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

We introduce a quantum algorithm that produces approximate solutions for combinatorial optimization problems. The algorithm depends on a positive integer p and the quality of the approximation improves as p is increased. The quantum circuit…

The Ryu-Takayanagi conjecture establishes a remarkable connection between quantum systems and geometry. Specifically, it relates the entanglement entropy to minimal surfaces within the setting of AdS/CFT correspondence. This Letter shows…

We discover the quantum analog of the well-known classical maximum power transfer theorem. Our theoretical framework considers the continuous steady-state problem of coherent energy transfer through an N-node bosonic network coupled to an…

A min-cut that seperates vertices s and t in a network is an edge set of minimum weight whose removal will disconnect s and t. This problem is the dual of the well known s-t max-flow problem. Several algorithms for the min-cut problem are…

The design of fast algorithms for combinatorial optimization greatly contributes to a plethora of domains such as logistics, finance, and chemistry. Quantum approximate optimization algorithms (QAOAs), which utilize the power of quantum…

A computational flow is a pair consisting of a sequence of computational problems of a certain sort and a sequence of computational reductions among them. In this paper we will develop a theory for these computational flows and we will use…

Computing routing schemes that support both high throughput and low latency is one of the core challenges of network optimization. Such routes can be formalized as $h$-length flows which are defined as flows whose flow paths are restricted…

We design quantum compression algorithms for parametric families of tensor network states. We first establish an upper bound on the amount of memory needed to store an arbitrary state from a given state family. The bound is determined by…

The Max-Flow/Min-Cut problem is a fundamental tool in graph theory, with applications in many domains, including data mining, image segmentation, transportation planning, and many types of assignment problems, in addition to being an…

Murray's theory of constrained minimum-power branchings is critically reviewed in a generalised framework for a range of cases: channels with arbitrary cross-section shape, laminar flows of Newtonian and non-Newtonian fluids, and low and…

Minimum cuts have been closely related to shortest paths in planar graphs via planar duality - so long as the graphs are undirected. Even maximum flows are closely related to shortest paths for the same reason - so long as the source and…

While the search for quantum advantage typically focuses on speedups in execution time, quantum algorithms also offer the potential for advantage in space complexity. Previous work has shown such advantages for data stream problems, in…

This paper aims to implement and evaluate the performance of quantum computing on solving combinatorial optimization problems arising from the operations of the power grid. To this end, we construct a novel mixed integer conic programming…

We develop a semidefinite programming method for the optimization of quantum networks, including both causal networks and networks with indefinite causal structure. Our method applies to a broad class of performance measures, defined…

We introduce a new approach to computing an approximately maximum s-t flow in a capacitated, undirected graph. This flow is computed by solving a sequence of electrical flow problems. Each electrical flow is given by the solution of a…

The optimally designed control of quantum systems is playing an increasingly important role to engineer novel and more efficient quantum technologies. Here, in the scenario represented by controlling an arbitrary quantum system via the…

Many combinatorial optimization problems admit a maximin fairness variant, where the aim is to find a distribution over possible solutions which maximizes an expected worst-case outcome. However, the support for an optimal distribution may…

Flows and colorings are disparate concepts in graph algorithms -- the former is tractable while the latter is intractable. Tutte introduced the concept of nowhere-zero flows to unify these two concepts. Jaeger showed that nowhere-zero flows…

A longstanding open problem in quantum information theory is to find the classical capacity of an optical communication link, modeled as a Gaussian bosonic channel. It has been conjectured that this capacity is achieved by a random coding…

Quantum networks are envisioned to enable reliable distribution and manipulation of quantum information across distances, forming the foundation of a future quantum internet. The fair and efficient allocation of communication resources in…