相关论文: Trellises for stabilizer codes: definition and use…
We address the task of verifying whether a quantum computer, designed to be protected by a specific stabilizer code, correctly encodes the corresponding logical qubits. To achieve this, we develop a general framework for subspace…
This work classifies stabilizer codes by the set of diagonal Clifford gates that can be implemented transversally on them. We show that, for any stabilizer code, its group of diagonal transversal Clifford gates on $\ell$ code blocks must be…
We investigate various aspects of operator quantum error-correcting codes or, as we prefer to call them, subsystem codes. We give various methods to derive subsystem codes from classical codes. We give a proof for the existence of subsystem…
In this paper, we introduce a construction of quantum convolutional codes (QCCs) based on difference triangle sets (DTSs). To construct QCCs, one must determine polynomial stabilizers $X(D)$ and $Z(D)$ that commute (symplectic…
In this paper we investigate stabilizer quantum error correction codes using controlled phase rotations of strong coherent probe states. We explicitly describe two methods to measure the Pauli operators which generate the stabilizer group…
Quantum error correction is the art of protecting fragile quantum information through suitable encoding and active interventions. After encoding $k$ logical qubits into $n>k$ physical qubits using a stabilizer code, this amounts to…
In the field of quantum information, classical optimizers play an important role. From experimentalists optimizing their physical devices to theorists exploring variational quantum algorithms, many aspects of quantum information require the…
Quantum codes are subspaces of the state space of a quantum system that are used to protect quantum information. Some common classes of quantum codes are stabilizer (or additive) codes, non-stabilizer (or non-additive) codes obtained from…
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…
Entanglement-assisted quantum (QUENTA) codes are a subclass of quantum error-correcting codes which use entanglement as a resource. These codes can provide error correction capability higher than the codes derived from the traditional…
I give an overview of the basic concepts behind quantum error correction and quantum fault tolerance. This includes the quantum error correction conditions, stabilizer codes, CSS codes, transversal gates, fault-tolerant error correction,…
We demonstrate the existence of a finite temperature threshold for a 1D stabilizer code under an error correcting protocol that requires only a fraction of the syndrome measurements. Below the threshold temperature, encoded states have…
Fault-tolerant quantum computation allows quantum computations to be carried out while resisting unwanted noise. Several error-correcting codes have been developed to achieve this task, but none alone are capable of universal quantum…
In this paper, embedding construction of tail-biting trellises for linear block codes is presented. With the new approach of constructing tail-biting trellises, most of the study of tail-biting trellises can be converted into the study of…
We present an algorithm that takes a CSS stabilizer code as input, and outputs another CSS stabilizer code such that the stabilizer generators all have weights $O(1)$ and such that $O(1)$ generators act on any given qubit. The number of…
The central focus of this work is to make progress towards understanding entanglement as a resource for computation by examining the quantum correlations that can be extracted from stabilizer states. As such, we focus on the stabilizer…
The performance of quantum error correction can be significantly improved if detailed information about the noise is available, allowing to optimize both codes and decoders. It has been proposed to estimate error rates from the syndrome…
Classical multidimensional scaling is a widely used method in dimensionality reduction and manifold learning. The method takes in a dissimilarity matrix and outputs a low-dimensional configuration matrix based on a spectral decomposition.…
Coherent errors are a dominant noise process in many quantum computing architectures. Unlike stochastic errors, these errors can combine constructively and grow into highly detrimental overrotations. To combat this, we introduce a simple…
Taking advantage of a recently discovered associativity property of rule compositions, we extend the classical concurrency theory for rewriting systems over adhesive categories. We introduce the notion of tracelets, which are defined as…