Related papers: Parallelized quantum error correction with fracton…
We introduce new algorithms and provide example constructions of stabilizer models for the gapped boundaries, domain walls, and $0D$ defects of Abelian composite-dimensional twisted quantum doubles. Using the physically intuitive concept of…
A promising approach to overcome decoherence in quantum computing schemes is to perform active quantum error correction using topology. Topological subsystem codes incorporate both the benefits of topological and subsystem codes, allowing…
Topological quantum error correction is a milestone in the scaling roadmap of quantum computers, which targets circuits with trillions of gates that would allow running quantum algorithms for real-world problems. The square-lattice surface…
The recently introduced detected-jump correcting quantum codes are capable of stabilizing qubit-systems against spontaneous decay processes arising from couplings to statistically independent reservoirs. These embedded quantum codes exploit…
Quantum low-density parity-check codes are a promising candidate for fault-tolerant quantum computing with considerably reduced overhead compared to the surface code. However, the lack of a practical decoding algorithm remains a barrier to…
In this paper we present an optimized parallel implementation of a flexible MAP decoder for synchronization error correcting codes, supporting a very wide range of code sizes and channel conditions. On mid-range GPUs we demonstrate decoding…
We study the subfield subcodes of projective Reed-Solomon codes and their duals: we provide bases for these codes and estimate their parameters. With this knowledge, we can construct symmetric and asymmetric entanglement-assisted quantum…
Quantum computers require error correction to achieve universal quantum computing. However, current decoding of quantum error-correcting codes relies on classical computation, which is slower than quantum operations in superconducting…
Given that quantum error correction processes are unreliable, an efficient error syndrome extraction circuit should use fewer ancillary qubits, quantum gates, and measurements, while maintaining low circuit depth, to minimizing the circuit…
Topological error correcting codes, and particularly the surface code, currently provide the most feasible roadmap towards large-scale fault-tolerant quantum computation. As such, obtaining fast and flexible decoding algorithms for these…
Quantum error correction (QEC) is essential for enabling quantum advantages, with decoding as a central algorithmic primitive. Owing to its importance and intrinsic difficulty, substantial effort has been made to QEC decoder design, among…
This is an expository article aiming to introduce the reader to the underlying mathematics and geometry of quantum error correction. Information stored on quantum particles is subject to noise and interference from the environment. Quantum…
We discuss stabilizer quantum-error correction codes implemented in a single multi-level qudit to avoid resource escalation typical of multi-qubit codes. These codes can be customized to the specific physical errors on the qudit,…
Quantum computing is poised to solve practically useful problems which are computationally intractable for classical supercomputers. However, the current generation of quantum computers are limited by errors that may only partially be…
The Tucker tensor decomposition is a natural extension of the singular value decomposition (SVD) to multiway data. We propose to accelerate Tucker tensor decomposition algorithms by using randomization and parallelization. We present two…
Quantum computers hold the promise of solving computational problems which are intractable using conventional methods. For fault-tolerant operation quantum computers must correct errors occurring due to unavoidable decoherence and limited…
A fault-tolerant quantum computer must decode and correct errors faster than they appear. The faster errors can be corrected, the more time the computer can do useful work. The Union-Find (UF) decoder is promising with an average time…
Color code is a promising topological code for fault-tolerant quantum computing. Insufficient research on the color code has delayed its practical application. In this work, we address several key issues to facilitate practical…
A promising strategy to protect quantum information from noise-induced errors is to encode it into the low-energy states of a topological quantum memory device. However, readout errors from such memory under realistic settings is less…
We construct new families of multi-error-correcting quantum codes for the amplitude damping channel. Our key observation is that, with proper encoding, two uses of the amplitude damping channel simulate a quantum erasure channel. This…