Related papers: Covariant Quantum Error-Correcting Codes with Metr…
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…
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…
Covariant codes are quantum codes such that a symmetry transformation on the logical system could be realized by a symmetry transformation on the physical system, usually with limited capability of performing quantum error correction (an…
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…
We develop a framework for constructing quantum error-correcting codes and logical gates for three types of spaces -- composite permutation-invariant spaces of many qubits or qudits, composite constant-excitation Fock-state spaces of many…
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…
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…
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 is believed to be essential for scalable quantum computation, but its implementation is challenging due to its considerable space-time overhead. Motivated by recent experiments demonstrating efficient manipulation…
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…
A permutationally invariant n-bit code for quantum error correction can be realized as a subspace stabilized by the non-Abelian group S_n. The code corresponds to bases for the trivial representation, and all other irreducible…
Quantum error correcting codes protect quantum computation from errors caused by decoherence and other noise. Here we study the problem of designing logical operations for quantum error correcting codes. We present an automated procedure…
We present a family of quantum error-correcting codes that support a universal set of transversal logic gates using only local operations on a two-dimensional array of physical qubits. The construction is a subsystem version of color codes…
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…
We describe a quantum error-detecting and error-correcting code embedded within irreducible representations of SU(3). These logical qutrits inherit the He(3) symmetries induced by the representation, while protecting against small SU(3)…
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…
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…
Efficient and high-performance quantum error correction is essential for achieving fault-tolerant quantum computing. Low-depth random circuits offer a promising approach to identifying effective and practical encoding strategies. In this…
Entanglement renormalization can be viewed as an encoding circuit for a family of approximate quantum error correcting codes. The logical information becomes progressively more well-protected against erasure errors at larger length scales.…
Quantum error-correcting codes are constructed that embed a finite-dimensional code space in the infinite-dimensional Hilbert space of a system described by continuous quantum variables. These codes exploit the noncommutative geometry of…