Related papers: Dynamical Logical Qubits in the Bacon-Shor Code
We examine the robustness of a logical qubit in the planar surface code subject to 'measurement-errors', i.e., to local Pauli measurements at known positions. This yields a measurement-only dynamics, which is driven by the competition…
Stabilizer codes form an important class of quantum error correcting codes which have an elegant theory, efficient error detection, and many known examples. Constructing stabilizer codes of length $n$ is equivalent to constructing subspaces…
Quantum computers have the potential to change the way we solve computational problems. Due to the noisy nature of qubits, the need arises to correct physical errors occurring during computation. The surface code is a promising candidate…
We propose a new model of quantum computation comprised of low-weight measurement sequences that simultaneously encode logical information, enable error correction, and apply logical gates. These measurement sequences constitute a new class…
We construct families of Floquet codes derived from colour code tilings of closed hyperbolic surfaces. These codes have weight-two check operators, a finite encoding rate and can be decoded efficiently with minimum-weight perfect matching.…
Quantum error-correcting codes are used to protect qubits involved in quantum computation. This process requires logical operators, acting on protected qubits, to be translated into physical operators (circuits) acting on physical quantum…
Fault-tolerant quantum computing demands many qubits with long lifetimes to conduct accurate quantum gate operations. However, external noise limits the computing time of physical qubits. Quantum error correction codes may extend such…
Fault-tolerant logical operations for qubits encoded by CSS codes are discussed, with emphasis on methods that apply to codes of high rate, encoding k qubits per block with k>1. It is shown that the logical qubits within a given block can…
Quantum computers hold the potential to surpass classical computers in solving complex computational problems. However, the fragility of quantum information and the error-prone nature of quantum operations make building large-scale,…
For quantum error correction codes the required number of measurement rounds typically increases with the code distance when measurements are faulty. Single-shot error correction allows for an error threshold with only one round of noisy…
Quantum error correction provides a fertile context for exploring the interplay of feedback control, microscopic physics and noncommutative probability. In this paper we deepen our understanding of this nexus through high-level analysis of…
We propose the X$^3$Z$^3$ Floquet code, a dynamical code with improved performance under biased noise compared to other Floquet codes. The enhanced performance is attributed to a simplified decoding problem resulting from a persistent…
We reapply our approach to designing nanophotonic quantum memories to formulate an optical network that autonomously protects a single logical qubit against arbitrary single-qubit errors. Emulating the 9 qubit Bacon-Shor subsystem code, the…
Stabilizer codes are the most widely studied class of quantum error-correcting codes and form the basis of most proposals for a fault-tolerant quantum computer. A stabilizer code is defined by a set of parity-check operators, which are…
Quantum error correction is a critical technique for transitioning from noisy intermediate-scale quantum (NISQ) devices to fully fledged quantum computers. The surface code, which has a high threshold error rate, is the leading quantum…
The realization of quantum error correction protocols whose logical error rates are suppressed far below physical error rates relies on an intricate combination: the error-correcting code's efficiency, the syndrome extraction circuit's…
We consider stabilizer measurements for surface codes with neutral atoms and identify gate protocols that minimize logical error rates in the presence of a fundamental error source -- spontaneous emission from Rydberg states. We demonstrate…
Achieving industrial quantum advantage is unlikely without the use of quantum error correction (QEC). Other QEC codes beyond surface code are being experimentally studied, such as color codes and quantum Low-Density Parity Check (qLDPC)…
Classical BCH codes that contain their (Euclidean or Hermitian) dual codes can be used to construct quantum stabilizer codes; this correspondence studies the properties of such codes. It is shown that a BCH code of length n can contain its…
Quantum information is fragile and must be protected by a quantum error-correcting code for large-scale practical applications. Recently, highly efficient quantum codes have been discovered which require a high degree of spatial…