Related papers: Quantum stabilizer codes and beyond
In this paper, we address the problem of state communication in finite-level quantum systems through noise-affected channels. Our approach is based on a self-consistent theory of decoding inner products associated with the code and error…
Quantum error correcting (QEC) stabilizer codes enable protection of quantum information against errors during storage and processing. Simulation of noisy QEC codes is used to identify the noise parameters necessary for advantageous…
Quantum error correction requires the use of error syndromes derived from measurements that may be unreliable. Recently, quantum data-syndrome (QDS) codes have been proposed as a possible approach to protect against both data and syndrome…
We establish the connection between a recent new construction technique for quantum error correcting codes, based on graphs, and the so-called stabilizer codes: Each stabilizer code can be realized as a graph code and vice versa.
These notes introduce quantum computation and quantum error correction, emphasising the importance of stabilisers and the mathematical foundations in basic Lie theory. We begin by using the double cover map $\mathrm{SU}_2 \rightarrow…
Achieving reliable performance on early fault-tolerant quantum hardware will depend on protocols that manage noise without incurring prohibitive overhead. We propose a novel framework that integrates quantum computation with the…
Quantum error correction is capable of digitizing quantum noise and increasing the robustness of qubits. Typically, error correction is designed with the target of eliminating all errors - making an error so unlikely it can be assumed that…
We define and show how to construct nonbinary quantum stabilizer codes. Our approach is based on nonbinary error bases. It generalizes the relationship between selforthogonal codes over $GF_{4}$ and binary quantum codes to one between…
Benchmarking the performance of quantum error correction codes in physical systems is crucial for achieving fault-tolerant quantum computing. Current methodologies, such as (shadow) tomography or direct fidelity estimation, fall short in…
Typical stabilizer codes aim to solve the general problem of fault-tolerance without regard for the structure of a specific system. By incorporating a broader representation-theoretic perspective, we provide a generalized framework that…
One formidable difficulty in quantum communication and computation is to protect information-carrying quantum states against undesired interactions with the environment. In past years, many good quantum error-correcting codes had been…
Operator quantum error correction is a recently developed theory that provides a generalized framework for active error correction and passive error avoiding schemes. In this paper, we describe these codes in the stabilizer formalism of…
Quantum error correction is an essential ingredient in the development of quantum technologies. Its subject is to investigate ways to embed quantum Hilbert spaces into a physical system such that this subspace is robust against small…
For realizing a quantum memory we suggest to first encode quantum information via a quantum error correcting code and then concatenate combined decoding and re-encoding operations. This requires that the encoding and the decoding operation…
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…
We introduce a high-level graphical framework for designing and analysing quantum error correcting codes, centred on what we term the coherent parity check (CPC). The graphical formulation is based on the diagrammatic tools of the…
A new class of error-correcting quantum codes is introduced capable of stabilizing qubits against spontaneous decay arising from couplings to statistically independent reservoirs. These quantum codes are based on the idea of using an…
Recent progress in quantum cryptography and quantum computers has given hope to their imminent practical realization. An essential element at the heart of the application of these quantum systems is a quantum error correction scheme. We…
With the advent of physical qubits exhibiting strong noise bias, it becomes increasingly relevant to identify which quantum gates can be efficiently implemented on error-correcting codes designed to address a single dominant error type.…
Stabiliser states play a central role in the theory of quantum computation. For example, they are used to encode computational basis states in the most common quantum error correction schemes. Arbitrary quantum states admit many stabiliser…