Related papers: Practical hybrid decoding scheme for parity-encode…
We propose a framework to solve non-linear and history-dependent mechanical problems based on a hybrid classical computer -- quantum annealer approach. Quantum Computers are anticipated to solve particular operations exponentially faster.…
The Learning Parity with Noise (LPN) problem underlines several classic cryptographic primitives. Researchers have attempted to demonstrate the algorithmic hardness of this problem by finding reductions from the decoding problem of linear…
The Ising machine is an unconventional computing architecture that can be used to solve NP-hard combinatorial optimization problems more efficiently than traditional von Neumann architectures. Fast, compact oscillator networks which provide…
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…
One of the most important tasks in modern quantum science is to coherently control and entangle many-body systems, and to subsequently use these systems to realize powerful quantum technologies such as quantum-enhanced sensors. However,…
Sphere decoding (SD) is a low complexity maximum likelihood (ML) detection algorithm, which has been adapted for different linear channels in digital communications. The complexity of the SD has been shown to be exponential in some cases,…
We develop and implement a method for modeling decoherence processes on an N-dimensional quantum system that requires only an $N^2$-dimensional quantum environment and random classical fields. This model offers the advantage that it may be…
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…
One of the main bottlenecks in solving combinatorial optimization problems with quantum annealers is the qubit connectivity in the hardware. A possible solution for larger connectivty is minor embedding. This techniques makes the…
We construct and analyze a family of low-density parity check (LDPC) quantum codes with a linear encoding rate, polynomial scaling distance and efficient decoding schemes. The code family is based on tessellations of closed,…
An Ising model is defined by a quadratic objective function known as the Hamiltonian, composed of spin variables that can take values of either $-1$ or $+1$. The goal is to assign spin values to these variables in a way that minimizes the…
The goal of this work is to construct and study hybrid and multiplicative two-level overlapping Schwarz algorithms with standard coarse spaces for the almost incompressible linear elasticity and Stokes systems, discretized by mixed finite…
Accurate exchange-correlation (XC) potentials are essential for density functional theory, yet reliable approximations remain challenging for strongly correlated systems. In this work, we present a quantum algorithmic framework to determine…
We consider linear-programming (LP) decoding of low-density parity-check (LDPC) codes. While it is clear that one can use any general-purpose LP solver to solve the LP that appears in the decoding problem, we argue in this paper that the LP…
I propose a new method to study computationally difficult problems. I consider a new system, larger than the one I want to simulate. The original system is recovered by imposing constraints on the large system. I simulate the large system…
Ising annealer is a promising quantum-inspired computing architecture for combinatorial optimization problems. In this paper, we introduce an Ising annealer based on the Hamiltonian Monte Carlo, which updates the variables of all dimensions…
We propose a novel coupling technique for the design of polar codes of length N, making them decodable through a sliding window of size M < N. This feature allows to reduce the computational complexity of the decoder, an important…
In this paper we present a novel method for decoding multiple input - multiple output (MIMO) transmission, which combines sphere decoding (SD) and zero forcing (ZF) techniques to provide near optimal low complexity and high performance…
This paper presents a CMOS-compatible Lechner-Hauke-Zoller (LHZ)--based analog tile structure as a fundamental unit for developing scalable analog Ising machines (IMs). In the designed LHZ tile, the voltage-controlled oscillators are…
We propose an efficient encoding algorithm for the binary and non-binary low-density parity-check codes. This algorithm transforms the parity part of the parity-check matrix into a block triangular matrix with low weight diagonal…