Related papers: A Relation between the Protocol Partition Number a…
This paper presents an acceleration framework for packing linear programming problems where the amount of data available is limited, i.e., where the number of constraints m is small compared to the variable dimension n. The framework can be…
We consider the problem of linearizing a pseudo-Boolean function $f : \{0,1\}^n \to \mathbb{R}$ by means of $k$ Boolean functions. Such a linearization yields an integer linear programming formulation with only $k$ auxiliary variables. This…
While quantum weight enumerators establish some of the best upper bounds on the minimum distance of quantum error-correcting codes, these bounds are not optimized to quantify the performance of quantum codes under the effect of arbitrary…
In this paper we give a unified treatment of two different definitions of complementarity partition of multifold conic programs introduced independently in [J. F. Bonnans and H. Ram\'irez C., Math. Program. 104 (2005), no. 2-3, Ser. B,…
The graph partition problem is the problem of partitioning the vertex set of a graph into a fixed number of sets of given sizes such that the sum of weights of edges joining different sets is optimized. In this paper we simplify a known…
Given that approximate quantum error-correcting (AQEC) codes have a potentially better performance than perfect quantum error correction codes, it is pertinent to quantify their performance. While quantum weight enumerators establish some…
We present a technique for reducing the computational requirements by several orders of magnitude in the evaluation of semidefinite relaxations for bounding the set of quantum correlations arising from finite-dimensional Hilbert spaces. The…
The problem of integer partitions is addressed using the microcanonical approach which is based on the analogy between this problem in the number theory and the calculation of microstates of a many-boson system. For ordinary…
A standard quadratic program is an optimization problem that consists of minimizing a (nonconvex) quadratic form over the unit simplex. We focus on reformulating a standard quadratic program as a mixed integer linear programming problem. We…
We revisit the linear programming bounds for the size vs. distance trade-off for binary codes, focusing on the bounds for the almost-balanced case, when all pairwise distances are between $d$ and $n-d$, where $d$ is the code distance and…
We show that Nechiporuk's method for proving lower bound for Boolean formulas can be extended to the quantum case. This leads to an n^2 / log^2 n lower bound for quantum formulas computing an explicit function. The only known previous…
We examine the number T of queries that a quantum network requires to compute several Boolean functions on {0,1}^N in the black-box model. We show that, in the black-box model, the exponential quantum speed-up obtained for partial functions…
In this paper we consider the classical problem of computing linear extensions of a given poset which is well known to be a difficult problem. However, in our setting the elements of the poset are multivariate polynomials, and only a small…
The most powerful technique known at present for bounding the size of quantum codes of prescribed minimum distance is the quantum linear programming bound. Unlike the classical linear programming bound, it is not immediately obvious that if…
We consider the problem of computing the partition function $\sum_x e^{f(x)}$, where $f: \{-1, 1\}^n \longrightarrow {\Bbb R}$ is a quadratic or cubic polynomial on the Boolean cube $\{-1, 1\}^n$. In the case of a quadratic polynomial $f$,…
Positive linear programs (LP), also known as packing and covering linear programs, are an important class of problems that bridges computer science, operations research, and optimization. Despite the consistent efforts on this problem, all…
Higher-order probabilistic programming languages allow programmers to write sophisticated models in machine learning and statistics in a succinct and structured way, but step outside the standard measure-theoretic formalization of…
We develop a framework for approximation limits of polynomial-size linear programs from lower bounds on the nonnegative ranks of suitably defined matrices. This framework yields unconditional impossibility results that are applicable to any…
We present an extension of known semidefinite and linear programming upper bounds for spherical codes. We apply the main result for the distance distribution of a spherical code and show that this method can work effectively In particular,…
This paper describes a fundamental correspondence between Boolean functions and projection operators in Hilbert space. The correspondence is widely applicable, and it is used in this paper to provide a common mathematical framework for the…