general), particular into how thermal effects govern the system dynamics. We show that a pause mid-way through the anneal can cause a dramatic change in the output distribution, and we provide evidence suggesting thermalization is indeed occurring during such a pause. We demonstrate that upon pausing the system in a narrow region shortly after the minimum gap, the probability of successfully finding the ground state of the problem Hamiltonian can be increased over an order of magnitude. We relate this effect to relaxation (i.e. thermalization) after diabatic and thermal excitations that occur in the region near to the minimum gap. For a set of large-scale problems of up to 500 qubits, we demonstrate that the distribution returned from the annealer very closely matches a (classical) Boltzmann distribution of the problem Hamiltonian, albeit one with a temperature at least 1.5 times higher than the (effective) temperature of the annealer. Moreover, we show that larger problems are more likely to thermalize to a classical Boltzmann distribution. arXiv:1810.05881v2 [quant-ph]

Reverse quantum annealing of the p -spin model with relaxation

“…with conventional quantum annealing, where the success probability exhibits a peak as a function of the pausing time, when the pause is inserted about 20 % later than s ∆ , and then rapidly returns to its baseline value [15,22]. In contrast, for s inv < s ∆ , the effect of the pause is negligible; the solid (with pause) and dotted (no pause) lines in Fig.…”

“…If the inversion point is chosen well, the output is an improved trial solution, i. e., a quantum state having larger overlap with the correct one. Reverse annealing can also be combined with the pausing features of the D-Wave machines, allowing to stop the annealing for an extended time period to favor relaxation towards the ground state [15].…”

Leveraging quantum annealing for large MIMO processing in centralized radio access networks

“…As discussed in Section 3.3, the |J F | that enforces a chain of qubits to return a series of values which are all in agreement (either all +1 or −1), and the annealing time T a are both key performance parameters that determine the net time to find a solution, and hence overall QA performance. We also introduce 1, 10, and 100 µs pause time T p in the middle of annealing (T a = 1 µs) with various pause positions s p , to see the effect of pausing [43] on our problems. Setting |J F | too large would wash out the problem information due to ICE, however |J F | on average should increase with the number of logical chains in fullyconnected problems in the absence of ICE [69].…”

“…• Second, the user may accelerate or delay A(t)/B(t) evolution, thus determining annealing time (1-300 µs), the duration of the machine's computation. • Finally, the user may introduce stops (anneal pause) in the annealing process, which have been shown to improve performance in certain settings [43].…”

Finding spin glass ground states using quantum walks

“…However, in the continuous-time setting, the application of quantum walks to optimization problems has not been studied in detail. There is increasing interest in quenches (Amin et al 2018) or pauses (Marshall et al 2019, Passarelli et al 2019 in quantum annealing, which effectively run an open-system version of a quantum walk during part of the computation. Thermal relaxation effects dominate in the regime currently accessible by flux qubit quantum annealers, which is the focus of these works.…”