Related papers: Building manifolds from quantum codes
To solve the quantum-mechanical problem the procedure of mapping onto linear space $W$ of generators of the (sub)group violated by given classical trajectory is formulated. The formalism is illustrated by the plane H-atom model. The problem…
We define a model for random (abstract) cell complexes (CCs), similiar to the well-known Erd\H{o}s-R\'enyi model for graphs and its extensions for simplicial complexes. To build a random cell complex, we first draw from an Erd\H{o}s-R\'enyi…
Towards better understanding of gate elimination, the only method known that can prove complexity lower bounds for explicit functions against unrestricted Boolean circuits, this work contributes: (1) formalizing circuit simplifications as a…
We introduce a simple cut-and-paste mechanism to construct both orientable and nonorientable four-manifolds from a given initial one. This mechanism alters the fundamental group while preserving other essential topological invariants. It…
Recently, Lin and Pryadko presented the quantum two-block group algebra codes, a generalization of bicycle codes obtained from Cayley graphs of non-Abelian groups. We notice that their construction is naturally suitable to obtain a quantum…
We study the relativistic Lee model on static Riemannian manifolds. The model is constructed nonperturbatively through its resolvent, which is based on the so-called principal operator and the heat kernel techniques. It is shown that making…
We construct quantum codes that support transversal $CCZ$ gates over qudits of arbitrary prime power dimension $q$ (including $q=2$) such that the code dimension and distance grow linearly in the block length. The only previously known…
We introduce a new model for random simplicial complexes which with high probability generates a complex that has a simply-connected double cover. Hence we develop a model for random simplicial complexes with fundamental group…
The question whether there exists a hypergraph whose degrees are equal to a given sequence of integers is a well-known reconstruction problem in graph theory, which is motivated by discrete tomography. In this paper we approach the problem…
We resurrect a standard construction of analytical mechanics dating from the last century. The technique allows one to pass from any dynamical system whose first order evolution equations are known, and whose bracket algebra is not…
In this work we address the reconstruction problem, investigating the construction of field theories from supersymmetric quantum mechanics. The procedure is reviewed, starting from reflectionless potentials that admit one and two bound…
We design logic circuits based on the notion of zero forcing on graphs; each gate of the circuits is a gadget in which zero forcing is performed. We show that such circuits can evaluate every monotone Boolean function. By using two vertices…
In this article, we prove that finite (weakly) systolic and Helly complexes can be reconstructed from their boundary distances (computed in their 1-skeleta). Furthermore, Helly complexes and 2-dimensional systolic complexes can be…
We show that numerical quasi-one-dimensional renormalization group allows accurate study of weakly coupled chains with modest computational effort. We perform a systematic comparison with exact diagonalization results in two and three-leg…
A relationship between quantum flag and Grassmann manifolds is revealed. This enables a formal diagonalization of quantum positive matrices. The requirement that this diagonalization defines a homomorphism leads to a left \Uh -- module…
Manifold learning and effective model building are generally viewed as fundamentally different types of procedure. After all, in one we build a simplified model of the data, in the other, we construct a simplified model of the another…
We propose a new method to define theories of random geometries, using an explicit and simple map between metrics and large hermitian matrices. We outline some of the many possible applications of the formalism. For example, a…
The number of measurements necessary to perform the quantum state reconstruction of a system of qubits grows exponentially with the number of constituents, creating a major obstacle for the design of scalable tomographic schemes. We work…
The architecture of circuital quantum computers requires computing layers devoted to compiling high-level quantum algorithms into lower-level circuits of quantum gates. The general problem of quantum compiling is to approximate any unitary…
Over the past six years, a detailed framework has been constructed to unravel the quantum nature of the Riemannian geometry of physical space. A review of these developments is presented at a level which should be accessible to graduate…