Related papers: Projective error models: Stabilizer codes, Cliffor…
We suggest concrete models for self-correcting quantum memory by reporting examples of local stabilizer codes in 3D that have no string logical operators. Previously known local stabilizer codes in 3D all have string-like logical operators,…
Orthogonal geometric constructions are the basis of many many quantum error-correcting codes (QEC), but strict orthogonality constraints limit design flexibility and resource efficiency. We introduce a quasi-orthogonal geometric framework…
The compass model on a square lattice provides a natural template for building subsystem stabilizer codes. The surface code and the Bacon-Shor code represent two extremes of possible codes depending on how many gauge qubits are fixed. We…
There is a growing gap between the impressive results of deep image generative models and classical algorithms that offer theoretical guarantees. The former suffer from mode collapse or memorization issues, limiting their application to…
One of the most promising routes towards fault-tolerant quantum computation utilizes topological quantum error correcting codes, such as the $\mathbb{Z}_2$ surface code. Logical qubits can be encoded in a variety of ways in the surface…
A weakly constrained code is a collection of finite-length strings over a finite alphabet in which certain substrings or patterns occur according to some prescribed frequencies. Buzaglo and Siegel (ITW 2017) gave a construction of weakly…
Quantum error correction and the use of quantum error correction codes is likely to be essential for the realisation of practical quantum computing. Because the error models of quantum devices vary widely, quantum codes which are tailored…
While stabilizer tableaus have proven exceptionally useful as a descriptive tool for additive quantum codes, they offer little guidance for concrete constructions or coding algorithm analysis. We introduce a representation of stabilizer…
We consider the problem of Clifford testing, which asks whether a black-box $n$-qubit unitary is a Clifford unitary or at least $\varepsilon$-far from every Clifford unitary. We give the first 4-query Clifford tester, which decides this…
Hybrid codes simultaneously encode both quantum and classical information, allowing for the transmission of both across a quantum channel. We construct a family of nonbinary error-detecting hybrid stabilizer codes that can detect one error…
Class-conditional generative models hold promise to overcome the shortcomings of their discriminative counterparts. They are a natural choice to solve discriminative tasks in a robust manner as they jointly optimize for predictive…
Twists are defects that are used to encode and process quantum information in topological codes like surface and color codes. Color codes can host three basic types of twists viz., charge-permuting, color-permuting and domino twists. In…
We propose a new approach to the theory of conditioning for numerical analysis problems for which both classical and stochastic perturbation theory fail to predict the observed accuracy of computed solutions. To motivate our ideas, we…
First, a canonical form for stabilizer parity check matrices of arbitrary size and rank is derived. Next, it is shown that the closely related canonical form of the Clifford group can be computed in time $O(n^3)$ for $n$ qubits, which…
The concept of open weak CAD is introduced. Every open CAD is an open weak CAD. On the contrary, an open weak CAD is not necessarily an open CAD. An algorithm for computing projection polynomials of open weak CADs is proposed. The key idea…
The present paper is concerned with the concept of the one-way quantum computer, beyond binary-systems, and its relation to the concept of stabilizer quantum codes. This relation is exploited to analyze a particular class of quantum…
Despite decades of research, SE lacks widely accepted models (that offer precise quantitative stable predictions) about what factors most influence software quality. This paper provides a promising result showing such stable models can be…
We study the error threshold of color codes, a class of topological quantum codes that allow a direct implementation of quantum Clifford gates suitable for entanglement distillation, teleportation and fault-tolerant quantum computation. We…
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…
Pseudocode is extensively used in introductory programming courses to instruct computer science students in algorithm design, utilizing natural language to define algorithmic behaviors. This learning approach enables students to convert…