Related papers: Quantum Deletion Codes Derived From Quantum Reed-S…
Quantum error correction holds the key to scaling up quantum computers. Cosmic ray events severely impact the operation of a quantum computer by causing chip-level catastrophic errors, essentially erasing the information encoded in a chip.…
Quantum states are very delicate, so it is likely some sort of quantum error correction will be necessary to build reliable quantum computers. The theory of quantum error-correcting codes has some close ties to and some striking differences…
Permutation codes and multi-permutation codes have been widely considered due to their various applications, especially in flash memory. In this paper, we consider permutation codes and multi-permutation codes against a burst of stable…
Quantum convolutional codes can be used to protect a sequence of qubits of arbitrary length against decoherence. In this paper, we give two new constructions of quantum MDS convolutional codes derived from generalized Reed-Solomon codes and…
We introduce new rounding methods to improve the accuracy of finite precision quantum arithmetic. These quantum rounding methods are applicable when multiple samples are being taken from a quantum program. We show how to use multiple…
Quantum error correction is capable of digitizing quantum noise and increasing the robustness of qubits. Typically, error correction is designed with the target of eliminating all errors - making an error so unlikely it can be assumed that…
We present a scheme for correcting qubit loss error while quantum computing with neutral atoms in an addressable optical lattice. The qubit loss is first detected using a quantum non-demolition measurement and then transformed into a…
We consider the problem of designing low-redundancy codes in settings where one must correct deletions in conjunction with substitutions or adjacent transpositions; a combination of errors that is usually observed in DNA-based data storage.…
We introduce a fully constructive characterisation of holographic quantum error-correcting codes. That is, given a code and an erasure error we give a recipe to explicitly compute the terms in the RT formula. Using this formalism, we employ…
Quantum error correction, which utilizes logical qubits that are encoded as redundant multiple physical qubits to find and correct errors in physical qubits, is indispensable for practical quantum computing. Surface code is considered to be…
It is possible to reduce some types of quantum computation errors by symmetrizing the quantum state of a redundant array. Various models are discussed.
Quantum computation and communication rely on the ability to manipulate quantum states robustly and with high fidelity. Thus, some form of error correction is needed to protect fragile quantum superposition states from corruption by…
The concept of quantum interleaver and a simple method of quantum burst-error correction is proposed. By using the quantum interleaver, any quantum burst-errors that have occurred spread over the interleaved code word, so that we can…
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 introduce a two-step error correction scheme for reconciliation in continuous-variable quantum key distribution systems. Using this scheme, it is possible to use error correction codes with small blocklengths (1000 bits), increasing…
Due to the fragility of quantum mechanical effects, real quantum computers are plagued by frequent noise effects that cause errors during computations. Quantum error-correcting codes address this problem by providing means to identify and…
Noise and errors are inevitable parts of any practical implementation of a quantum computer. As a result, large-scale quantum computation will require ways to detect and correct errors on quantum information. Here, we present such a quantum…
In this paper, we prove the equivalence of inserting separable quantum states and deletions. Hence any quantum code that corrects deletions automatically corrects separable insertions. First, we describe the quantum insertion/deletion error…
We present for the first time a general theory of error correction for permutation invariant (PI) codes. Using representation theory of the symmetric group we construct efficient algorithms that can correct any correctible error on any PI…
The error correcting capabilities of the Calderbank-Shor-Steane [[7,1,3]] quantum code, together with a fault-tolerant syndrome extraction by means of several ancilla states, have been numerically studied. A simple probability expression to…