scholarly journals Experimental demonstration of quantum advantage for NP verification with limited information

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Federico Centrone ◽  
Niraj Kumar ◽  
Eleni Diamanti ◽  
Iordanis Kerenidis
Keyword(s):  
Verification Task ◽  
Specific Task ◽  
Limited Information ◽  
Experimental Demonstration ◽  
Theoretical Interest ◽  
Exponential Time ◽  
Complete Problem ◽  
Computational Advantage ◽  
Np Complete ◽  
Classical Computer

AbstractIn recent years, many computational tasks have been proposed as candidates for showing a quantum computational advantage, that is an advantage in the time needed to perform the task using a quantum instead of a classical machine. Nevertheless, practical demonstrations of such an advantage remain particularly challenging because of the difficulty in bringing together all necessary theoretical and experimental ingredients. Here, we show an experimental demonstration of a quantum computational advantage in a prover-verifier interactive setting, where the computational task consists in the verification of an NP-complete problem by a verifier who only gets limited information about the proof sent by an untrusted prover in the form of a series of unentangled quantum states. We provide a simple linear optical implementation that can perform this verification task efficiently (within a few seconds), while we also provide strong evidence that, fixing the size of the proof, a classical computer would take much longer time (assuming only that it takes exponential time to solve an NP-complete problem). While our computational advantage concerns a specific task in a scenario of mostly theoretical interest, it brings us a step closer to potential useful applications, such as server-client quantum computing.

scholarly journals Experimental demonstration of quantum advantage for NP verification

2020 ◽  
Author(s):  
Federico Centrone ◽  
Niraj Kumar ◽  
Eleni Diamanti ◽  
Iordanis Kerenidis
Keyword(s):  
Limited Information ◽  
Experimental Demonstration ◽  
Linear Optics ◽  
Exponential Time ◽  
Complete Problem ◽  
Complete Problems ◽  
Np Complete ◽  
Age Of The Universe ◽  
Classical Computer ◽  
The Universe

Abstract We show the first experimental demonstration of a computational quantum advantage (also referred to as quantum supremacy) with linear optics, by studying the computational task of the verification of an NP-complete problem by a verifier who only gets limited information about the proof. We provide a simple linear optical implementation that can perform this task efficiently (within a few seconds), while we also provide strong evidence that a classical computer would take time greater than the age of the universe (assuming only that classically it takes exponential time to solve an NP-complete problem). The verification of NP-complete problems with limited information brings us a step closer to real-world useful applications, such as server-client quantum computing.

scholarly journals Statistical mechanics of an NP-complete problem: subset sum

2001 ◽  
Vol 34 (44) ◽  
pp. 9555-9567 ◽  
Author(s):  
Tomohiro Sasamoto ◽  
Taro Toyoizumi ◽  
Hidetoshi Nishimori
Keyword(s):  
Statistical Mechanics ◽  
Complete Problem ◽  
Subset Sum ◽  
Np Complete

scholarly journals Consecutive Colouring of Oriented Graphs

2021 ◽  
Vol 76 (4) ◽  
Author(s):  
Marta Borowiecka-Olszewska ◽  
Ewa Drgas-Burchardt ◽  
Nahid Yelene Javier-Nol ◽  
Rita Zuazua
Keyword(s):  
Planar Graphs ◽  
Maximum Degree ◽  
Bipartite Graphs ◽  
Complete Graphs ◽  
Oriented Graphs ◽  
Complete Problem ◽  
Np Complete

AbstractWe consider arc colourings of oriented graphs such that for each vertex the colours of all out-arcs incident with the vertex and the colours of all in-arcs incident with the vertex form intervals. We prove that the existence of such a colouring is an NP-complete problem. We give the solution of the problem for r-regular oriented graphs, transitive tournaments, oriented graphs with small maximum degree, oriented graphs with small order and some other classes of oriented graphs. We state the conjecture that for each graph there exists a consecutive colourable orientation and confirm the conjecture for complete graphs, 2-degenerate graphs, planar graphs with girth at least 8, and bipartite graphs with arboricity at most two that include all planar bipartite graphs. Additionally, we prove that the conjecture is true for all perfect consecutively colourable graphs and for all forbidden graphs for the class of perfect consecutively colourable graphs.

Dealing with Hardness

2017 ◽  
Author(s):  
Lance Fortnow
Keyword(s):  
Brute Force ◽  
Complete Problem ◽  
Hard Problems ◽  
Np Complete ◽  
Np Problems ◽  
Single Technique

This chapter demonstrates several approaches for dealing with hard problems. These approaches include brute force, heuristics, and approximation. Typically, no single technique will suffice to handle the difficult NP problems one needs to solve. For moderate-sized problems one can search over all possible solutions with the very fast computers available today. One can use algorithms that might not work for every problem but do work for many of the problems one cares about. Other algorithms may not find the best possible solution but still a solution that's good enough. Other times one just cannot get a solution for an NP-complete problem. One has to try to solve a different problem or just give up.

Quality of Service for Multimedia and Real-Time Services

2010 ◽  
Vol 5 (4) ◽  
pp. 1-22
Author(s):  
F. W. Albalas ◽  
B. A. Abu-Alhaija ◽  
A. Awajan ◽  
A. Awajan ◽  
Khalid Al-Begain
Keyword(s):  
Decision Making ◽  
Quality Of Service ◽  
Real Time ◽  
Qos Routing ◽  
Routing Algorithms ◽  
Complete Problem ◽  
Filtering Technique ◽  
Np Complete ◽  
Multiple Metrics

New web technologies have encouraged the deployment of various network applications that are rich with multimedia and real-time services. These services demand stringent requirements are defined through Quality of Service (QoS) parameters such as delay, jitter, loss, etc. To guarantee the delivery of these services QoS routing algorithms that deal with multiple metrics are needed. Unfortunately, QoS routing with multiple metrics is considered an NP-complete problem that cannot be solved by a simple algorithm. This paper proposes three source based QoS routing algorithms that find the optimal path from the service provider to the user that best satisfies the QoS requirements for a particular service. The three algorithms use the same filtering technique to prune all the paths that do not meet the requirements which solves the complexity of NP-complete problem. Next, each of the three algorithms integrates a different Multiple Criteria Decision Making method to select one of the paths that have resulted from the route filtering technique. The three decision making methods used are the Analytic Hierarchy Process (AHP), Multi-Attribute Utility Theory (MAUT), and Kepner-Tregoe KT. Results show that the algorithms find a path using multiple constraints with a high ability to handle multimedia and real-time applications.

Towards Efficient Bounds on Completion Time and Resource Provisioning for Scheduling Workflows on Heterogeneous Processing Systems

2017 ◽  
Vol 9 (3) ◽  
pp. 60-82 ◽  
Author(s):  
D. Sirisha ◽  
G. Vijayakumari
Keyword(s):  
Completion Time ◽  
High Performance ◽  
Turnaround Time ◽  
Resource Provisioning ◽  
Optimal Solutions ◽  
Complete Problem ◽  
Heterogeneous Processing ◽  
Heuristic Scheduling ◽  
Np Complete ◽  
Workflow Tasks

Compute intensive applications featured as workflows necessitate Heterogeneous Processing Systems (HPS) for attaining high performance to minimize the turnaround time. Efficient scheduling of the workflow tasks is paramount to attain higher potentials of HPS and is a challenging NP-Complete problem. In the present work, Branch and Bound (BnB) strategy is applied to optimally schedule the workflow tasks. The proposed bounds are tighter, simpler and less complex than the existing bounds and the upper bound is closer to the exact solution. Moreover, the bounds on the resource provisioning are devised to execute the workflows in the minimum possible time and optimally utilize the resources. The performance of the proposed BnB strategy is evaluated on a suite of benchmark workflows. The experimental results reveal that the proposed BnB strategy improved the optimal solutions compared to the existing heuristic scheduling algorithms for more than 20 percent of the cases and generated better schedules over 7 percent for 82.6 percent of the cases.

scholarly journals Applying Neural Networks to Find the Minimum Cost Coverage of a Boolean Function

VLSI Design ◽  
1995 ◽  
Vol 3 (1) ◽  
pp. 13-19 ◽  
Author(s):  
Pong P. Chu
Keyword(s):  
Neural Network ◽  
Boolean Function ◽  
Input Data ◽  
Selection Process ◽  
Optimal Solution ◽  
Minimum Cost ◽  
Hopfield Network ◽  
Neural Network Approach ◽  
Complete Problem ◽  
Np Complete

To find a minimal expression of a boolean function includes a step to select the minimum cost cover from a set of implicants. Since the selection process is an NP-complete problem, to find an optimal solution is impractical for large input data size. Neural network approach is used to solve this problem. We first formalize the problem, and then define an “energy function” and map it to a modified Hopfield network, which will automatically search for the minima. Simulation of simple examples shows the proposed neural network can obtain good solutions most of the time.

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