Related papers: The Near-optimal Performance of Quantum Error Corr…
We study coding schemes for error correction in interactive communications. Such interactive coding schemes simulate any $n$-round interactive protocol using $N$ rounds over an adversarial channel that corrupts up to $\rho N$ transmissions.…
We derive simple necessary and sufficient conditions under which a quantum channel obtained from an arbitrary perturbation from the identity can be reversed on a given code to the lowest order in fidelity. We find the usual Knill-Laflamme…
Color codes are promising quantum error correction (QEC) codes because they have an advantage over surface codes in that all Clifford gates can be implemented transversally. However, thresholds of color codes under circuit-level noise are…
The surface code is a promising candidate for fault-tolerant quantum computation, achieving a high threshold error rate with nearest-neighbor gates in two spatial dimensions. Here, through a series of numerical simulations, we investigate…
The surface code represents a promising candidate for fault-tolerant quantum computation due to its high error threshold and experimental accessibility with nearest-neighbor interactions. However, current exact surface code threshold…
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…
Noise rates in quantum computing experiments have dropped dramatically, but reliable qubits remain precious. Fault-tolerance schemes with minimal qubit overhead are therefore essential. We introduce fault-tolerant error-correction…
The theory of error-correcting codes is concerned with constructing codes that optimize simultaneously transmission rate and relative minimum distance. These conflicting requirements determine an asymptotic bound, which is a continuous…
Quantum error correction is an essential ingredient for universal quantum computing. Despite tremendous experimental efforts in the study of quantum error correction, to date, there has been no demonstration in the realisation of universal…
Topological quantum error correction codes are extremely practical, typically requiring only a 2-D lattice of qubits with tunable nearest neighbor interactions yet tolerating high physical error rates p. It is computationally expensive to…
We present a nonintrusive method for reliably estimating the noise level during quantum computation and quantum communication protected by quantum error-correcting codes. As preprocessing of quantum error correction, our scheme estimates…
Error correction has long been suggested to extend the sensitivity of quantum sensors into the Heisenberg Limit. However, operations on logical qubits are only performed through universal gate sets consisting of finite-sized gates such as…
Quantum error correction provides a path to reach practical quantum computing by combining multiple physical qubits into a logical qubit, where the logical error rate is suppressed exponentially as more qubits are added. However, this…
We discuss families of approximate quantum error correcting codes which arise as the nearly-degenerate ground states of certain quantum many-body Hamiltonians composed of non-commuting terms. For exact codes, the conditions for error…
Quantum error correction plays an important role in fault-tolerant quantum information processing. It is usually difficult to experimentally realize quantum error correction, as it requires multiple qubits and quantum gates with high…
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…
In quantum error correction, it is an important assumption that errors on different qubits are independent. In our previous work [Phys. Rev. A {\bf 92}, 052320 (2015)], the generality of the concatenated five-qubit code has been investgated…
Two observations are given on the fidelity of schemes for quantum information processing. In the first one, we show that the fidelity of a symplectic (stabilizer) code, if properly defined, exactly equals the `probability' of the…
Quantum computers hold the promise of solving computational problems which are intractable using conventional methods. For fault-tolerant operation quantum computers must correct errors occurring due to unavoidable decoherence and limited…
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…