Related papers: A Satisfiability Algorithm for Sparse Depth Two Th…
Let $S_d(n)$ denote the minimum number of wires of a depth-$d$ (unbounded fan-in) circuit encoding an error-correcting code $C:\{0, 1\}^n \to \{0, 1\}^{32n}$ with distance at least $4n$. G\'{a}l, Hansen, Kouck\'{y}, Pudl\'{a}k, and Viola…
The linear complementarity problem (LCP) is a general set membership problem that includes quadratic cone programming as a special case. In this work we consider a homogeneous embedding of the LCP, which encodes both the optimality…
Let $ACC \circ THR$ be the class of constant-depth circuits comprised of AND, OR, and MOD$m$ gates (for some constant $m > 1$), with a bottom layer of gates computing arbitrary linear threshold functions. This class of circuits can be seen…
We explore algorithms and limitations for sparse optimization problems such as sparse linear regression and robust linear regression. The goal of the sparse linear regression problem is to identify a small number of key features, while the…
We study the problem of maximizing a monotone submodular function with viability constraints. This problem originates from computational biology, where we are given a phylogenetic tree over a set of species and a directed graph, the…
Constraint satisfaction is a critical component in a wide range of engineering applications, including but not limited to safe multi-agent control and economic dispatch in power systems. This study explores violation-free distributed…
A long-standing open question in Integer Programming is whether integer programs with constraint matrices with bounded subdeterminants are efficiently solvable. An important special case thereof are congruency-constrained integer programs…
Satisfiability of Boolean circuits is among the most known and important problems in theoretical computer science. This problem is NP-complete in general but becomes polynomial time when restricted either to monotone gates or linear gates.…
We introduce a classical algorithm for sampling the output of shallow, noisy random circuits on two-dimensional qubit arrays. The algorithm builds on the recently-proposed "space-evolving block decimation" (SEBD) and extends it to the case…
Variational quantum algorithms are the centerpiece of modern quantum programming. These algorithms involve training parameterized quantum circuits using a classical co-processor, an approach adapted partly from classical machine learning.…
The NP-hardness of the closest vector problem (CVP) is an important basis for quantum-secure cryptography, in much the same way that integer factorisation's conjectured hardness is at the foundation of cryptosystems like RSA. Recent work…
A canonical result about satisfiability theory is that the 2-SAT problem can be solved in linear time, despite the NP-hardness of the 3-SAT problem. In the quantum 2-SAT problem, we are given a family of 2-qubit projectors $\Pi_{ij}$ on a…
We consider the densest submatrix problem, which seeks the submatrix of fixed size of a given binary matrix that contains the most nonzero entries. This problem is a natural generalization of fundamental problems in combinatorial…
Partitioning the vertices of a graph into two roughly equal parts while minimizing the number of edges crossing the cut is a fundamental problem (called Balanced Separator) that arises in many settings. For this problem, and variants such…
A matching in a graph is induced if no two of its edges are joined by an edge, and finding a large induced matching is a very hard problem. Lin et al. (Approximating weighted induced matchings, Discrete Applied Mathematics 243 (2018)…
Deep convolutional neural networks are a powerful model class for a range of computer vision problems, but it is difficult to interpret the image filtering process they implement, given their sheer size. In this work, we introduce a method…
Understanding how neural networks arrive at their predictions is essential for debugging, auditing, and deployment. Mechanistic interpretability pursues this goal by identifying circuits - minimal subnetworks responsible for specific…
We present an algorithm to reduce the computational effort for the multiplication of a given matrix with an unknown column vector. The algorithm decomposes the given matrix into a product of matrices whose entries are either zero or integer…
Constraint satisfiability problems, crucial to several applications, are solved on a quantum computer using Grover's search algorithm, leading to a quadratic improvement over the classical case. The solutions are obtained with high…
Linear reversible circuits represent a subclass of reversible circuits with many applications in quantum computing. These circuits can be efficiently simulated by classical computers and their size is polynomially bounded by the number of…