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We consider several models of 1-round classical and quantum communication, some of these models have not been defined before. We "almost separate" the models of simultaneous quantum message passing with shared entanglement and the model of…

A variety of problems in distributed control involve a networked system of autonomous agents cooperating to carry out some complex task in a decentralized fashion, e.g., orienting a flock of drones, or aggregating data from a network of…

Many classical theorems in combinatorics establish the emergence of substructures within sufficiently large collections of objects. Well-known examples are Ramsey's theorem on monochromatic subgraphs and the Erd\H{o}s-Rado sunflower lemma.…

We show that the Guided Local Hamiltonian problem for stoquastic Hamiltonians is (promise) BPP-hard. The Guided Local Hamiltonian problem extends the Local Hamiltonian problem by incorporating an additional input known as a guiding state,…

The Bin Packing Problem (BPP) stands out as a paradigmatic combinatorial optimization problem in logistics. Quantum and hybrid quantum-classical algorithms are expected to show an advantage over their classical counterparts in obtaining…

We prove a direct sum theorem for bounded round entanglement-assisted quantum communication complexity. To do so, we use the fully quantum definition for information cost and complexity that we recently introduced, and use both the fact…

Protocols for tossing a common coin play a key role in the vast majority of implementations of consensus. Even though the common coins in the literature are usually \emph{fair} (they have equal chance of landing heads or tails), we focus on…

This paper considers a problem of quantum communication between parties that are connected through a network of quantum channels. The model in this paper assumes that there is no prior entanglement shared among any of the parties, but that…

Communication complexity problems (CCPs) are tasks in which separated parties attempt to compute a function whose inputs are distributed among the parties. Their communication is limited so that not all inputs can be sent. We show that…

Three decades of research in communication complexity have led to the invention of a number of techniques to lower bound randomized communication complexity. The majority of these techniques involve properties of large submatrices…

Alice and Bob want to know if two strings of length n are almost equal. That is, do they differ on \textit{at most} a bits? Let 0\leq a\leq n-1. We show that any deterministic protocol, as well as any error-free quantum protocol (C*…

We study the problem of estimating an unknown parameter in a distributed and online manner. Existing work on distributed online learning typically either focuses on asymptotic analysis, or provides bounds on regret. However, these results…

A restricted path integral method is proposed to simulate a type of quantum system or Hamiltonian called a sum of controlled few-fermions on a classical computer using Monte Carlo without a numerical sign problem. Then a universality is…

In this paper, we consider a network of processors aiming at cooperatively solving mixed-integer convex programs subject to uncertainty. Each node only knows a common cost function and its local uncertain constraint set. We propose a…

This thesis is concerned with the design of distributed algorithms for solving optimization problems. We consider networks where each node has exclusive access to a cost function, and design algorithms that make all nodes cooperate to find…

Randomisation is a critical tool in designing distributed systems. The common coin primitive, enabling the system members to agree on an unpredictable random number, has proven to be particularly useful. We observe, however, that it is…

Solving combinatorial optimization problems of the kind that can be codified by quadratic unconstrained binary optimization (QUBO) is a promising application of quantum computation. Some problems of this class suitable for practical…

The trade-offs between error probabilities in quantum hypothesis testing are by now well-understood in the centralized setting, but much less is known for distributed settings. Here, we study a distributed binary hypothesis testing problem…

We study two fundamental problems in communication, Document Exchange (DE) and Error Correcting Code (ECC). In the first problem, two parties hold two strings, and one party tries to learn the other party's string through communication. In…

Molecular computing promises massive parallelization to explore solution spaces, but so far practical implementations remain limited due to off-target binding and exponential proliferation of competing structures. Here, we investigate the…