Time-space complexity advantages for quantum computing

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14330%2F17%3A00100568" target="_blank" >RIV/00216224:14330/17:00100568 - isvavai.cz</a>

Result on the web

<a href="http://dx.doi.org/10.1007/978-3-319-71069-3_24" target="_blank" >http://dx.doi.org/10.1007/978-3-319-71069-3_24</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/978-3-319-71069-3_24" target="_blank" >10.1007/978-3-319-71069-3_24</a>

Result language

angličtina

Original language name

Time-space complexity advantages for quantum computing

Original language description

It has been proved that quantum computing has advantages in query complexity, communication complexity and also other computing models. However, it is hard to prove strictly that quantum computing has advantage in the Turing machine models in time complexity. For example, we do not know how to prove that Shor’s algorithm is strictly better than any classical algorithm, since we do not know the lower bound of time complexity of the factoring problem in Turing machine. In this paper, we consider the time-space complexity and prove strictly that quantum computing has advantages compared to their classical counterparts. We prove: (1) a time-space upper bound for recognition of the languages LI N T(n) on two-way finite automata with quantum and classical states (2QCFA): TS= O(n3/2log n), whereas a lower bound on probabilistic Turing machine is TS= Omega(n2); (2) a time-space upper bound for recognition of the languages LN E(n) on exact 2QCFA: TS= O(n1.87log n), whereas a lower bound on probabilistic Turing machine is TS= Omega(n2). It has been proved (Klauck, STOC’00) that the exact one-way quantum finite automata have no advantage comparing to classical finite automata in recognizing languages. However, the result (2) shows that the exact 2QCFA do have an advantage in comparison with their classical counterparts, which is the first example showing that the exact quantum computing has advantage in time-space complexity comparing to classical computing.

Czech name

—

Czech description

—

Type

D - Article in proceedings

CEP classification

—

OECD FORD branch

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Project

—

Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2017

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Article name in the collection

Lecture Notes in Computer Science, Volume 10687: 6th International Conference on Theory and Practice of Natural Computing, TPNC 2017

ISBN

9783319710686

ISSN

0302-9743

e-ISSN

—

Number of pages

13

Pages from-to

305-317

Publisher name

Springer

Place of publication

Cham, Switzerland

Event location

Praha

Event date

Jan 1, 2017

Type of event by nationality

WRD - Celosvětová akce

UT code for WoS article

000450354700024