Related papers: Optimal Nonadditive Quantum Error-Detecting Code
A permutationally invariant n-bit code for quantum error correction can be realized as a subspace stabilized by the non-Abelian group S_n. The code corresponds to bases for the trivial representation, and all other irreducible…
Imperfect measurement can degrade a quantum error correction scheme. A solution that restores fault tolerance is to add redundancy to the process of syndrome extraction. In this work, we show how to optimize this process for an arbitrary…
This paper characterizes Goppa codes of certain maximal curves over finite fields defined by equations of the form $y^n = x^m + x$. We investigate Algebraic Geometric and quantum stabilizer codes associated with these maximal curves and…
Concatenating quantum error correction codes scales error correction capability by driving logical error rates down double-exponentially across levels. However, the noise structure shifts under concatenation, making it hard to choose an…
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…
We can encode a qubit in the energy levels of a quantum system. Relaxation and other dissipation processes lead to decay of the fidelity of this stored information. Is it possible to preserve the quantum information for a longer time by…
Using nuclear magnetic resonance techniques, we experimentally investigated the effects of applying a two bit phase error detection code to preserve quantum information in nuclear spin systems. Input states were stored with and without…
We consider the problem of designing an optimal quantum detector to minimize the probability of a detection error when distinguishing between a collection of quantum states, represented by a set of density operators. We show that the design…
Noise causes severe difficulties in implementing quantum computing and quantum cryptography. Several schemes have been suggested to reduce this problem, mainly focusing on quantum computation. Motivated by quantum cryptography, we suggest a…
Bosonic codes with rotational symmetry are currently one of the best performing quantum error correcting codes. Little is known about error propagation and code distance for these rotation codes in contrast with qubit codes and Bosonic…
High-rate and large-distance quantum codes are expected to make fault-tolerant quantum computing more efficient, but most of them lack efficient fault-tolerant encoded-state preparation methods. We propose such a fault-tolerant encoder for…
This paper presents conditions for constructing permutation-invariant quantum codes for deletion errors and provides a method for constructing them. Our codes give the first example of quantum codes that can correct two or more deletion…
Given that approximate quantum error-correcting (AQEC) codes have a potentially better performance than perfect quantum error correction codes, it is pertinent to quantify their performance. While quantum weight enumerators establish some…
Quantum error correction becomes a practical possibility only if the physical error rate is below a threshold value that depends on a particular quantum code, syndrome measurement circuit, and decoding algorithm. Here we present an…
The calculation of the error threshold of quantum error correcting codes typically proceeds as follows. First, syndromes are measured. Then, a decoder infers the error chain and the corresponding correction is applied. The threshold is then…
Explicit non-asymptotic upper bounds on the sizes of multiple-deletion correcting codes are presented. In particular, the largest single-deletion correcting code for $q$-ary alphabet and string length $n$ is shown to be of size at most…
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…
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…
Error-correction process has to be carried out periodically to prevent accumulation of errors in fault-tolerant quantum computation. It is believed that the best choice to get maximum threshold value is carrying out an error-correction…
Surface codes are among the best candidates to ensure the fault-tolerance of a quantum computer. In order to avoid the accumulation of errors during a computation, it is crucial to have at our disposal a fast decoding algorithm to quickly…