Related papers: A Sparse $Z_2$ Chain Complex Without a Sparse Lift

We construct a nontrivial three-dimensional subshift of finite type whose projective $\Z$-subdynamics, or $\Z$-trace, is 2-sparse, meaning that there are at most two nonzero symbols in any vertical column. The subshift is deterministic in…

Current implementations of quantum computers suffer from large numbers of control lines per qubit, becoming unmanageable with system scale up. Here, we discuss a sparse spin-qubit architecture featuring integrated control electronics…

We study the realizability of scale free-networks with a given degree sequence, showing that the fraction of realizable sequences undergoes two first-order transitions at the values 0 and 2 of the power-law exponent. We substantiate this…

This paper presents a novel class of complex-valued sparse complementary pairs (SCPs), each consisting of a number of zero values and with additional zero-correlation zone (ZCZ) property for the aperiodic autocorrelations and…

We adapt the construction of subsets of {1, 2, ..., N} that contain no k-term arithmetic progressions to give a relatively thick subset of an arbitrary set of N integers. Particular examples include a thick subset of {1, 4, 9, ..., N^2}…

A large (infinitely-dimensional) class of completely integrable (possibly non-autonomous) spin chains is discovered associated to an infinite-dimensional Lie Algebra of infinite rank. The complete set of integrals of motion is constructed…

Scale-free percolation is a percolation model on $\mathbb{Z}^d$ which can be used to model real-world networks. We prove bounds for the graph distance in the regime where vertices have infinite degrees. We fully characterize transience vs.…

We present a new class of sparse and easily invertible circulant matrices that can have a sparse inverse though not being permutation matrices. Their study is useful in the design of quasi-cyclic low-density generator matrix codes, that are…

Preparing a quantum circuit that implements a given sparse state is an important building block that is necessary for many different quantum algorithms. In the context of fault-tolerant quantum computing, the so-called non-Clifford gates…

We study (tame) frieze patterns over subsets of the complex numbers, with particular emphasis on the corresponding quiddity cycles. We provide new general transformations for quiddity cycles of frieze patterns. As one application, we…

This paper addresses the challenge of preparing mixed quantum states -- both arbitrary states in general and highly sparse ones in particular -- an area that has received far less attention than the preparation of pure states. We present…

A weak order on the set of maximal chains of the non-crossing partition lattice is introduced and studied. A $0$-Hecke algebra action is used to compute the radius of the graph on these chains in which two chains are adjacent if they differ…

Inspired by the challenge of scaling up existing silicon quantum hardware, we investigate compilation strategies for sparsely-connected 2d qubit arrangements and propose a spin-qubit architecture with minimal compilation overhead. Our…

We study the existence and the distribution of "long" chains in the Weihrauch degrees, mostly focusing on chains with uncountable cofinality. We characterize when such chains have an upper bound and prove that there are no cofinal chains…

The emergence of spinon quasiparticles, which carry spin but lack charge, is a hallmark of collective quantum phenomena in low-dimensional quantum spin systems. While the existence of spinons has been demonstrated through scattering…

Lattice-free gradient polyhedra can be used to certify optimality for mixed-integer convex minimization models. We consider how to construct these polyhedra for unconstrained models with two integer variables under the assumption that all…

In principle a 1D array of nearest-neighbour linked qubits is compatible with fault tolerant quantum computing. However such a restricted topology necessitates a large overhead for shuffling qubits and consequently the fault tolerance…

We present a construction of integrable quantum spin chains where local spin-spin interactions are weighted by ``position''-dependent potential containing abelian non-local spin dependance. This construction applies to the previously…

We show that, in general, there is no degree corresponding to the composition of two problems in the computable reducibility lattice.

In this paper, we propose three classes of systematic approaches for constructing zero correlation zone (ZCZ) sequence families. In most cases, these approaches are capable of generating sequence families that achieve the upper bounds on…