相关论文: Graphs, Quadratic Forms, and Quantum Codes

Deciding if a given family of quantum states is topologically ordered is an important but nontrivial problem in condensed matter physics and quantum information theory. We derive necessary and sufficient conditions for a family of graph…

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…

In this paper, we study some codes of algebraic geometry related to certain maximal curves. Quantum stabilizer codes obtained through the self orthogonality of Hermitian codes of this error correcting do not always have good parameters.…

We introduce tile codes, a simple yet powerful way of constructing quantum codes that are local on a planar 2D-lattice. Tile codes generalize the usual surface code by allowing for a bit more flexibility in terms of locality and stabilizer…

We show a simple example of a secret sharing scheme encoding classical secret to quantum shares that can realize an access structure impossible by classical information processing with limitation on the size of each share. The example is…

Graph states are widely used in quantum information theory, including entanglement theory, quantum error correction, and one-way quantum computing. Graph states have a nice structure related to a certain graph, which is given by either a…

We consider the CSS algorithm relating self-orthogonal classical linear codes to q-ary quantum stabilizer codes and we show that to such a pair of a classical and a quantum code one can associate geometric spaces constructed using methods…

A curve attaining the Hasse-Weil bound is called a maximal curve. Usually classical error-correcting codes obtained from a maximal curve have good parameters. However, the quantum stabilizer codes obtained from such classical…

Stabilizer states are a prime resource for a number of applications in quantum information science, such as secret-sharing and measurement-based quantum computation. This motivates us to study the entanglement of noisy stabilizer states…

We investigate generalized quadratic forms with values in the set of rational integers over quadratic fields. We characterize the real quadratic fields which admit a positive definite binary generalized form of this type representing every…

We extend the stabilizer formalism to a class of non-additive quantum codes which are constructed from non-linear classical codes. As an example, we present infinite families of non-additive codes which are derived from Goethals and…

We show that the Quantum State Distinguishability (QSD), which is a QSZK-complete problem, and the Quantum Circuit Distinguishability (QCD), which is a QIP-complete problem, can be solved by the verifier who can perform only single-qubit…

We investigate the controllability of an infinite-dimensional quantum system: a quantum particle confined on a Thick Quantum Graph, a generalisation of Quantum Graphs whose edges are allowed to be manifolds of arbitrary dimension with…

We outline some recent proofs of quantum ergodicity on large graphs and give new applications in the context of irregular graphs. We also discuss some remaining questions.

A quantum error correcting code is a subspace $\mathcal{C}$ such that allowed errors acting on any state in $\mathcal{C}$ can be corrected. A quantum code for which state recovery is only required up to a logical rotation within…

In this paper, we examine algebraic geometric (AG) codes associated with curves generated by separated polynomials, and we create AG codes and quantum stabilizer codes from these curves by varying their parameters. Our research involves a…

Quantum computing (QC) is a new computational paradigm whose foundations relate to quantum physics. Notable progress has been made, driving the birth of a series of quantum-based algorithms that take advantage of quantum computational…

Two-level quantum systems, qubits, are not the only basis for quantum computation. Advantages exist in using qudits, d-level quantum systems, as the basic carrier of quantum information. We show that color codes, a class of topological…

In this work, we propose novel families of positional encodings tailored to graph neural networks obtained with quantum computers. These encodings leverage the long-range correlations inherent in quantum systems that arise from mapping the…

With respect to the transversal gate group (an invariant of quantum codes), we demonstrate that non-additive codes can outperform stabilizer codes. We do this by constructing spin codes that correspond to permutation-invariant multiqubit…