Boosting quantum annealer performance via sample persistence

Abstract

We propose a novel method for reducing the number of variables in quadratic unconstrained binary optimization problems, using a quantum annealer (or any sampler) to fix the value of a large portion of the variables to values that have a high probability of being optimal. The resulting problems are usually much easier for the quantum annealer to solve, due to their being smaller and consisting of disconnected components. This approach significantly increases the success rate and number of observations of the best known energy value in samples obtained from the quantum annealer, when compared with calling the quantum annealer without using it, even when using fewer annealing cycles. Use of the method results in a considerable improvement in success metrics even for problems with high-precision couplers and biases, which are more challenging for the quantum annealer to solve. The results are further enhanced by applying the method iteratively and combining it with classical pre-processing. We present results for both Chimera graph-structured problems and embedded problems from a real-world application

A hybrid quantum-classical paradigm to mitigate embedding costs in quantum annealing

“…To see this, let us consider the case when the best classical algorithm can solve a single instance P i in time T C (P i ). 13 We are interested, in particular, in the case when a raw quantum speedup (i.e., t proc (P i ) < T C (P i )) is negated by the embedding (i.e., T Q (P i ) > T C (P i )). Although the standard classical approach to solving R is to use the classical algorithm to solve each P i , and would thus take time t 1 (R) + i T C (P i ), we should not assume this is the best classical approach to solving R, and for a fair comparison the hybrid approach should be benchmarked against the best known classical algorithm for R.…”

“…This embedding is generally very time-consuming, and experimental studies indicate that its quality can have strong effects on performance [12]. Indeed, hybrid approaches themselves have previously been used to reduce the cost and size of these embeddings [13]. We formulate a hybrid approach that can mitigate this cost on problems where many related embeddings must be performed by modifying the problem pipeline to reuse or modify embeddings already performed, thereby allowing any potential advantage to be accessed more directly [14].…”

“…More precisely, one expects the annealing time to be exponential in general, and if an exponential amount of classical processing is also required, it seems likely that no speedup will be possible. This condition could nonetheless be relaxed to obtain an advantage with the hybrid approach, as long as a raw speedup is still present when the annealing and processing times are combined (i.e., tproc + t2), but negated by the embedding if the annealer is used in the standard, more naive, way; however, we make this assumption to simplify our analysis 13. We emphasise that, since we are interested in practical, not only asymptotic, gains, we can not easily assume that TC (Pi) = TC (Pj) for i = j.14 If not, then again the problem is not suitable for the hybrid approach, as a much more efficient classical algorithmic approach exists.…”

On Post-processing the Results of Quantum Optimizers

“…It also assumes that the qubits that show the same configuration across multiple runs are more likely to be the correct values for the global minimum solution and thus, they are fixed. More details about their work can be found in their papers [21,22] Ochoa et al's technique: Recently, we came to know of the work done by Ochoa et al [27] for improving the sampling done by a quantum annealer. The aim of this approach is to arrive at lower energy samples (or runs) (compared to the set of samples/runs that it begins with) during its polynomial time sampling procedure.…”

Effective optimization using sample persistence: A case study on quantum annealers and various Monte Carlo optimization methods

“…Our research is based on an idea first proposed specifically for use with quantum annealers [33], and studied only on a narrow problem set. In this work, we utilize a modified and improved version of the algorithm outlined in [33], and show that it is effective for a range of solvers and hard problem sets. The original algorithm has several limitations that are mitigated in the method presented in this work (see Section II B).…”