Superiority of exact quantum automata for promise problems
نویسندگان
چکیده
In this note, we present an infinite family of promise problems which can be solved exactly by just tuning transition amplitudes of a two-state quantum finite automata operating in realtime mode, whereas the size of the corresponding classical automata grow without bound.
منابع مشابه
Potential of Quantum Finite Automata with Exact Acceptance
The potential of the exact quantum information processing is an interesting, important and intriguing issue. For examples, it has been believed that quantum tools can provide significant, that is larger than polynomial, advantages in the case of exact quantum computation only, or mainly, for problems with very special structures. We will show that this is not the case. In this paper the potenti...
متن کاملExact quantum algorithms for promise problems in automata theory
In this note, we show that quantum finite automata can be polynomially more succinct than their classical counterparts for promise problems in case of exact computation. Additionally, in terms of language recognition, the same result is shown to be valid up to a constant factor depending on how bigger the size of the alphabet is.
متن کاملCommunication complexity of promise problems and their applications to finite automata
Equality and disjointness are two of the most studied problems in communication complexity. They have been studied for both classical and also quantum communication and for various models and modes of communication. Buhrman et al. [6] proved that the exact quantum communication complexity for a promise version of the equality problem is O(logn) while the classical deterministic communication co...
متن کاملImplications of Quantum Automata for Contextuality
We construct zero-error quantum finite automata (QFAs) for promise problems which cannot be solved by bounded-error probabilistic finite automata (PFAs). Here is a summary of our results: 1. There is a promise problem solvable by an exact two-way QFA in exponential expected time, but not by any bounded-error sublogarithmic space probabilistic Turing machine (PTM). 2. There is a promise problem ...
متن کاملClassical Automata on Promise Problems
Promise problems were mainly studied in quantum automata theory. Here we focus on state complexity of classical automata for promise problems. First, it was known that there is a family of unary promise problems solvable by quantum automata by using a single qubit, but the number of states required by corresponding one-way deterministic automata cannot be bounded by a constant. For this family,...
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:
- Inf. Process. Lett.
دوره 112 شماره
صفحات -
تاریخ انتشار 2012