Related papers: Nonbinary Error-Detecting Hybrid Codes
Quantum computing is an emerging technology that has the potential to achieve exponential speedups over their classical counterparts. To achieve quantum advantage, quantum principles are being applied to fields such as communications,…
Quantum computing offers the potential for superior computational capabilities, particularly for data-intensive tasks. However, the current state of quantum hardware puts heavy restrictions on input size. To address this, hybrid transfer…
Recently, operator quantum error-correcting codes have been proposed to unify and generalize decoherence free subspaces, noiseless subsystems, and quantum error-correcting codes. This note introduces a natural construction of such codes in…
Recently, Lechner, Hauke and Zoller [Science Advances, 1(9)e1500838, (2015)] have proposed a quantum annealing architecture, in which a classical spin glass with all-to-all connectivity is simulated by a spin glass with geometrically local…
We present a method for implementing stabilizer-based codes with encoding schemes of the operator quantum error correction paradigm, e.g., the "standard" five-qubit and CSS codes, on solid-state qubits with Ising or XY-type interactions.…
We introduce a class of bosonic quantum error-correcting codes, termed \emph{extended binomial codes}, which generalize the structure of one-mode binomial codes by incorporating ideas from high-rate qubit stabilizer codes. These codes are…
Additive codes and some nonadditive codes use the single and multiple invariant subspaces of the stabilizer G, respectively, to construct quantum codes, so the selection of the invariant subspaces is a key problem. In this paper, I provide…
We construct families of high performance quantum amplitude damping codes. All of our codes are nonadditive and most modestly outperform the best possible additive codes in terms of encoded dimension. One family is built from nonlinear…
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…
When sending quantum information over a channel, we want to ensure that the message remains intact. Quantum error correction and quantum authentication both aim to protect (quantum) information, but approach this task from two very…
We introduce quantum pin codes: a class of quantum CSS codes. Quantum pin codes are a generalization of quantum color codes and Reed-Muller codes and share a lot of their structure and properties. Pin codes have gauge operators, an…
Using quantum devices supported by classical computational resources is a promising approach to quantum-enabled computation. One example of such a hybrid quantum-classical approach is the variational quantum eigensolver (VQE) built to…
This is an expository article aiming to introduce the reader to the underlying mathematics and geometry of quantum error correction. Information stored on quantum particles is subject to noise and interference from the environment. Quantum…
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…
We show a simple example of a secret sharing scheme encoding classical secret to quantum shares that can realize an access structure impossible by classical information processing with limitation on the size of each share. The example is…
This paper is on identification of classical information by the use of quantum channels. We focus on simultaneous ID codes which use measurements being useful to identify an arbitrary message. We give a direct and a converse part of the…
Hybrid quantum systems seek to combine the strength of its constituents to master the fundamental conflicting requirements of quantum technology: fast and accurate systems control together with perfect shielding from the environment,…
A promising strategy to protect quantum information from noise-induced errors is to encode it into the low-energy states of a topological quantum memory device. However, readout errors from such memory under realistic settings is less…
Quantum error correction (QEC) is a way to protect quantum information against noise. It consists of encoding input information into entangled quantum states known as the code space. Furthermore, to classify if the encoded information is…
We investigate various aspects of operator quantum error-correcting codes or, as we prefer to call them, subsystem codes. We give various methods to derive subsystem codes from classical codes. We give a proof for the existence of subsystem…