Related papers: Sparse Quantum Codes from Quantum Circuits
Spin qubits in quantum dots provide a promising platform for realizing large-scale quantum processors since they have a small characteristic size of a few tens of nanometers. One difficulty of controlling e.g., a few thousand qubits on a…
We prove by construction that the Bravyi-Poulin-Terhal bound on the spatial density of stabilizer codes does not generalize to stabilizer circuits. To do so, we construct a fault tolerant quantum computer with a coding rate above 5% and…
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…
A long-standing open problem in fault-tolerant quantum computation has been to find a universal set of transversal gates. As three of us proved in arXiv: 0706.1382, such a set does not exist for binary stabilizer codes. Here we generalize…
This paper introduces a construction of quantum CSS codes from a tuple of component CSS codes and two collections of subsets. The resulting codes have parallelizable encoding and syndrome measurement circuits and built-in redundancy in the…
We give a broad generalisation of the mapping, originally due to Dennis, Kitaev, Landahl and Preskill, from quantum error correcting codes to statistical mechanical models. We show how the mapping can be extended to arbitrary stabiliser or…
As a generalization of cyclic codes, quasi-cyclic (QC) codes contain many good linear codes. But quasi-cyclic codes studied so far are mainly limited to one generator (1-generator) QC codes. In this correspondence, 2-generator and…
We introduce sequential and parallel decoders for quantum Tanner codes. When the Tanner code construction is applied to a sufficiently expanding square complex with robust local codes, we obtain a family of asymptotically good quantum…
We describe a quantum error correction scheme aimed at protecting a flow of quantum information over long distance communication. It is largely inspired by the theory of classical convolutional codes which are used in similar circumstances…
Graphs are closely related to quantum error-correcting codes: every stabilizer code is locally equivalent to a graph code, and every codeword stabilized code can be described by a graph and a classical code. For the construction of good…
Quantum error-correcting codes (QECCs) sit between noisy quantum hardware and reliable computation, so the code parameters used in practice must be trustworthy. The single number that summarizes a code's strength is its distance, yet…
Concatenating quantum error correction codes scales error correction capability by driving logical error rates down double-exponentially across levels. However, the noise structure shifts under concatenation, making it hard to choose an…
Quantum error correction is necessary to perform large-scale quantum computations in the presence of noise and decoherence. As a result, several aspects of quantum error correction have already been explored. These have been primarily…
We introduce a flexible and graphically intuitive framework that constructs complex quantum error correction codes from simple codes or states, generalizing code concatenation. More specifically, we represent the complex code constructions…
Color codes are promising quantum error correction (QEC) codes because they have an advantage over surface codes in that all Clifford gates can be implemented transversally. However, thresholds of color codes under circuit-level noise are…
Quantum error correction (QEC) is a cornerstone of quantum computing, enabling reliable information processing in the presence of noise. Sparse stabilizer codes -- referred to generally as quantum low-density parity-check (QLDPC) codes --…
In quantum coding theory, stabilizer codes are probably the most important class of quantum codes. They are regarded as the quantum analogue of the classical linear codes and the properties of stabilizer codes have been carefully studied in…
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…
Quantum computers will need effective error-correcting codes. Current quantum processors require precise control of each particle, so having fewer particles to control might be beneficial. Although traditionally quantum computers are…
Generalized-bicycle (GB) and more general two-block group-algebra (2BGA) quantum error-correcting codes have naturally redundant minimum-weight stabilizer generators. To use this redundancy, we constructed a large number of ``planar'' 2BGA…