Copying quantum computer makes NP-complete problems tractable
نویسنده
چکیده
Under the assumption that a quantum computer can exactly copy quantum superpositions, we show that NP-complete problems can be solved probabilistically in polynomial time. We also propose two methods that could potentially allow to avoid the use of a quantum copymachine. Supported by the Academy of Finland under grant 14047. To be presented at MCU'98, March 1998, Metz, France. TUCS Research Group Theory Group: Mathematical Methods in Computer Science
منابع مشابه
Anderson localization makes adiabatic quantum optimization fail.
Understanding NP-complete problems is a central topic in computer science (NP stands for nondeterministic polynomial time). This is why adiabatic quantum optimization has attracted so much attention, as it provided a new approach to tackle NP-complete problems using a quantum computer. The efficiency of this approach is limited by small spectral gaps between the ground and excited states of the...
متن کاملNonlinear quantum mechanics implies polynomial-time solution for NP-complete and #P problems
If quantum states exhibit small nonlinearities during time evolution, then quantum computers can be used to solve NP-complete problems in polynomial time. We provide algorithms that solve NP-complete and #P oracle problems by exploiting nonlinear quantum logic gates. It is argued that virtually any deterministic nonlinear quantum theory will include such gates, and the method is explicitly demo...
متن کاملNP-complete Problems and Physical Reality
Can NP-complete problems be solved efficiently in the physical universe? I survey proposals including soap bubbles, protein folding, quantum computing, quantum advice, quantum adiabatic algorithms, quantum-mechanical nonlinearities, hidden variables, relativistic time dilation, analog computing, Malament-Hogarth spacetimes, quantum gravity, closed timelike curves, and “anthropic computing.” The...
متن کاملOn the computational complexity of finding a minimal basis for the guess and determine attack
Guess-and-determine attack is one of the general attacks on stream ciphers. It is a common cryptanalysis tool for evaluating security of stream ciphers. The effectiveness of this attack is based on the number of unknown bits which will be guessed by the attacker to break the cryptosystem. In this work, we present a relation between the minimum numbers of the guessed bits and uniquely restricted...
متن کاملTractable Constraints on Ordered Domains
Finding solutions to a constraint satisfaction problem is known to be an NP-complete problem in general, but may be tractable in cases where either the set of allowed constraints or the graph structure is restricted. In this paper we identify a restricted set of contraints which gives rise to a class of tractable problems. This class generalizes the notion of a Horn formula in propositional log...
متن کامل