Related papers: Engineering autonomous error correction in stabili…
We describe a quantum error correction scheme aimed at protecting a flow of quantum information over long distance communication. It is largely inspired by the theory of classical convolutional codes which are used in similar circumstances…
Recently Shor showed how to perform fault tolerant quantum computation when the error probability is logarithmically small. We improve this bound and describe fault tolerant quantum computation when the error probability is smaller than…
We present a unifying approach to quantum error correcting code design that encompasses additive (stabilizer) codes, as well as all known examples of nonadditive codes with good parameters. We use this framework to generate new codes with…
Logical operations are essential for quantum computation within quantum error-correcting codes. However, discovering their physical realizations is challenging, especially for non-additive codes that lack a stabilizer description. We…
We present analytic estimates of the performances of various approximate quantum error correction schemes for the generalized amplitude damping (GAD) qubit channel. Specifically, we consider both stabilizer and nonadditive quantum codes.…
We investigate a novel class of quantum error correcting codes to correct errors on both qubits and higher-state quantum systems represented as qudits. These codes arise from an original graph-theoretic representation of sets of quantum…
A powerful method for analyzing quantum error-correcting codes is to map them onto classical statistical mechanics models. Such mappings have thus far mostly focused on static codes, possibly subject to repeated syndrome measurements.…
We discuss the existence of stable topological quantum memory at finite temperature. At stake here is the fundamental question of whether it is, in principle, possible to store quantum information for macroscopic times without the…
We theoretically analyze a scheme for fast stabilization of arbitrary qubit states with high fidelities, extending a protocol recently demonstrated experimentally [Lu et al., Phys. Rev. Lett. 119, 150502 (2017)]. That experiment utilized…
We propose a new approach to study the evolution of a quantum state that is encoded in a system which is continuously subject to the operations required to implement a quantum error correcting code. In the limit of continuous error…
Quantum error correction offers a promising path to suppress errors in quantum processors, but the resources required to protect logical operations from noise, especially non-Clifford operations, pose a substantial challenge to achieve…
Quantum error correction has recently emerged as a tool to enhance quantum sensing under Markovian noise. It works by correcting errors in a sensor while letting a signal imprint on the logical state. This approach typically requires a…
Quantum error correction is important to quantum information processing, which allows us to reliably process information encoded in quantum error correction codes. Efficient quantum error correction benefits from the knowledge of error…
Passive error correction protects logical information forever in the thermodynamic limit by updating the system based only on local information and few-body interactions. A paradigmatic example is the classical two-dimensional Ising model:…
Stabilizer codes form an important class of quantum error correcting codes which have an elegant theory, efficient error detection, and many known examples. Constructing stabilizer codes of length $n$ is equivalent to constructing subspaces…
Fault-tolerant quantum computation allows quantum computations to be carried out while resisting unwanted noise. Several error-correcting codes have been developed to achieve this task, but none alone are capable of universal quantum…
Quantum computers will eventually reach a size at which quantum error correction becomes imperative. Quantum information can be protected from qubit imperfections and flawed control operations by encoding a single logical qubit in multiple…
The ability to extend the lifetime of a logical qubit beyond that of the best physical qubit available within the same system, i.e., the break-even point, is a prerequisite for building practical quantum computers. So far, this point has…
Quantum information is fragile and must be protected by a quantum error-correcting code for large-scale practical applications. Recently, highly efficient quantum codes have been discovered which require a high degree of spatial…
Codeword stabilized (CWS) codes are a general class of quantum codes that includes stabilizer codes and many families of non-additive codes with good parameters. For such a non-additive code correcting all t-qubit errors, we propose an…