Related papers: Quantum Information Set Decoding Algorithms
The ultimate goal of any sparse coding method is to accurately recover from a few noisy linear measurements, an unknown sparse vector. Unfortunately, this estimation problem is NP-hard in general, and it is therefore always approached with…
Quantum error correction, which utilizes logical qubits that are encoded as redundant multiple physical qubits to find and correct errors in physical qubits, is indispensable for practical quantum computing. Surface code is considered to be…
We examine information loss, resource costs, and run time from practical application of quantum data compression. Compressing quantum data to fewer qubits enables efficient use of resources, as well as applications for quantum communication…
This paper studies information-theoretically secure quantum homomorphic encryption (QHE) schemes of classical data. Previous works on information-theoretically secure QHE schemes (like Childs'05, Liang'13, and others) are typically based on…
Encryption schemes attempt to provide a means for entities to communicate confidentially over a public channel. Such schemes have been studied for centuries, and their use has become widespread. However, developments in the area of quantum…
Recently, there has been increasing interest in designing schemes for quantum computations that are robust against errors. Although considerable research has been devoted to developing quantum error correction schemes, much less attention…
To improve the efficiency of the encoding and the decoding is the important problem in the quantum error correction. In a preceding work, a general algorithm for decoding the stabilizer code is shown. This paper will show an decoding which…
We initiate a systematic study of pseudo-deterministic quantum algorithms. These are quantum algorithms that, for any input, output a canonical solution with high probability. Focusing on the query complexity model, our main contributions…
McEliece cryptosystem represents a smart open key system based on the hardness of the decoding of an arbitrary linear code, which is believed to be able to resist the advent of quantum computers. But the original McEliece cryptosystem,…
Randomness plays a key role in the design of attacks on cryptographic systems and cyber security algorithms in general. Random walks and quantum walks are powerful tools for mastering random phenomena. In this article, I propose a…
Optimal encoding of classical data for statistical inference using quantum computing is investigated. A universal encoder is sought that is optimal for a wide array of statistical inference tasks. Accuracy of any statistical inference is…
Measurement-based quantum computing (MBQC) in linear optical systems is promising for near-future quantum computing architecture. However, the nondeterministic nature of entangling operations and photon losses hinder the large-scale…
We construct an explicit quantum coding scheme which achieves a communication rate not less than the coherent information when used to transmit quantum information over a noisy quantum channel. For Pauli and erasure channels we also present…
Quantum error correction is an essential technique for constructing a scalable quantum computer. In order to implement quantum error correction with near-term quantum devices, a fast and near-optimal decoding method is demanded. A decoder…
Quantum hypothesis testing is one of the most fundamental problems in quantum information theory, with crucial implications in areas like quantum sensing, where it has been used to prove quantum advantage in a series of binary photonic…
In this paper we investigate the role of local information in the decoding of the repetition and surface error correction codes for the protection of quantum states. Our key result is an improvement in resource efficiency when local…
In this paper, ensembles of quasi-cyclic moderate-density parity-check (MDPC) codes based on protographs are introduced and analyzed in the context of a McEliece-like cryptosystem. The proposed ensembles significantly improve the error…
Claude Shannon proved in 1949 that information-theoretic-secure encryption is possible if the encryption key is used only once, is random, and is at least as long as the message itself. Notwithstanding, when information is encoded in a…
Efficiently distributing secret keys over long distances remains a critical challenge in the development of quantum networks. "First-generation" quantum repeater chains distribute entanglement by executing protocols composed of…
Quantum stabilizer codes constructed from sparse matrices have good performance and can be efficiently decoded by belief propagation (BP). A conventional BP decoding algorithm treats binary stabilizer codes as additive codes over GF(4).…