Quantum query algorithms are completely bounded forms

S Arunachalam, J Briët, C Palazuelos - SIAM Journal on Computing, 2019 - SIAM
We prove a characterization of t-query quantum algorithms in terms of the unit ball of a
space of degree-(2t) polynomials. Based on this, we obtain a refined notion of approximate …

Synergies between operations research and quantum information science

O Parekh - INFORMS Journal on Computing, 2023 - pubsonline.informs.org
This article highlights synergies between quantum information science (QIS) and operations
research for QIS-curious operations researchers (and vice versa), and the author challenges …

Influence in completely bounded block-multilinear forms and classical simulation of quantum algorithms

N Bansal, M Sinha, R de Wolf - arxiv preprint arxiv:2203.00212, 2022 - arxiv.org
The Aaronson-Ambainis conjecture (Theory of Computing'14) says that every low-degree
bounded polynomial on the Boolean hypercube has an influential variable. This conjecture …

Influences of Fourier Completely Bounded Polynomials and Classical Simulation of Quantum Algorithms

FE Gutiérrez - arxiv preprint arxiv:2304.06713, 2023 - arxiv.org
We give a new presentation of the main result of Arunachalam, Bri\" et and Palazuelos
(SICOMP'19) and show that quantum query algorithms are characterized by a new class of …

Applications of optimization to factorization ranks and quantum information theory

S Gribling - 2019 - research.tilburguniversity.edu
Optimization is a fundamental area in mathematics and computer science, with many real-
world applications. In this thesis we study the efficiency with which we can solve certain …

On converses to the polynomial method

J Briët, FE Gutiérrez - arxiv preprint arxiv:2204.12303, 2022 - arxiv.org
A surprising'converse to the polynomial method'of Aaronson et al.(CCC'16) shows that any
bounded quadratic polynomial can be computed exactly in expectation by a 1-query …

Understanding Christensen-Sinclair factorization via semidefinite programming

F Escudero-Gutiérrez - arxiv preprint arxiv:2407.13716, 2024 - arxiv.org
We show that the Christensen-Sinclair factorization theorem, when the underlying Hilbert
spaces are finite dimensional, is an instance of strong duality of semidefinite programming …

Grothendieck inequalities characterize converses to the polynomial method

J Briët, FE Gutiérrez, S Gribling - Quantum, 2024 - quantum-journal.org
A surprising'converse to the polynomial method'of Aaronson et al.(CCC'16) shows that any
bounded quadratic polynomial can be computed exactly in expectation by a 1-query …