Related papers: On the Hardnesses of Several Quantum Decoding Prob…
In this paper, we consider quantum error correction over depolarizing channels with non-binary low-density parity-check codes defined over Galois field of size $2^p$ . The proposed quantum error correcting codes are based on the binary…
Modern program verifiers use logic-based encodings of the verification problem that are discharged by a back end reasoning engine. However, instances of such encodings for large programs can quickly overwhelm these back end solvers. Hence,…
The computational problem of distinguishing two quantum channels is central to quantum computing. It is a generalization of the well-known satisfiability problem from classical to quantum computation. This problem is shown to be…
The more than thirty years old issue of the (classical) information capacity of quantum communication channels was dramatically clarified during the last years, when a number of direct quantum coding theorems was discovered. The present…
Decoding sparse quantum codes can be accomplished by syndrome-based decoding using a belief propagation (BP) algorithm.We significantly improve this decoding scheme by developing a new feedback adjustment strategy for the standard BP…
Quantum cryptography via key distribution mechanisms that utilize quantum entanglement between sender-receiver pairs will form the basis of future large-scale quantum networks. A key engineering challenge in such networks will be the…
Among various classes of quantum error correcting codes (QECCs), non-stabilizer codes have rich properties and are of theoretical and practical interest. Decoding non-stabilizer codes is, however, a highly non-trivial task. In this paper,…
Fault-tolerant quantum computation demands extremely low logical error rates, yet superconducting qubit arrays are subject to radiation-induced correlated noise arising from cosmic-ray muon-generated quasiparticles. The quasiparticle…
Inspired by holographic codes and tensor-network decoders, we introduce tensor-network stabilizer codes which come with a natural tensor-network decoder. These codes can correspond to any geometry, but, as a special case, we generalize…
Quantum computing is an emerging technology that has the potential to achieve exponential speedups over their classical counterparts. To achieve quantum advantage, quantum principles are being applied to fields such as communications,…
The five-qubit quantum error correcting code encodes one logical qubit to five physical qubits, and protects the code from a single error. It was one of the first quantum codes to be invented, and various encoding circuits have been…
Quantum error correction is believed to be essential for scalable quantum computation, but its implementation is challenging due to its considerable space-time overhead. Motivated by recent experiments demonstrating efficient manipulation…
With the rapid developments in quantum hardware comes a push towards the first practical applications on these devices. While fully fault-tolerant quantum computers may still be years away, one may ask if there exist intermediate forms of…
Quantum error-correcting codes with good parameters can be constructed by evaluating polynomials at the roots of the polynomial trace. In this paper, we propose to evaluate polynomials at the roots of trace-depending polynomials (given by a…
The essential insight of quantum error correction was that quantum information can be protected by suitably encoding this quantum information across multiple independently erred quantum systems. Recently it was realized that, since the most…
Decoding algorithms are essential to fault-tolerant quantum-computing architectures. In this perspective we explore decoding algorithms for the surface code; a prototypical quantum low-density parity-check code that underlies many of the…
We investigate layer codes, a family of three-dimensional stabilizer codes that can achieve optimal scaling of code parameters and a polynomial energy barrier, as candidates for self-correcting quantum memories. First, we introduce two…
The disjointness of a stabilizer code is a quantity used to constrain the level of the logical Clifford hierarchy attainable by transversal gates and constant-depth quantum circuits. We show that for any positive integer constant $c$, the…
Noise causes severe difficulties in implementing quantum computing and quantum cryptography. Several schemes have been suggested to reduce this problem, mainly focusing on quantum computation. Motivated by quantum cryptography, we suggest a…
The current paper investigates the bounded distance decoding (BDD) problem for ensembles of lattices whose generator matrices have sub-Gaussian entries. We first prove that, for these ensembles the BDD problem is NP-hard in the worst case.…