A Quantum Approach to Subset-Sum and Similar Problems
نویسنده
چکیده
In this paper, we study the subset-sum problem by using a quantum heuristic approach similar to the verification circuit of quantum Arthur-Merlin games [1]. Under described certain assumptions, we show that the exact solution of the subset sum problem my be obtained in polynomial time and the exponential speed-up over the classical algorithms may be possible. We give a numerical example and discuss the complexity of the approach and its further application to the knapsack problem.
منابع مشابه
Quantum Computation and Lattice Problems
We present the first explicit connection between quantum computation and lattice problems. Namely, our main result is a solution to the Unique Shortest Vector Problem (SVP) under the assumption that there exists an algorithm that solves the hidden subgroup problem on the dihedral group by coset sampling. Additionally, we present an approach to solving the hidden subgroup problem on the dihedral...
متن کاملBQIABC: A new Quantum-Inspired Artificial Bee Colony Algorithm for Binary Optimization Problems
Artificial bee colony (ABC) algorithm is a swarm intelligence optimization algorithm inspired by the intelligent behavior of honey bees when searching for food sources. The various versions of the ABC algorithm have been widely used to solve continuous and discrete optimization problems in different fields. In this paper a new binary version of the ABC algorithm inspired by quantum computing, c...
متن کاملHow Hard Is Deciding Trivial Versus Nontrivial in the Dihedral Coset Problem?
We study the hardness of the dihedral hidden subgroup problem. It is known that lattice problems reduce to it, and that it reduces to random subset sum with density > 1 and also to quantum sampling subset sum solutions. We examine a decision version of the problem where the question asks whether the hidden subgroup is trivial or order two. The decision problem essentially asks if a given vector...
متن کاملInternship Report – NEC 2008
This report summarizes the work done at NEC Labs America, Princeton from 28th May 2008 to 29th August 2008. I worked under the supervision of Martin Roetteler and collaborated with Hari Krovi. We worked on the hidden subgroup problem(HSP) for dihedral group. Dihedral HSP will solve f(n)-shortest vector lattice problem for f(n) = n 1 2 ([1]), which imply connection with some cryptographic protoc...
متن کاملThe Subset Sum Problem: Reducing Time Complexity of NP-Completeness with Quantum Search
Abstract. The Subset Sum Problem is a member of the NP-complete class, so no known polynomial time algorithm exists for it. Although there are polynomial time approximations and heuristics, these are not always acceptable, yet exact-solution algorithms are unfeasible for large input. Quantum computation offers new insights for not only the Subset Sum Problem but also the entire NP-complete clas...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- CoRR
دوره abs/1707.08730 شماره
صفحات -
تاریخ انتشار 2017