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The four point functions of chiral primary BPS operators in ${\cal N}=4$ superconformal Yang Mills are expressed in a form manifestly satisfying the superconformal Ward identities. They are subsequently expanded in terms of conformal…
We study the limitations of deterministic programmability of quantum circuits, e.g., quantum computer. More precisely, we analyse the programming of quantum observables and channels via quantum multimeters. We show that the programming…
A finite number of rational functions are compatible if they satisfy the compatibility conditions of a first-order linear functional system involving differential, shift and q-shift operators. We present a theorem that describes the…
The uncertainty relation is a fundamental concept in quantum theory, plays a pivotal role in various quantum information processing tasks. In this study, we explore the additive uncertainty relation pertaining to two or more observables, in…
Interpretation methods and their restrictions to polynomials have been deeply used to control the termination and complexity of first-order term rewrite systems. This paper extends interpretation methods to a pure higher order functional…
In binary polynomial optimization, the goal is to find a binary point maximizing a given polynomial function. In this paper, we propose a novel way of formulating this general optimization problem, which we call factorized binary polynomial…
We study equivalence determination of unitary operations, a task analogous to quantum state discrimination. The candidate states are replaced by unitary operations given as a quantum sample, i.e., a black-box device implementing a candidate…
Maximum subarray is a classical problem in computer science that given an array of numbers aims to find a contiguous subarray with the largest sum. We focus on its use for a noisy statistical problem of localizing an interval with a mean…
Supervised machine learning is the classification of new data based on already classified training examples. In this work, we show that the support vector machine, an optimized binary classifier, can be implemented on a quantum computer,…
We apply polynomial techniques (linear programming) to obtain lower and upper bounds on the covering radius of spherical designs as function of their dimension, strength, and cardinality. In terms of inner products we improve the lower…
We continue our analysis of bad theories, focusing on quiver theories with bad unitary and special unitary gauge groups in three dimensions. By extending the dualization algorithm we prove that the partition function of bad linear quivers…
Typical arguments for results like Kleene's Second Recursion Theorem and the existence of self-writing computer programs bear the fingerprints of equational reasoning and combinatory logic. In fact, the connection of combinatory logic and…
The problem of determining whether a probabilistic program terminates almost surely (i.e.~with probability one) is undecidable, and actually $\Pi^0_2$-complete. For this reason, a growing literature has explored classes of programs for…
Quantum computation represents a computational paradigm whose distinctive attributes confer the ability to devise algorithms with asymptotic performance levels significantly superior to those achievable via classical computation. Recent…
Applying the classical Serre-Swan theorem, as this is extended to topological (non-normed) algebras, one attains a classification of elementary particles via their spin-structure. In this context, our argument is virtually based on a…
This study investigates an explainable reasoning method for financial decision-making based on knowledge-enhanced large language model agents. To address the limitations of traditional financial decision methods that rely on parameterized…
This work takes place over a conformally flat spin manifold (M,g). We prove existence and uniqueness of the conformally equivariant quantization valued in spinor differential operators, and provide an explicit formula for it when restricted…
This work provides data-processing and majorization inequalities for $f$-divergences, and it considers some of their applications to coding problems. This work also provides tight bounds on the R\'{e}nyi entropy of a function of a discrete…
We use the lexicographic order to define a hierarchy of primal and dual bounds on the optimum of a bounded integer program. These bounds are constructed using lex maximal and minimal feasible points taken under different permutations. Their…
This thesis focuses on the intersection of mathematical and computational optimization and quantum information. Main contributions are open-source software code: A hybrid approach mixing "traditional" nonconvex and convex methods can make…