We demonstrate that the performance of a quantum annealer on hard random Ising optimization problems can be substantially improved using quantum annealing correction (QAC). Our error correction strategy is tailored to the D-Wave Two device. We find that QAC provides a statistically significant enhancement in the performance of the device over a classical repetition code, improving as a function of problem size as well as hardness. Moreover, QAC provides a mechanism for overcoming the precision limit of the device, in addition to correcting calibration errors. Performance is robust even to missing qubits. We present evidence for a constructive role played by quantum effects in our experiments by contrasting the experimental results with the predictions of a classical model of the device. Our work demonstrates the importance of error correction in appropriately determining the performance of quantum annealers.
This paper investigates the application of adaptive topological optimization to enhance the performance of quantum error correction (QEC) codes. Traditional QEC codes rely on pre-defined, static topologies, which may not be optimally suited to specific noise environments and the characteristics of individual quantum devices. We propose a novel framework utilizing quantum annealing to dynamically optimize the topology of a QEC code. This framework employs a simulated annealing approach, where quantum annealing is used to model the topological evolution of the QEC code under various noise conditions. The algorithm iteratively explores different topological configurations, evaluating their error correction capabilities based on simulated quantum circuits. The core claim of this work is to actively adjust the topology of the error correction code, rather than relying solely on predefined designs, thereby improving error correction efficiency. The key mechanism involves the use of quantum annealing to simulate the evolutionary process of the code's topology and selecting the optimal structure based on the simulated outcomes. This approach represents a significant advancement in the field of QEC by introducing a dynamic and adaptive strategy.
Abstract In this chapter, we analyze the typical performance of adiabatic reverse annealing (ARA) for Sourlas codes. Sourlas codes are representative error-correcting codes related to p-body spin-glass models and have a first-order phase transition for
p>2 p > 2 , which degrades the estimation performance. In the ARA formulation, we introduce the initial Hamiltonian which incorporates the prior information of the solution into a vanilla quantum annealing (QA) formulation. The ground state of the initial Hamiltonian represents the initial candidate solution. To avoid the first-order phase transition, we apply ARA to Sourlas codes. We evaluate the typical ARA performance for Sourlas codes using the replica method. We show that ARA can avoid the first-order phase transition if we prepare for the proper initial candidate solution.