Related papers: Conic approach to quantum graph parameters using l…
Convex sets of completely positive maps and positive semidefinite kernels are considered in the most general context of modules over $C^*$-algebras and a complete charaterization of their extreme points is obtained. As a byproduct, we…
Quantum computing has been a prominent research area for decades, inspiring transformative fields such as quantum simulation, quantum teleportation, and quantum machine learning (QML), which are undergoing rapid development. Within QML,…
We apply numerical optimization and linear algebra algorithms for classical computers to the problem of automatically synthesizing algorithms for quantum computers. Using our framework, we apply several common techniques from these…
Quantum computers promise improving machine learning. We investigated the performance of new quantum neural network designs. Quantum neural networks currently employed rely on a feature map to encode the input into a quantum state. This…
Meta-kernelization theorems are general results that provide polynomial kernels for large classes of parameterized problems. The known meta-kernelization theorems, in particular the results of Bodlaender et al. (FOCS'09) and of Fomin et al.…
Research of cycles through specific vertices is a central topic in graph theory. In this context, we focus on a well-studied computational problem, \textsc{$T$-Cycle}: given an undirected $n$-vertex graph $G$ and a set of $k$ vertices…
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…
We prove that any perfect quantum strategy for the two-prover game encoding a constraint satisfaction problem (CSP) can be simulated via a perfect classical strategy with an extra classical communication channel, whose size depends only on…
We consider a symmetric matrix, the entries of which depend linearly on some parameters. The domains of the parameters are compact real intervals. We investigate the problem of checking whether for each (or some) setting of the parameters,…
We consider systems of polynomial equations and inequalities in $\mathbb{Q}[\boldsymbol{y}][\boldsymbol{x}]$ where $\boldsymbol{x} = (x_1, \ldots, x_n)$ and $\boldsymbol{y} = (y_1, \ldots,y_t)$. The $\boldsymbol{y}$ indeterminates are…
Parameter-free stochastic optimization aims to design algorithms that are agnostic to the underlying problem parameters while still achieving convergence rates competitive with optimally tuned methods. While some parameter-free methods do…
We investigate quantum circuits for graph representation learning, and propose equivariant quantum graph circuits (EQGCs), as a class of parameterized quantum circuits with strong relational inductive bias for learning over graph-structured…
An important question in the study of quasi-perfect codes is whether such codes can be constructed for all possible lengths $n$. In this paper, we address this question for specific values of $n$. First, we investigate the existence of…
Quantum Markov chains (QMCs) are positive maps on a trace-class space describing open quantum dynamics on graphs. Such objects have a statistical resemblance with classical random walks, while at the same time it allows for internal…
Polynomial optimization encompasses a broad class of problems in which both the objective function and constraints are polynomial functions of the decision variables. In recent years, a substantial body of research has focused on…
To demonstrate supremacy of quantum computing, increasingly large-scale superconducting quantum computing chips are being designed and fabricated. However, the complexity of simulating quantum systems poses a significant challenge to…
We develop and implement automated methods for optimizing quantum circuits of the size and type expected in quantum computations that outperform classical computers. We show how to handle continuous gate parameters and report a collection…
I develop a theory of classicality from quantum systems. This theory stems from the study of classical and quantum stationary stochastic processes. The stochastic processes are characterized by polyhedral (classical) and semidefinite…
This work shows an approach to reduce the dimensionality of matrix representations of quantum channels. It is achieved by finding a base of the cone of positive semidefinite matrices which represent quantum channels. Next, this is…
We show how it is possible to realize quantum computations on a system in which most of the parameters are practically unknown. We illustrate our results with a novel implementation of a quantum computer by means of bosonic atoms in an…