Related papers: Monotonic and Non-Monotonic Solution Concepts for …
What makes a class of quantum circuits efficiently classically simulable on average? I present a framework that applies harmonic analysis of groups to circuits with a structure encoded by group parameters. Expanding the circuits in a…
In this short note, we reduce lower bounds on monotone projections of polynomials to lower bounds on extended formulations of polytopes. Applying our reduction to the seminal extended formulation lower bounds of Fiorini, Massar, Pokutta,…
The synthesis approaches for quantum circuits typically aim at minimizing the number of lines or gates. Given the tight restrictions on those logical resources in physical implementations, we propose to view the problem fundamentally…
We study the extremal competitive ratio of Boolean function evaluation. We provide the first non-trivial lower and upper bounds for classes of Boolean functions which are not included in the class of monotone Boolean functions. For the…
Inspired by recent strides in empirical efficacy of implicit learning in many robotics tasks, we seek to understand the theoretical benefits of implicit formulations in the face of nearly discontinuous functions, common characteristics for…
We generalize the celebrated isoperimetric inequality of Khot, Minzer, and Safra~(SICOMP 2018) for Boolean functions to the case of real-valued functions $f \colon \{0,1\}^d\to\mathbb{R}$. Our main tool in the proof of the generalized…
A defining feature in the field of quantum computing is the potential of a quantum device to outperform its classical counterpart for a specific computational task. By now, several proposals exist showing that certain sampling problems can…
Polymorphic circuits are a special kind of circuits which possess some different build-in functions and these functions are activated by environment parameters, like light and VDD. Some theories have been proposed to guide the design of…
This paper depicts algorithms for solving the decision Boolean Satisfiability Problem. An extreme problem is formulated to analyze the complexity of algorithms and the complexity for solving it. A novel and easy reformulation as a lottery…
In the article we discuss the notion of the generalized invariant manifold introduced in our previous study. In the literature the method of the differential constraints is well known as a tool for constructing particular solutions for the…
Constrained-random simulation is the predominant approach used in the industry for functional verification of complex digital designs. The effectiveness of this approach depends on two key factors: the quality of constraints used to…
$ \newcommand{\cclass}[1]{{\normalfont\textsf{##1}}} $We show average-case lower bounds for explicit Boolean functions against bounded-depth threshold circuits with a superlinear number of wires. We show that for each integer $d > 1$, there…
We introduce a generalization of Glimm's random choice method, which provides us with an approximation of entropy solutions to quasilinear hyperbolic system of balance laws. The flux-function and the source term of the equations may depend…
The implementation of reliable and efficient geometric algorithms is a challenging task. The reason is the following conflict: On the one hand, computing with rounded arithmetic may question the reliability of programs while, on the other…
It is widely accepted that noisy quantum devices are limited to logarithmic depth circuits unless mid-circuit measurements and error correction are employed. However, this conclusion holds only for unital error channels, such as…
We test the principle of majorization [J. I. Latorre and M. A. Martin-Delgado, Phys. Rev. A 66, 022305 (2002)] in random circuits. Three classes of circuits were considered: (i) universal, (ii) classically simulatable, and (iii) neither…
Extensively evaluating the capabilities of (large) language models is difficult. Rapid development of state-of-the-art models induce benchmark saturation, while creating more challenging datasets is labor-intensive. Inspired by the recent…
We give a general method of construting quantum circuit for random \QTR{it}{satisfiability} (SAT) problems with the basic logic gates such as multi-qubit controlled-NOT and NOT gates. The sizes of these circuits are almost the same as the…
Algorithms for min-max optimization and variational inequalities are often studied under monotonicity assumptions. Motivated by non-monotone machine learning applications, we follow the line of works [Diakonikolas et al., 2021, Lee and Kim,…
Many promising quantum algorithms in economics, medical science, and material science rely on circuits that are parameterized by a large number of angles. To ensure that these algorithms are efficient, these parameterized circuits must be…