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We propose a practical hybrid decoding scheme for the parity-encoding architecture. This architecture was first introduced by N. Sourlas as a computational technique for tackling hard optimization problems, especially those modeled by spin…

Quantum annealing aims to exploit quantum mechanics to speed up the search for the solution to optimization problems. Most problems exhibit complete connectivity between the logical spin variables after they are mapped to the Ising spin…

The Sourlas-Lechner-Hauke-Zoller (SLHZ) scheme for quantum annealing uses the parity to encode logical variables and has several advantages, but it has not been implemented for large-scale quantum annealers. If the SLHZ-based approach can…

F. Pastawski and J. Preskill discussed error correction of quantum annealing (QA) based on a parity-encoded spin system, known as the Sourlas-Lechner-Hauke-Zoller (SLHZ) system. They pointed out that the SLHZ system is closely related to a…

Quantum annealing (QA) has emerged as a promising candidate for fast solvers for combinatorial optimization problems (COPs) and has attracted the interest of many researchers. Since COP is logically encoded in the Ising interaction among…

Lechner, Hauke, and Zoller proposed a parity-encoded spin-embedding scheme for quantum annealing (QA) with all-to-all connectivity to avoid the issue of limited connectivity in near-term QA hardware and to enable the implementation thereof…

Recently, Lechner, Hauke and Zoller [Science Advances, 1(9)e1500838, (2015)] have proposed a quantum annealing architecture, in which a classical spin glass with all-to-all connectivity is simulated by a spin glass with geometrically local…

Nearest-neighbour clustering is a powerful set of heuristic algorithms that find natural application in the decoding of signals transmitted using the M-Quadrature Amplitude Modulation (M-QAM) protocol. Lloyd et al. proposed a quantum…

We perform exact diagonalization and time evolution of the Lechner-Hauke-Zoller (LHZ) annealing architecture [Science Advances 1(9), e1500838 (2015)] for ten physical qubits. Thereby, on a training set consisting of $2400$ problem…

In order to treat all-to-all connected quadratic binary optimization problems (QUBO) with hardware quantum annealers, an embedding of the original problem is required due to the sparsity of the hardware's topology. Embedding fully-connected…

Fast classical processing is essential for most quantum fault-tolerance architectures. We introduce a sliding-window decoding scheme that provides fast classical processing for the surface code through parallelism. Our scheme divides the…

To enhance the performance of quantum annealing machines, several methods have been proposed to reduce the number of spins by fixing spin values through preprocessing. We proposed a hybrid optimization method that combines a simulated…

Conventional classical solvers are commonly used for solving matrix equation systems resulting from the discretization of SIEs in computational electromagnetics (CEM). However, the memory requirement would become a bottleneck for classical…

We explored decoding methods for the surface code under depolarizing noise by mapping the problem into the Ising model optimization. We consider two kinds of mapping with and without a soft constraint and also various optimization solvers,…

Quantum annealing provides a promising route for the development of quantum optimization devices, but the usefulness of such devices will be limited in part by the range of implementable problems as dictated by hardware constraints. To…

We introduce harmonization, an ensembling method that combines several "noisy" decoders to generate highly accurate decoding predictions. Harmonized ensembles of MWPM-based decoders achieve lower logical error rates than their individual…

There is a significant ongoing effort in realizing quantum annealing with different physical platforms. The challenge is to achieve a fully programmable quantum device featuring coherent adiabatic quantum dynamics. Here we show that…

Massive MIMO systems are seen by many researchers as a paramount technology toward next generation networks. This technology consists of hundreds of antennas that are capable of sending and receiving simultaneously a huge amount of data.…

The family of Multiscale Hybrid-Mixed (MHM) finite element methods has received considerable attention from the mathematics and engineering community in the last few years. The MHM methods allow solving highly heterogeneous problems on…

Hybrid precoding has been recognized as a promising technology to combat the path loss of millimeter wave signals in massive multiple-input multiple-output (MIMO) systems. However, due to the joint optimization of the digital and analog…