相关论文: Local invariants of stabilizer codes

We study subsystem codes whose gauge group has local generators in the 2D geometry. It is shown that there exists a family of such codes defined on lattices of size LxL with the number of logical qubits k and the minimum distance d both…

Quantum convolutional codes can be used to protect a sequence of qubits of arbitrary length against decoherence. We introduce two new families of quantum convolutional codes. Our construction is based on an algebraic method which allows to…

Error-correcting codes that admit local decoding and correcting algorithms have been the focus of much recent research due to their numerous theoretical and practical applications. An important goal is to obtain the best possible tradeoffs…

Utilizing a quantum system for reservoir computing has recently received a lot of attention. Key challenges are related to how on can optimally en- and decode classical information, as well as what constitutes a good reservoir. Our main…

In this paper, by utilizing the idea of stabilizer codes, we give some relationships between one local unitary representation of braid group in N-qubit tensor space and the corresponding entanglement properties of the N-qubit pure state…

The success of tensor network approaches in simulating strongly correlated quantum systems crucially depends on whether the many body states that are relevant for the problem can be encoded in a local tensor network. Despite numerous…

In this paper, we introduce code distances, a new family of invariants for linear codes. We establish some properties and prove bounds on the code distances, and show that they are not invariants of the matroid (for a linear block code) or…

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…

By defining projective error models we study the mathematical structure of Clifford codes and stabilizer codes using tools from projective representation theory. Furthermore, we introduce a new class of codes which we have called weak…

It has long been envisioned that the strength of the barcode invariant of filtered cellular complexes could be increased using cohomology operations. Leveraging recent advances in the computation of Steenrod squares, we introduce a new…

In this article we investigate the possibility of encoding classical information onto multipartite quantum states in the distant laboratory framework. We show that for all states generated by Clifford operation there always exist such an…

A special class of quantum channels, named subspace local (SL), are defined and investigated. The proposed definition of subspace locality of quantum channels is an attempt to answer the question of what kind of restriction should be put on…

A major difficulty in quantum computation is the ability to implement fault tolerant computations, protecting information against undesired interactions with the environment. Stabiliser codes were introduced as a means to protect…

We investigate stabilizer codes with carrier qudits of equal dimension $D$, an arbitrary integer greater than 1. We prove that there is a direct relation between the dimension of a qudit stabilizer code and the size of its corresponding…

Non-invertible symmetries of quantum field theories and many-body systems generalize the concept of symmetries by allowing non-invertible operations in addition to more ordinary invertible ones described by groups. The aim of this paper is…

Non-local properties of symmetric two-qubit states are quantified in terms of a complete set of entanglement invariants. We prove that negative values of some of the invariants are signatures of quantum entanglement. This leads us to…

We present computable criterion for completely classifying multi-qubit quantum states under local unitary operations. The criterion can be used to detect whether two quantum states in multi-qubit systems are local unitary equivalent or not.…

A theory for wave mechanical systems with local inversion and translation symmetries is developed employing the two-dimensional solution space of the stationary Schr\"odinger equation. The local symmetries of the potential are encoded into…

We construct a family of quantum low-density parity-check codes locally equivalent to higher-dimensional quantum hypergraph-product (QHP) codes. Similarly to QHP codes, the proposed codes have highly redundant sets of low-weight stabilizer…

We give a broad generalisation of the mapping, originally due to Dennis, Kitaev, Landahl and Preskill, from quantum error correcting codes to statistical mechanical models. We show how the mapping can be extended to arbitrary stabiliser or…