相关论文: Quantum Max-Flow Min-Cut theorem

Numerous networks, such as transportation, distribution and delivery networks optimize their designs in order to increase efficiency and lower costs, improving the stability of its intended functions, etc. Networks that distribute goods,…

We propose a novel proof technique that can be applied to attack a broad class of problems in computational complexity, when switching the order of universal and existential quantifiers is helpful. Our approach combines the standard min-max…

We present an $\tilde{O}\left(m^{\frac{10}{7}}U^{\frac{1}{7}}\right)$-time algorithm for the maximum $s$-$t$ flow problem and the minimum $s$-$t$ cut problem in directed graphs with $m$ arcs and largest integer capacity $U$. This matches…

We present a quantum algorithm that additively approximates the value of a tensor network to a certain scale. When combined with existing results, this provides a complete problem for quantum computation. The result is a simple new way of…

Inspired by the recent developments in the fields of quantum distributed computing, quantum systems are analyzed as networks of quantum nodes to reduce the complexity of the analysis. This gives rise to the distributed quantum consensus…

Several concepts borrowed from graph theory are routinely used to better understand the inner workings of the (human) brain. To this end, a connectivity network of the brain is built first, which then allows one to assess quantities such as…

Optimising quantum circuits to minimise resource usage is crucial, especially with near-term hardware limited by quantum volume. This paper introduces an optimisation algorithm aiming to minimise non-Clifford gate count and two-qubit gate…

The quantum threshold theorem shows that a noisy quantum computer can accurately and efficiently simulate any ideal quantum computation provided that noise is weakly correlated and its strength is below a critical value known as the quantum…

I introduce a new approach to the maximum flow problem by a simple algorithm with a slightly better runtime. This approach is based on sorting arcs insight of vertices on a residual graph. This new approach leads to an O(mn^0.5) time bound…

We give a combinatorial algorithm for computing exact maximum flows in directed graphs with $n$ vertices and edge capacities from $\{1,\dots,U\}$ in $\tilde{O}(n^{2}\log U)$ time, which is near-optimal on dense graphs. This shaves an…

We present a parallel algorithm for computing $(1+\epsilon)$-approximate mincost flow on an undirected graph with $m$ edges, where capacities and costs are assigned to both edges and vertices. Our algorithm achieves $\hat{O}(m)$ work and…

Tensor networks represent the state-of-the-art in computational methods across many disciplines, including the classical simulation of quantum many-body systems and quantum circuits. Several applications of current interest give rise to…

Among the models of quantum computation, the One-way Quantum Computer is one of the most promising proposals of physical realization, and opens new perspectives for parallelization by taking advantage of quantum entanglement. Since a…

In this paper, we develop a theory of new classes of discrete convex functions, called L-extendable functions and alternating L-convex functions, defined on the product of trees. We establish basic properties for optimization: a…

We consider the problem of finding the value of a maximum flow over time in a network with uniform edge lengths where the edge capacities change at specific time instants. To solve this problem, we show how to construct a condensed version…

We prove a one-shot "minimax" converse bound for quantum channel coding assisted by positive partial transpose channels between sender and receiver. The bound is similar in spirit to the converse by Polyanskiy, Poor, and Verdu [IEEE Trans.…

Optimized quantum control can enhance the performance and noise resilience of quantum metrology. However, the optimization quickly becomes intractable when multiple control operations are applied sequentially. In this work, we propose…

We conducted quantum simulations of strongly correlated systems using the quantum flow (QFlow) approach, which enables sampling large sub-spaces of the Hilbert space through coupled eigenvalue problems in reduced dimensionality active…

We independently assign a non-negative value, as a capacity for the quantity of flows per unit time, with a distribution F to each edge on the Z^d lattice. We consider the maximum flows through the edges of two disjoint sets, that is from a…

The terminal backup problems (Anshelevich and Karagiozova (2011)) form a class of network design problems: Given an undirected graph with a requirement on terminals, the goal is to find a minimum cost subgraph satisfying the connectivity…