相关论文: Floquet codes without parent subsystem codes

Flag-style fault-tolerance has become a linchpin in the realization of small fault-tolerant quantum-error correction experiments. The flag protocol's utility hinges on low qubit overhead, which is typically much smaller than in other…

A fundamental problem in fault-tolerant quantum computation is the tradeoff between universality and dimensionality, exemplified by the the Bravyi-K\"onig bound for $n$-dimensional topological stabilizer codes. In this work, we extend…

Coherent errors are a dominant noise process in many quantum computing architectures. Unlike stochastic errors, these errors can combine constructively and grow into highly detrimental overrotations. To combat this, we introduce a simple…

In order to build a scalable quantum computer error correction will be required to reduce the impact of errors. Implementing error correction in the framework of measurement based computation manifests itself as the construction of fault…

Convolutional codes are constructed, designed and analysed using row and/or block structures of unit algebraic schemes. Infinite series of such codes and of codes with specific properties are derived. Properties are shown algebraically and…

Recently Haah introduced a new quantum error correcting code embedded on a cubic lattice. One of the defining properties of this code is the absence of string logical operator. We present new codes with similar properties by relaxing the…

Quantum error correction codes associated with the hyperbolic plane have been explored extensively in the context of the AdS$_3$/CFT$_2$ correspondence. In this paper we initiate a systematic study of codes associated with holographic…

In this work, we introduce a new family of [[6k, 2k, 2]] codes designed specifically to be compatible with adiabatic quantum computation. These codes support computationally universal sets of weight-two logical operators and are…

A great deal of work has been done developing quantum codes with varying overhead and connectivity constraints. However, given the such an abundance of codes, there is a surprising shortage of fault-tolerant logical gates supported therein.…

This paper generalizes and expands upon the work [Phys. Rev. Lett. 102, 070502 (2009)] where we introduced a scheme for fault-tolerant holonomic quantum computation (HQC) on stabilizer codes. HQC is an all-geometric strategy based on…

Topological subsystem codes in three spatial dimensions allow for quantum error correction with no time overhead, even in the presence of measurement noise. The physical origins of this single-shot property remain elusive, in part due to…

We propose a protocol to prepare a high-fidelity magic state on a two-dimensional (2D) color code using a three-dimensional (3D) color code. Our method modifies the known code switching protocol with (i) a recently discovered transversal…

We show how to perform a fault-tolerant universal quantum computation in 2D architectures using only transversal unitary operators and local syndrome measurements. Our approach is based on a doubled version of the 2D color code. It enables…

In this study, we investigate the construction of quantum CSS duadic codes with dimensions greater than one. We introduce a method for extending smaller splittings of quantum duadic codes to create larger, potentially degenerate quantum…

Quasi-cyclic codes have been recently employed in the constructions of quantum error-correcting codes. In this paper, we propose a construction of infinite families of quasi-cyclic codes over $\F_q$ which are self-orthogonal with respect to…

Collective coherent noise poses challenges for fault-tolerant quantum error correction (FTQEC), as it falls outside the usual stochastic noise models. While constant excitation (CE) codes can naturally avoid coherent noise, a complete…

We introduce a new family of Fountain codes that are systematic and also have sparse parities. Given an input of $k$ symbols, our codes produce an unbounded number of output symbols, generating each parity independently by linearly…

Conventional unsupervised hashing methods usually take advantage of similarity graphs, which are either pre-computed in the high-dimensional space or obtained from random anchor points. On the one hand, existing methods uncouple the…

Quantum computers face significant challenges from quantum deviations or coherent noise, particularly during gate operations, which pose a complex threat to the efficacy of quantum error correction (QEC) protocols. In this study, we…

Dynamical stabilizer codes (DSCs) have recently emerged as a powerful generalization of static stabilizer codes for quantum error correction, replacing a fixed stabilizer group with a sequence of non-commuting measurements. This dynamical…