Related papers: The Quantum Decoding Problem : Tight Achievability…
Geometrically local quantum codes, which are error correction codes embedded in $\mathbb{R}^D$ with checks acting only on qubits within a fixed spatial distance, have garnered significant interest. Recently, it has been demonstrated how to…
Topological quantum error-correcting codes are defined by geometrically local checks on a two-dimensional lattice of quantum bits (qubits), making them particularly well suited for fault-tolerant quantum information processing. Here, we…
We introduce a quantum packing bound on the minimal resources required by nondegenerate error correction codes for any kind of noise. We prove that degenerate codes can outperform nondegenerate ones in the presence of correlated noise, by…
We study the following one-way asymmetric transmission problem, also a variant of model-based compressed sensing: a resource-limited encoder has to report a small set $S$ from a universe of $N$ items to a more powerful decoder (server). The…
We consider the problem of implementing two-party interactive quantum communication over noisy channels, a necessary endeavor if we wish to fully reap quantum advantages for communication. For an arbitrary protocol with $n$ messages,…
We describe a slightly sub-exponential time algorithm for learning parity functions in the presence of random classification noise. This results in a polynomial-time algorithm for the case of parity functions that depend on only the first…
The main promise of quantum computing is to efficiently solve certain problems that are prohibitively expensive for a classical computer. Most problems with a proven quantum advantage involve the repeated use of a black box, or oracle,…
Recent research has demonstrated that quantum computers can solve certain types of problems substantially faster than the known classical algorithms. These problems include factoring integers and certain physics simulations. Practical…
Noise and decoherence are two major obstacles to the implementation of large-scale quantum computing. Because of the no-cloning theorem, which says we cannot make an exact copy of an arbitrary quantum state, simple redundancy will not work…
Quantum error correction is an important building block for reliable quantum information processing. A challenging hurdle in the theory of quantum error correction is that it is significantly more difficult to design error-correcting codes…
We approach the theoretical problem of compressing a signal dominated by Gaussian noise. We present expressions for the compression ratio which can be reached, under the light of Shannon's noiseless coding theorem, for a linearly quantized…
Quantum computing (QC) promises significant advantages on certain hard computational tasks over classical computers. However, current quantum hardware, also known as noisy intermediate-scale quantum computers (NISQ), are still unable to…
Turbo coding is a powerful class of forward error correcting codes, which can achieve performances close to the Shannon limit. The turbo principle can be applied to the problem of side-information source coding, and we investigate here its…
Future beyond-5G and 6G systems demand ultra-reliable, low-latency communication with short blocklengths, motivating the development of universal decoding algorithms. Guessing decoding, which infers the noise or codeword candidate in order…
A model of quantum noisy channel with input encoding by a classical random vector is described. An equation of optimality is derived to determine a complete set of wave functions describing quantum decodings based on quasi-measurements…
We study quantum algorithms for several fundamental string problems, including Longest Common Substring, Lexicographically Minimal String Rotation, and Longest Square Substring. These problems have been widely studied in the stringology…
The robustness of quantum memory against physical noises is measured by two methods: the exact and approximate quantum error correction (QEC) conditions for error recoverability, and the decoder-dependent error threshold which assesses if…
Departing from traditional communication theory where decoding algorithms are assumed to perform without error, a system where noise perturbs both computational devices and communication channels is considered here. This paper studies…
Recent years have seen rapid development in the subject of quantum coding theory, with breakthroughs on many exciting classes of codes, including quantum LDPC codes, quantum locally testable codes, and quantum codes with interesting…
Quantum error correction (QEC) is required for large-scale computation, but incurs a significant resource overhead. Recent advances have shown that by jointly decoding logical qubits in algorithms composed of transversal gates, the number…