相关论文: Topological Quantum Error Correction with Optimal …

Quantum error-correcting codes so far proposed have not worked in the presence of noise which introduces more than one bit of entropy per qubit sent through a quantum channel, nor can any code which identifies the complete error syndrome.…

We present a full quantum error correcting procedure with the semion code: an off-shell extension of the double semion model. We construct open strings operators that recover the quantum memory from arbitrary errors and closed string…

I report two general methods to construct quantum convolutional codes for quantum registers with internal $N$ states. Using one of these methods, I construct a quantum convolutional code of rate 1/4 which is able to correct one general…

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…

Topological quantum error correction is a milestone in the scaling roadmap of quantum computers, which targets circuits with trillions of gates that would allow running quantum algorithms for real-world problems. The square-lattice surface…

Topological quantum computing has recently proven itself to be a very powerful model when considering large- scale, fully error corrected quantum architectures. In addition to its robust nature under hardware errors, it is a software driven…

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…

We investigate the use of Quantum Neural Networks for discovering and implementing quantum error-correcting codes. Our research showcases the efficacy of Quantum Neural Networks through the successful implementation of the Bit-Flip quantum…

This paper provides a new instance of quantum deletion error-correcting codes. This code can correct any single quantum deletion error, while our code is only of length 4. This paper also provides an example of an encoding quantum circuit…

We present a unifying approach to quantum error correcting code design that encompasses additive (stabilizer) codes, as well as all known examples of nonadditive codes with good parameters. We use this framework to generate new codes with…

Topological quantum error correction codes have high thresholds and are well suited to physical implementation. The minimum weight perfect matching algorithm can be used to efficiently handle errors in such codes. We perform a timing…

Methods of finding good quantum error correcting codes are discussed, and many example codes are presented. The recipe C_2^{\perp} \subseteq C_1, where C_1 and C_2 are classical codes, is used to obtain codes for up to 16 information qubits…

Surface codes exploit topological protection to increase error resilience in quantum computing devices and can in principle be implemented in existing hardware. They are one of the most promising candidates for active error correction, not…

Topological quantum error-correcting codes (QECC) encode a variety of topological invariants in their code space. A classic structure that has not been encoded directly is that of obstruction classes of a fiber bundle, such as the Chern or…

The performance of a quantum error-correction process is determined by the likelihood that a random configuration of errors introduced to the system will lead to the corruption of encoded logical information. In this work we compare two…

Efficient and high-performance quantum error correction is essential for achieving fault-tolerant quantum computing. Low-depth random circuits offer a promising approach to identifying effective and practical encoding strategies. In this…

We give new constructions of two classes of algebraic code families which are efficiently list decodable with small output list size from a fraction $1-R-\epsilon$ of adversarial errors where $R$ is the rate of the code, for any desired…

We propose a novel optimization scheme designed to find optimally correctable subspace codes for a known quantum noise channel. To each candidate subspace code we first associate a universal recovery map, as if the code was perfectly…

The paper introduces the application of information geometry to describe the ground states of Ising models by utilizing parity-check matrices of cyclic and quasi-cyclic codes on toric and spherical topologies. The approach establishes a…

Quantum error correction and symmetry arise in many areas of physics, including many-body systems, metrology in the presence of noise, fault-tolerant computation, and holographic quantum gravity. Here we study the compatibility of these two…