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A central theme in distributed network algorithms concerns understanding and coping with the issue of locality. Inspired by sequential complexity theory, we focus on a complexity theory for distributed decision problems. In the context of…
Circuit knitting, a method for connecting quantum circuits across multiple processors to simulate nonlocal quantum operations, is a promising approach for distributed quantum computing. While various techniques have been developed for…
The edge list model is arguably the simplest input model for graphs, where the graph is specified by a list of its edges. In this model, we study the quantum query complexity of three variants of the triangle finding problem. The first asks…
We show that any classical two-way communication protocol with shared randomness that can approximately simulate the result of applying an arbitrary measurement (held by one party) to a quantum state of $n$ qubits (held by another), up to…
In this paper we consider a network of processors aiming at cooperatively solving linear programming problems subject to uncertainty. Each node only knows a common cost function and its local uncertain constraint set. We propose a…
Sketching is widely used in randomized linear algebra for low-rank matrix approximation, column subset selection, and many other problems, and it has gained significant traction in machine learning applications. However, sketching large…
We provide an $\Omega(log(n))$ lower bound for the depth of any quantum circuit generating the unique groundstate of Kitaev's spherical code. No circuit-depth lower bound was known before on this code in the general case where the gates can…
We study the wake-up problem in distributed networks, where an adversary awakens a subset of nodes at arbitrary times, and the goal is to wake up all other nodes as quickly as possible by sending only few messages. We prove the following…
Color code is a promising topological code for fault-tolerant quantum computing. Insufficient research on the color code has delayed its practical application. In this work, we address several key issues to facilitate practical…
Quantum information processing is the emerging field that defines and realizes computing devices that make use of quantum mechanical principles, like the superposition principle, entanglement, and interference. In this review we study the…
A number of recent papers -- e.g. Brandt et al. (STOC 2016), Chang et al. (FOCS 2016), Ghaffari & Su (SODA 2017), Brandt et al. (PODC 2017), and Chang & Pettie (FOCS 2017) -- have advanced our understanding of one of the most fundamental…
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…
We settle the complexity of the $(\Delta+1)$-coloring and $(\Delta+1)$-list coloring problems in the CONGESTED CLIQUE model by presenting a simple deterministic algorithm for both problems running in a constant number of rounds. This…
We consider the communication complexity of some fundamental convex optimization problems in the point-to-point (coordinator) and blackboard communication models. We strengthen known bounds for approximately solving linear regression,…
We consider a class of popular distributed non-convex optimization problems, in which agents connected by a network $\mathcal{G}$ collectively optimize a sum of smooth (possibly non-convex) local objective functions. We address the…
We present efficient and practical algorithms for a large, distributed system of processors to achieve reliable computations in a secure manner. Specifically, we address the problem of computing a general function of several private inputs…
We analyze implementations of bipartite unitaries by means of local operations and classical communication (LOCC) assisted by shared entanglement. We employ concepts and techniques developed in quantum Shannon theory to study an asymptotic…
We provide novel deterministic distributed vertex coloring algorithms. As our main result, we give a deterministic distributed algorithm to compute a $(\Delta+1)$-coloring of an $n$-node graph with maximum degree $\Delta$ in…
In this work, we study the Lov\'asz local lemma (LLL) problem in the area of distributed quantum computing, which has been the focus of attention of recent advances in quantum computing [STOC'24, STOC'25, STOC'25]. We prove a lower bound of…
Quantum algorithms for graph problems are considered, both in the adjacency matrix model and in an adjacency list-like array model. We give almost tight lower and upper bounds for the bounded error quantum query complexity of Connectivity,…