Related papers: A Note on Nonuniform versus Uniform ACC^k Circuits…

In this work, drawing inspiration from the type of noise present in real hardware, we study the output distribution of random quantum circuits under practical non-unital noise sources with constant noise rates. We show that even in the…

The circuits of a polyhedron are a superset of its edge directions. Circuit walks, a sequence of steps along circuits, generalize edge walks and are "short" if they have few steps or small total length. Both interpretations of short are…

For any elements b,c of a number field K, let G(b,c) denote the backwards orbit of b under the map f_c: C-->C given by f_c(x)=x^2+c. We prove an upper bound on the number of elements of G(b,c) whose degree over K is at most some constant B.…

A class of graphs that lies strictly between the classes of graphs of genus (at most) $k-1$ and $k$ is studied. For a fixed orientable surface $S_k$ of genus $k$, let $A_{xy}^k$ be the minor-closed class of graphs with terminals $x$ and $y$…

This paper presents the following results on sets that are complete for NP. 1. If there is a problem in NP that requires exponential time at almost all lengths, then every many-one NP-complete set is complete under length-increasing…

Unitary transformations are an essential tool for the theoretical understanding of many systems by mapping them to simpler effective models. A systematically controlled variant to perform such a mapping is a perturbative continuous unitary…

In this paper, we develop spectral analysis of a discrete non-Hermitian quantum system that is a discrete counterpart of some continuous quantum systems on a complex contour. In particular, simple conditions for discreteness of the spectrum…

The polynomial-time computability of the permanent over fields of characteristic 3 for k-semi-unitary matrices (i.e. square matrices such that the differences of their Gram matrices and the corresponding identity matrices are of rank k) in…

We show that the computational power of the non-causal circuit model, i.e., the circuit model where the assumption of a global causal order is replaced by the assumption of logical consistency, is completely characterized by the complexity…

Let $A$ be a commutative noetherian ring, let $\mathfrak a$ be an ideal of $A$. In this paper, we extend Hartshorne's characterization of cofinite complexes to more general classes of rings. We also determine conditions under which…

We prove that for every class $C$ of graphs with effectively bounded expansion, given a first-order sentence $\varphi$ and an $n$-element structure $\mathbb{A}$ whose Gaifman graph belongs to $C$, the question whether $\varphi$ holds in…

We characterize the structure of the periods of a neuronal recurrence equation. Firstly, we give a characterization of k-chains in 0-1 periodic sequences. Secondly, we characterize the periods of all cycles of some neuronal recurrence…

We define different classes of local random quantum circuits (L-RQC) and show that: a) statistical properties of L-RQC are encoded into an associated family of completely positive maps and b) average purity dynamics can be described by the…

This paper classifies the equivalence classes of irreducible unitary representations with nonvanishing Dirac cohomology for complex $E_6$. This is achieved by using our finiteness result, and by improving the computing method.

Let $A$ be a non-unital Banach algebra, S. J. Bhatt and H. V. Dedania showed that $A$ has the unique uniform norm property (UUNP) if and only if its unitization has UUNP. Here we prove this result for any non-unital algebra.

The vast majority of quantum states and unitaries have circuit complexity exponential in the number of qubits. In a similar vein, most of them also have exponential minimum description length, which makes it difficult to pinpoint examples…

We investigate the power of non-deterministic circuits over restricted sets of base gates. We note that the power of non-deterministic circuits exhibit a dichotomy, in the following sense: For weak enough bases, non-deterministic circuits…

Let $k,a,b$ be positive integers with $a+b=k$. A $k$-uniform hypergraph is called an $(a,b)$-cycle if there is a partition $(A_0,B_0,A_1,B_1,\ldots,A_{t-1},B_{t-1})$ of the vertex set with $|A_i|=a$, $|B_i|=b$ such that $A_i\cup B_i$ and…

We consider in-depth and characterize in certain aspects those rings whose non-units are strongly nil-clean in the sense that they are a sum of commuting nilpotent and idempotent. In addition, we examine those rings in which the non-units…

We generalise to signed graphs a classical result of Tutte [Canad. J. Math. 8 (1956), 13--28] stating that every integer flow can be expressed as a sum of characteristic flows of circuits. In our generalisation, the r\^ole of circuits is…