Related papers: Degenerate Viterbi decoding
We construct a new error-suppression scheme that makes use of the adjoint of reversible quantum algorithms. For decoherence induced errors such as depolarization, it is presented that provided the depolarization error probability is less…
Variational quantum circuits have arisen as an important method in quantum computing. A crucial step of it is parameter optimization, which is typically tackled through gradient-descent techniques. We advantageously explore instead the use…
Degenerate quantum codes are codes that do not reveal the complete error syndrome. Their ability to conceal the complete error syndrome makes them powerful resources in certain quantum information processing tasks. In particular, the most…
Topological color codes defined by the 4.8.8 semiregular lattice feature geometrically local check operators and admit transversal implementation of the entire Clifford group, making them promising candidates for fault-tolerant quantum…
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…
Performing experiments on small-scale quantum computers is certainly a challenging endeavor. Many parameters need to be optimized to achieve high-fidelity operations. This can be done efficiently for operations acting on single qubits as…
Random classical linear codes are widely believed to be hard to decode. While slightly sub-exponential time algorithms exist when the coding rate vanishes sufficiently rapidly, all known algorithms at constant rate require exponential time.…
Qubit loss errors constitute a dominant source of noise in many quantum hardware systems, particularly in neutral atom quantum computers. We develop a theoretical framework to effectively detect and correct loss errors in logical algorithms…
We suggest a technique for constructing lower (existence) bounds for the fault-tolerant threshold to scalable quantum computation applicable to degenerate quantum codes with sublinear distance scaling. We give explicit analytic expressions…
Quantum error-correcting codes (QECCs) and decoherence-free subspace (DFS) codes provide active and passive means, respectively, to address certain types of errors that arise during quantum computation. The latter technique is suitable to…
The state-of-the-art error correcting codes are based on large random constructions (random graphs, random permutations, ...) and are decoded by linear-time iterative algorithms. Because of these features, they are remarkable examples of…
Quantum computing has the potential to solve problems that are intractable for classical systems, yet the high error rates in contemporary quantum devices often exceed tolerable limits for useful algorithm execution. Quantum Error…
Quantum error-correcting codes protect fragile quantum information by encoding it redundantly, but identifying codes that perform well in practice with minimal overhead remains difficult due to the combinatorial search space and the high…
Quantum error correction codes are usually designed to correct errors regardless of their physical origins. In large-scale devices, this is an essential feature. In smaller-scale devices, however, the main error sources are often…
The development and use of large-scale quantum computers relies on integrating quantum error-correcting (QEC) schemes into the quantum computing pipeline. A fundamental part of the QEC protocol is the decoding of the syndrome to identify a…
Block encoding is a key ingredient in the recently developed quantum singular value transformation (QSVT) framework, which provides a unifying description for many quantum algorithms. Initially introduced to simplify and optimize resource…
The development of practical, high-performance decoding algorithms reduces the resource cost of fault-tolerant quantum computing. Here we propose a decoder for the surface code that finds low-weight correction operators for errors produced…
Quantum error correction codes (QECC) are a key component for realizing the potential of quantum computing. QECC, as its classical counterpart (ECC), enables the reduction of error rates, by distributing quantum logical information across…
Quantum degeneracy in error correction is a feature unique to quantum error correcting codes, unlike their classical counterpart. It allows a quantum error correcting code to correct errors even when they can not uniquely pinpoint the…
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…