Related papers: Linear programming bounds for quantum channels act…
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…
Tradeoffs between the information rate and fidelity of quantum error-correcting codes are discussed. Quantum channels to be considered are those subject to independent errors and modeled as tensor products of copies of a general completely…
Quantum error mitigation is expected to play a crucial role in the practical applications of quantum machines for the foreseeable future. Thus it is important to put the numerous quantum error mitigation schemes proposed under a coherent…
We define and investigate a notion of entropy for quantum error correcting codes. The entropy of a code for a given quantum channel has a number of equivalent realisations, such as through the coefficients associated with the Knill-Laflamme…
Quantum metrology has many important applications in science and technology, ranging from frequency spectroscopy to gravitational wave detection. Quantum mechanics imposes a fundamental limit on measurement precision, called the Heisenberg…
Modular quantum computing architectures require error correction schemes that remain effective in the presense of noisy inter-processor operations. We introduce a distributed quantum error correction framework based on approximate codes to…
The goal of this paper is to review the theoretical basis for achieving a faithful quantum information transmission and processing in the presence of noise. Initially encoding and decoding, implementing gates and quantum error correction…
Quantum error correction is an essential technique for constructing a scalable quantum computer. In order to implement quantum error correction with near-term quantum devices, a fast and near-optimal decoding method is demanded. A decoder…
Quantum computers require error correction to achieve universal quantum computing. However, current decoding of quantum error-correcting codes relies on classical computation, which is slower than quantum operations in superconducting…
We present a semidefinite program optimization approach to quantum error correction that yields codes and recovery procedures that are robust against significant variations in the noise channel. Our approach allows us to optimize the…
We introduce a quantum packing bound on the minimal resources required by nondegenerate error correction codes for any kind of noise. We prove that degenerate codes can outperform nondegenerate ones in the presence of correlated noise, by…
A linear-programming decoder for \emph{nonbinary} expander codes is presented. It is shown that the proposed decoder has the maximum-likelihood certificate properties. It is also shown that this decoder corrects any pattern of errors of a…
Noise is typically treated as the adversary of quantum information processing. For open quantum dynamics, however, dissipation is part of the target physics, creating a tension with fault-tolerant architectures designed to suppress…
In this paper, we address the problem of state communication in finite-level quantum systems through noise-affected channels. Our approach is based on a self-consistent theory of decoding inner products associated with the code and error…
Recent work on approximate quantum error correction (QEC) has opened up the possibility of constructing subspace codes that protect information with high fidelity in scenarios where perfect error correction is impossible. Motivated by this,…
We develop an intrinsic enumerator framework for quantum error correction in unitary representations of symmetry groups. An intrinsic quantum code is a subspace of a representation $V$ of a group $G$, and errors are organized by the…
We study relationships between worst-case and random-noise properties of error correcting codes. More concretely, we consider connections between minimum distance, list decoding radius, and block error probability on noisy channels. A…
Quantum synchronizable error-correcting codes are special quantum error-correcting codes that are designed to correct both the effect of quantum noise on qubits and misalignment in block synchronization. It is known that in principle such a…
A lower bound on the maximum likelihood (ML) decoding error exponent of linear block code ensembles, on the erasure channel, is developed. The lower bound turns to be positive, over an ensemble specific interval of erasure probabilities,…
Approximation errors must be taken into account when compiling quantum programs into a low-level gate set. We present a methodology that tracks such errors automatically and then optimizes accuracy parameters to guarantee a specified…