Related papers: Pseudocodeword-based Decoding of Quantum Color Cod…
Achieving practical quantum advantage requires a classical decoding algorithm to identify and correct faults during computation. This classical decoding algorithm must deliver both accuracy and speed, but in what combination? When is a…
We study the performance of common quantum stabilizer codes in the presence of asymmetric and correlated errors. Specifically, we consider the depolarizing noisy quantum memory channel and perform quantum error correction via the five and…
Continuous-variable systems protected by bosonic quantum error-correcting codes have emerged as a promising platform for quantum information processing. To date, design of codewords has centered on optimizing the occupation of basis states…
The realization of quantum error correction is an essential ingredient for reaching the full potential of fault-tolerant universal quantum computation. Using a range of different schemes, logical qubits can be redundantly encoded in a set…
Hybrid codes simultaneously encode both quantum and classical information, allowing for the transmission of both across a quantum channel. We construct a family of nonbinary error-detecting hybrid stabilizer codes that can detect one error…
The relation between stabilizer codes and binary codes provided by Gottesman and Calderbank et al. is a celebrated result, as it allows the lifting of classical codes to quantum codes. An equivalent way to state this result is that the work…
In this thesis, we study concepts in quantum computing using graphical languages, specifically using the ZX-calculus. The core of the research revolves around (graphical) stabilizer decompositions. The first major focus is on the…
Quantum error correction is a key ingredient for large scale quantum computation, protecting logical information from physical noise by encoding it into many physical qubits. Topological stabilizer codes are particularly appealing due to…
Quantum information science strives to leverage the quantum-mechanical nature of our universe in order to achieve large improvements in certain information processing tasks. In deep-space optical communications, current receivers for the…
The information in quantum computers is often stored in identical two-level systems (spins or pseudo-spins) that are separated by a distance shorter than the characteristic wavelength of a reservoir which is responsible for decoherence. In…
In this work, we study the Codeword Stabilized Quantum Codes (CWS codes) a generalization of the stabilizers quantum codes using a new approach, the algebraic structure of modules, a generalization of linear spaces. We show then a new…
Errors in surface code have typically been decoded by Minimum Weight Perfect Matching (MWPM) based method. Recently, neural-network-based Machine Learning (ML) techniques have been employed for this purpose. Here we propose a two-level (low…
Simulating the dynamical properties of large-scale many-fermion systems is a longstanding goal of quantum chemistry, material science and condensed matter. Local fermion-to-qubit encodings have opened a new path for practical fermionic…
In this work we develop a general tensor network decoder for 2D codes. Specifically, we propose a decoder that approximates maximally likelihood decoding for 2D stabiliser and subsystem codes subject to Pauli noise. For a code consisting of…
Quantum error correction (QEC) is essential for scalable quantum computing. However, it requires classical decoders that are fast and accurate enough to keep pace with quantum hardware. While quantum low-density parity-check codes have…
Measurements can detect errors in a decohered quantum memory allowing active error correction to increase the memory time. Previous understanding of this mechanism has focused on evaluating the performance of error correction algorithms…
While it seems possible that quantum computers may allow for algorithms offering a computational speed-up over classical algorithms for some problems, the issue is poorly understood. We explore this computational speed-up by investigating…
Quantum error correction is the art of protecting fragile quantum information through suitable encoding and active interventions. After encoding $k$ logical qubits into $n>k$ physical qubits using a stabilizer code, this amounts to…
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…
We introduce and analyze a new type of decoding algorithm called General Color Clustering (GCC), based on renormalization group methods, to be used in qudit color codes. The performance of this decoder is analyzed under code capacity…