Related papers: Applications of semi-definite optimization in quan…
We consider semidefinite programming (SDP) for the binary stochastic block model with equal-sized communities. Prior work of Hajek, Wu, and Xu proposed an SDP (sym-SDP) for the symmetric case where the intra-community edge probabilities are…
Two quantum algorithms are presented, which tackle well--known problems in the context of numerical semigroups: the numerical semigroup membership problem (NSMP) and the Sylvester denumerant problem (SDP).
Support vector machines (SVMs) are well-studied supervised learning models for binary classification. In many applications, large amounts of samples can be cheaply and easily obtained. What is often a costly and error-prone process is to…
The problem of sparse approximation and the closely related compressed sensing have received tremendous attention in the past decade. Primarily studied from the viewpoint of applied harmonic analysis and signal processing, there have been…
Practical applications of quantum computers require millions of physical qubits and it will be challenging for individual quantum processors to reach such qubit numbers. It is therefore timely to investigate the resource requirements of…
Semidefinite programming (SDP) is a fundamental class of convex optimization problems with diverse applications in mathematics, engineering, machine learning, and related disciplines. This paper investigates the application of the…
Quantum optimization holds promise for addressing classically intractable combinatorial problems, yet a standardized framework for benchmarking its performance, particularly in terms of solution quality, computational speed, and scalability…
While current network intrusion detection systems achieve satisfactory accuracy, they often lack explainability. Subgroup Discovery (SD) addresses this by building interpretable rules that characterize feature interactions associated with…
Packing and covering semidefinite programs (SDPs) appear in natural relaxations of many combinatorial optimization problems as well as a number of other applications. Recently, several techniques were proposed, that utilize the particular…
Recent advancements in quantum computing have spurred substantial research into the application of quantum algorithms to combinatorial optimization problems. Among these challenges, the Total Domination Problem (TDP) emerges as a classic…
In this thesis, we present optimization tools for different problems in quantum information theory. First, we introduce an algorithm for quantum estate estimation. The algorithm consists of orthogonal projections on intersecting…
Quantum Key Distribution (QKD) protocols enable two distant parties to communicate with information-theoretically proven secrecy. However, these protocols are generally vulnerable to potential mismatches between the physical modeling and…
Quantum cryptography has attracted much attention in recent years. In most existing quantum cryptographic protocols, players usually need the full quantum power of generating, manipulating or measuring quantum states. Semiquantum…
Quantum error correction (QEC) is an essential element of physical quantum information processing systems. Most QEC efforts focus on extending classical error correction schemes to the quantum regime. The input to a noisy system is embedded…
In this paper, we consider a simplified error-correcting problem: for a fixed encoding process, to find a cascade connected quantum channel such that the worst fidelity between the input and the output becomes maximum. With the use of the…
The general adversary bound is a semi-definite program (SDP) that lower-bounds the quantum query complexity of a function. We turn this lower bound into an upper bound, by giving a quantum walk algorithm based on the dual SDP that has query…
Semidefinite relaxations of polynomial optimization have become a central tool for addressing the non-convex optimization problems over non-commutative operators that are ubiquitous in quantum information theory and, more in general,…
Distributed algorithms for solving coupled semidefinite programs (SDPs) commonly require many iterations to converge. They also put high computational demand on the computational agents. In this paper we show that in case the coupled…
With the birth of Noisy Intermediate Scale Quantum (NISQ) devices and the verification of "quantum supremacy" in random number sampling and boson sampling, more and more fields hope to use quantum computers to solve specific problems, such…
In this paper we present a new proof technique for semi-quantum key distribution protocols which makes use of a quantum entropic uncertainty relation to bound an adversary's information. Our new technique provides a more optimistic key-rate…