Related papers: New perspectives on covariant quantum error correc…
Quantum error correction and symmetry arise in many areas of physics, including many-body systems, metrology in the presence of noise, fault-tolerant computation, and holographic quantum gravity. Here we study the compatibility of these two…
Quantum error correction and symmetries play central roles in quantum information science and physics. It is known that quantum error-correcting codes that obey (are covariant with respect to) continuous symmetries in a certain sense cannot…
Quantum error correction (QEC) is a key concept in quantum computation as well as many areas of physics. There are fundamental tensions between continuous symmetries and QEC. One vital situation is unfolded by the Eastin--Knill theorem,…
Error correcting codes with a universal set of transversal gates are a desideratum for quantum computing. Such codes, however, are ruled out by the Eastin-Knill theorem. Moreover, the theorem also rules out codes which are covariant with…
We systematically study the fundamental competition between quantum error correction (QEC) and continuous symmetries, two key notions in quantum information and physics, in a quantitative manner. Three meaningful measures of approximate…
To perform reliable quantum computation, quantum error correction is indispensable. In certain cases, continuous covariance symmetry of the physical system can make exact error correction impossible. In this work we study the approximate…
We present a simple proof of the approximate Eastin-Knill theorem, which connects the quality of a quantum error-correcting code (QECC) with its ability to achieve a universal set of transversal logical gates. Our derivation employs…
The Eastin-Knill theorem is a central result of quantum error correction theory and states that a quantum code cannot correct errors exactly, possess continuous symmetries, and implement a universal set of gates transversely. As a way to…
Quantum error correction and symmetries play central roles in quantum information science and physics. It is known that quantum error-correcting codes covariant with respect to continuous symmetries cannot correct erasure errors perfectly…
Transversal encoded gatesets are highly desirable for fault tolerant quantum computing. However, a quantum error correcting code which exactly corrects for local erasure noise and supports a universal set of transversal gates is ruled out…
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…
The low-energy subspace of a conformal field theory (CFT) can serve as a quantum error correcting code, with important consequences in holography and quantum gravity. We consider generic 1+1D CFT codes under extensive local dephasing…
Topological quantum error correction codes are currently among the most promising candidates for efficiently dealing with the decoherence effects inherently present in quantum devices. Numerically, their theoretical error threshold can be…
The existence of quantum error correcting codes is one of the most counterintuitive and potentially technologically important discoveries of quantum information theory. However, standard error correction refers to abstract quantum…
Quantum error correction protects quantum information against environmental noise. When using qubits, a measure of quality of a code is the maximum number of errors that it is able to correct. We show that a suitable notion of ``number of…
The quantum computing devices of today have tens to hundreds of qubits that are highly susceptible to noise due to unwanted interactions with their environment. The theory of quantum error correction provides a scheme by which the effects…
A long-standing challenge in quantum error correction is the infeasibility of universal transversal gates, as shown by the Eastin-Knill theorem. We obtain a necessary and sufficient condition for a quantum code to have universal transversal…
We introduce an intrinsic formulation of quantum error correction based on representation theory, in which error-protection structure is encoded directly in a unitary group representation, rather than being tied to a particular embedding…
Quantum states are very delicate, so it is likely some sort of quantum error correction will be necessary to build reliable quantum computers. The theory of quantum error-correcting codes has some close ties to and some striking differences…
We study quasi-exact quantum error correcting codes and quantum computation with them. A quasi-exact code is an approximate code such that it contains a finite number of scaling parameters, the tuning of which can flow it to corresponding…