Related papers: Entanglement-Assisted Quantum Error-Correcting Cod…
For a simple model of mutually interacting qubits it is shown how the errors induced by mutual interactions can be eliminated using concatenated coding. The model is solved exactly for arbitrary interaction strength, for two well-known…
Universal fault-tolerant quantum computation requires overcoming the Eastin--Knill theorem on quantum error correction (QEC) codes that protect information from noise. This is often accomplished through strategies like magic state…
Searches for axion and axionlike dark matter based on solid-state spin qubits are fundamentally limited by strong longitudinal dephasing, which rapidly suppresses the sensitivity gains offered by entanglement. Here we show that quantum…
We consider the effects of local interactions upon quantum mechanically entangled systems. In particular we demonstrate that non-local correlations cannot increase through local operations on any of the subsystems, but that through the use…
Quantum error-correcting codes are used to protect quantum information from decoherence. A raw state is mapped, by an encoding circuit, to a codeword so that the most likely quantum errors from a noisy quantum channel can be removed after a…
In this paper, we study Euclidean and Hermitian hulls of generalized Reed-Solomon codes and twisted generalized Reed-Solomon codes, as well as the Hermitian hulls of Roth-Lempel typed codes. We present explicit constructions of MDS and AMDS…
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 present a theoretical framework for state-adaptive quantum error correction that bridges the gap between quantum computing and error correction paradigms. By incorporating knowledge of quantum states into the error correction process, we…
We introduce the concept of quantum locally recoverable codes (qLRCs) with intersecting recovery sets. We derive a singleton-like bound for these codes by leveraging the additional information provided by the intersecting recovery sets.…
We introduce the notion of entanglement of subspaces as a measure that quantify the entanglement of bipartite states in a randomly selected subspace. We discuss its properties and in particular we show that for maximally entangled subspaces…
Efficient entanglement strategies are essential for advancing variational quantum circuits (VQCs) for quantum machine learning (QML). However, most current approaches use fixed entanglement topologies that are not adaptive to task…
In this work, we develop the theory of quasi-exact fault-tolerant quantum (QEQ) computation, which uses qubits encoded into quasi-exact quantum error-correction codes ("quasi codes"). By definition, a quasi code is a parametric approximate…
Entanglement purification protocols (EPP) and quantum error-correcting codes (QECC) provide two ways of protecting quantum states from interaction with the environment. In an EPP, perfectly entangled pure states are extracted, with some…
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…
We propose VQE circuit fabrics with advantageous properties for the simulation of strongly correlated ground and excited states of molecules and materials under the Jordan-Wigner mapping that can be implemented linearly locally and preserve…
We show how good quantum error-correcting codes can be constructed using generalized concatenation. The inner codes are quantum codes, the outer codes can be linear or nonlinear classical codes. Many new good codes are found, including both…
We work out a theory of approximate quantum error correction that allows us to derive a general lower bound for the entanglement fidelity of a quantum code. The lower bound is given in terms of Kraus operators of the quantum noise. This…
Quantum computing holds transformative potential for various fields, yet its practical application is hindered by the susceptibility to errors. This study makes a pioneering contribution by applying quantum error correction codes (QECCs)…
We investigate a family of fault-tolerant quantum error correction schemes based on the concatenation of small error detection or error correction codes with the three-dimensional cluster state. We propose fault-tolerant state preparation…
Brun, Devetak, and Hsieh [Science 314, 436 (2006)] demonstrated that pre-shared entanglement between sender and receiver enables quantum communication protocols that have better parameters than schemes without the assistance of…