Related papers: Quantum Codes and Symplectic Matroids
We analyze combinatorial structures which play a central role in determining spectral properties of the volume operator in loop quantum gravity (LQG). These structures encode geometrical information of the embedding of arbitrary valence…
General algebraic properties of the algebras of vector fields over quantum linear groups $GL_q(N)$ and $SL_q(N)$ are studied. These quantum algebras appears to be quite similar to the classical matrix algebra. In particular, quantum…
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…
We present the first examples of topological phases of matter with uniform power for measurement-based quantum computation. This is possible thanks to a new framework for analyzing the computational properties of phases of matter that is…
Recent research on distributed storage systems (DSSs) has revealed interesting connections between matroid theory and locally repairable codes (LRCs). The goal of this chapter is to introduce the reader to matroids and polymatroids, and…
QCD is constructed as a lattice gauge theory in which the elements of the link matrices are represented by non-commuting operators acting in a Hilbert space. The resulting quantum link model for QCD is formulated with a fifth Euclidean…
Since masking of quantum information was introduced by Modi et al. in [PRL 120, 230501 (2018)], many discussions on this topic have been published. In this paper, we consider relationship between quantum multipartite maskers (QMMs) and…
In this paper, we demonstrate a direct correspondence between phase-free ZX diagrams, a graphical notation for representing and manipulating a certain class of linear maps on qubits, and Calderbank-Shor-Steane (CSS) codes, a large family of…
We give complete presentations for the dagger-compact props of affine Lagrangian and coisotropic relations over an arbitrary field. This provides a unified family of graphical languages for both affinely constrained classical mechanical…
The following open problems, which concern a fundamental limit on coding properties of quantum codes with realistic physical constraints, are analyzed and partially answered here: (a) the upper bound on code distances of quantum…
We find that the overlapping of a topological quantum color code state, representing a quantum memory, with a factorized state of qubits can be written as the partition function of a 3-body classical Ising model on triangular or Union Jack…
Quantum matrix models in the large-N limit arise in many physical systems like Yang-Mills theory with or without supersymmetry, quantum gravity, string-bit models, various low energy effective models of string theory, M(atrix) theory,…
Graphs and recently hypergraphs have been known as an important tool for considering different properties of quantum many-body systems. In this paper, we study a mapping between an important class of quantum systems namely quantum…
In these proceedings, we review recent advances in applying quantum computing to lattice field theory. Quantum computing offers the prospect to simulate lattice field theories in parameter regimes that are largely inaccessible with the…
By exploiting the connection between scattered $\mathbb{F}_q$-subspaces of $\mathbb{F}_{q^m}^3$ and minimal non degenerate $3$-dimensional rank metric codes of $\mathbb{F}_{q^m}^{n}$, $n \geq m+2$, described in [2], we will exhibit a new…
The connection between secret sharing and matroid theory is well established. In this paper, we generalize the concepts of secret sharing and matroid ports to $q$-polymatroids. Specifically, we introduce the notion of an access structure on…
The Lagrangian of Quantum Chromodynamics is invariant under conformal transformations. Although this symmetry is broken by quantum corrections, it has important consequences for strong interactions at short distances and provides one with…
We consider the strong coupling limit of lattice QCD with massless staggered quarks and study the resource requirements for quantum simulating the theory in its Hamiltonian formulation. The bosonic Hilbert space of the color-singlet degrees…
One of the central tasks in quantum error-correction is to construct quantum codes that have good parameters. In this paper, we construct three new classes of quantum MDS codes from classical Hermitian self-orthogonal generalized…
Quantum synchronizable error-correcting codes are special quantum error-correcting codes that are designed to correct both the effect of quantum noise on qubits and misalignment in block synchronization. It is known that in principle such a…