Related papers: OPI x Soft Decoders
Topological error correcting codes, and particularly the surface code, currently provide the most feasible roadmap towards large-scale fault-tolerant quantum computation. As such, obtaining fast and flexible decoding algorithms for these…
We speed up existing decoding algorithms for three code classes in different metrics: interleaved Gabidulin codes in the rank metric, lifted interleaved Gabidulin codes in the subspace metric, and linearized Reed-Solomon codes in the…
For more than a century, the diffraction limit has defined the resolution achievable by passive optical imaging systems. Although some resolution improvement can be gained through classical data processing of the image, it is limited by the…
Quantum error correction promises a viable path to fault-tolerant computations, enabling exponential error suppression when the device's error rates remain below the protocol's threshold. This threshold, however, strongly depends on the…
In this paper, a new algebraic soft-decision decoding algorithm for Reed-Solomon code is presented. It is based on rational interpolation and the interpolation points are constructed by Berlekamp-Messay algorithm. Unlike the traditional…
Qudit toric codes are a natural higher-dimensional generalization of the well-studied qubit toric code. However standard methods for error correction of the qubit toric code are not applicable to them. Novel decoders are needed. In this…
Achieving superpolynomial speedups for optimization has long been a central goal for quantum algorithms. Here we introduce Decoded Quantum Interferometry (DQI), a quantum algorithm that uses the quantum Fourier transform to reduce…
Decoding quantum error-correcting codes is a key challenge in enabling fault-tolerant quantum computation. In the classical setting, linear programming (LP) decoders offer provable performance guarantees and can leverage fast practical…
Physics-informed (PI) methodologies have surged to become a pillar route to solve Differential Equations (DEs), sustained by the growth of machine learning methods in scientific contexts. The main proposition of PI is to minimise…
We introduce a novel universal soft-decision decoding algorithm for binary block codes called ordered reliability direct error pattern testing (ORDEPT). Our results, obtained for a variety of popular short high-rate codes, demonstrate that…
We introduce two block coordinate descent algorithms for solving optimization problems with ordinary differential equations (ODEs) as dynamical constraints. The algorithms do not need to implement direct or adjoint sensitivity analysis…
Quantum computing is emerging as a new computing resource that could be superior to conventional computing for certain classes of optimization problems. However, in principle, most existing approaches to quantum optimization are intended to…
Quantum error correction is indispensable to achieving reliable quantum computation. When quantum information is encoded redundantly, a larger Hilbert space is constructed using multiple physical qubits, and the computation is performed…
The typical model for measurement noise in quantum error correction is to randomly flip the binary measurement outcome. In experiments, measurements yield much richer information - e.g., continuous current values, discrete photon counts -…
Quantum algorithms have the potential to provide exponential speedups over some of the best known classical algorithms. These speedups may enable quantum devices to solve currently intractable problems such as those in the fields of…
The design and implementation of error correcting codes has long been informed by two fundamental results: Shannon's 1948 capacity theorem, which established that long codes use noisy channels most efficiently; and Berlekamp, McEliece, and…
Error-correcting codes are a method for representing data, so that one can recover the original information even if some parts of it were corrupted. The basic idea, which dates back to the revolutionary work of Shannon and Hamming about a…
Realizing the full potential of quantum computation requires quantum error correction (QEC), with most recent breakthrough demonstrations of QEC using the surface code. QEC codes use multiple noisy physical qubits to encode information in…
An iterative algorithm is presented for soft-input-soft-output (SISO) decoding of Reed-Solomon (RS) codes. The proposed iterative algorithm uses the sum product algorithm (SPA) in conjunction with a binary parity check matrix of the RS…
Atom loss is a major error source in neutral-atom quantum computers, accounting for over 40% of the total physical errors in recent experiments. Its nonlinear and correlated nature poses significant challenges: current syndrome extraction…