Benchmarking simulation of hybrid decoding scheme for parity-encoded spin systems

Abstract

This paper presents classical benchmark simulations of a practical hybrid decoding scheme for parity-encoded spin systems, which is well-suited to the development of quantum annealing devices based on on-chip superconducting technology. We compared the performance of finding the optimal solution using two embedding schemes for emulating all-to-all connectivity from local interactions: the SLHZ scheme, proposed by Sourlas, Lechner, Hauke, and Zoller, and the commonly used minor embedding (ME) scheme. We found that the SLHZ scheme is more efficient than the ME scheme when combined with postreadout classical decoding based on the classical bit-flipping algorithm, although the SLHZ scheme itself is substantially less efficient than the ME scheme.

Figures (6)

• Figure 1: Conducted four types of benchmarking experiments. These correspond to: (a) exhaustive search of the optimal state, (b) search based on the classical annealing, (c) search based on the classical annealing combined with postreadout classical decoding, and (d) exhaustive search combined with postreadout classical decoding.
• Figure 2: Architecture of the SLHZ scheme for $N=5$ logical spins. The black and red circles indicate physical spins and syndromes, respectively. Numbers within the circles define the indices for each spin and syndrome.
• Figure 3: Landscapes of the success probability distribution for the SLHZ scheme plotted as functions of the Lagrange weights $(\beta,\gamma=\beta C_{i})$. The left and right plots are the results for (b) a classical annealing-based search and (c) a classical annealing-based search combined with postreadout BF decoding, respectively. White arrows indicate optimal conditions for the weights $(\beta,\gamma)$.
• Figure 4: Landscapes of the success probability distribution for the modified SLHZ scheme. The left and right plots are the results for (b) a classical annealing-based search and (c) a classical annealing-based search combined with postreadout BF decoding, respectively.
• Figure 5: Landscapes of the success probability distribution for the ME scheme. The left and right plots are the results for (b) a classical annealing-based search and (c) a classical annealing-based search combined with postreadout MV decoding, respectively.