Related papers: Synchronizable hybrid subsystem codes
Mapping quantum error correcting codes to classical disordered statistical mechanics models and studying the phase diagram of the latter has proven a powerful tool to study the fundamental error robustness and associated critical error…
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…
We face the following dilemma for designing low-density parity-check codes (LDPC) for quantum error correction. 1) The row weights of parity-check should be large: The minimum distances are bounded above by the minimum row weights of…
Achieving reliable performance on early fault-tolerant quantum hardware will depend on protocols that manage noise without incurring prohibitive overhead. We propose a novel framework that integrates quantum computation with the…
We establish dihedral quantum codes of short block length, a class of CSS codes obtained by the lifted product construction. We present the code construction and give a formula for the code dimension, depending on the two classical codes…
Fitting geometric models onto outlier contaminated data is provably intractable. Many computer vision systems rely on random sampling heuristics to solve robust fitting, which do not provide optimality guarantees and error bounds. It is…
There have been various constructions of classical codes from polynomial valuations in literature \cite{ARC04, LNX01,LX04,XF04,XL00}. In this paper, we present a construction of classical codes based on polynomial construction again. One of…
Generalized bicycle (GB) codes have emerged as a promising class of quantum error-correcting codes with practical decoding capabilities. While numerous asymptotically good quantum codes and quantum low-density parity-check code…
Machine learning techniques have led to broad adoption of a statistical model of computing. The statistical distributions natively available on quantum processors are a superset of those available classically. Harnessing this attribute has…
A filtering problem for a class of quantum systems disturbed by a classical stochastic process is investigated in this paper. The classical disturbance process, which is assumed to be described by a linear stochastic differential equation,…
Additive codes and some nonadditive codes use the single and multiple invariant subspaces of the stabilizer G, respectively, to construct quantum codes, so the selection of the invariant subspaces is a key problem. In this paper, I provide…
CSS-T codes were recently introduced as quantum error-correcting codes that respect a transversal gate. A CSS-T code depends on a CSS-T pair, which is a pair of binary codes $(C_1, C_2)$ such that $C_1$ contains $C_2$, $C_2$ is even, and…
Coherent errors, which arise from collective couplings, are a dominant form of noise in many realistic quantum systems, and are more damaging than oft considered stochastic errors. Here, we propose integrating stabilizer codes with…
In fault-tolerant quantum computing, quantum algorithms are implemented through quantum circuits capable of error correction. These circuits are typically constructed based on specific quantum error correction codes, with consideration…
To build a fault-tolerant quantum computer, it is necessary to implement a quantum error correcting code. Such codes rely on the ability to extract information about the quantum error syndrome while not destroying the quantum information…
In recent years, the number of hybrid algorithms that combine quantum and classical computations has been continuously increasing. These two approaches to computing can mutually enhance each others' performances thus bringing the promise of…
We present a quantum circuit synthesis algorithm for implementing universal fault-tolerant quantum computing based on concatenated codes. To realize fault-tolerant quantum computing, the fault-tolerant quantum protocols should be…
Powerful Quantum Error Correction Codes (QECCs) are required for stabilizing and protecting fragile qubits against the undesirable effects of quantum decoherence. Similar to classical codes, hashing bound approaching QECCs may be designed…
Entanglement-assisted quantum error correcting codes (EAQECCs) are a simple and fundamental class of codes. They allow for the construction of quantum codes from classical codes by relaxing the duality condition and using pre-shared…
One of the main objectives of quantum error-correction theory is to construct quantum codes with optimal parameters and properties. In this paper, we propose a class of 2-generator quasi-cyclic codes and study their applications in the…