Two-way finite automata with quantum and classical state

@article{Ambainis2002TwowayFA,
  title={Two-way finite automata with quantum and classical state},
  author={Andris Ambainis and John Watrous},
  journal={Theor. Comput. Sci.},
  year={2002},
  volume={287},
  pages={299-311}
}
  • A. Ambainis, J. Watrous
  • Published 16 November 1999
  • Computer Science, Mathematics, Physics
  • Theor. Comput. Sci.
We introduce 2-way finite automata with quantum and classical states (2qcfa's). This is a variant on the 2-way quantum finite automata (2qfa) model which may be simpler to implement than unrestricted 2qfa's; the internal state of a 2qcfa may include a quantum part that may be in a (mixed) quantum state, but the tape head position is required to be classical.We show two languages for which 2qcfa's are better than classical 2-way automata. First, 2qcfa's can recognize palindromes, a language that… 
View PDF on arXiv
124 Citations
Highly Influential Citations
23
Background Citations
46
Methods Citations
24
Results Citations
3

124 Citations

Citation Type

Citation Type

2-tape 1-way Quantum Finite State Automata
TLDR
It is established that 2-tape 1-way quantum finite state automaton (2T1QFA(2)) can accept all regular languages and it is shown that a language which cannot be accepted by any multi-head deterministic finite automaton can be acceptedBy exploiting the superposition property of quantum automata.
State succinctness of two-way finite automata with quantum and classical states
TLDR
This paper shows that there is a promise problem A^e^q(m) which can be solved by a 2QCFA with one-sided error @e in a polynomial expected running time with a constant number (that depends neither on m nor on @e) of quantum states and O([email protected]) classical states.
One-way quantum finite automata together with classical states
TLDR
A new computing model of 1QFA, namely, one-way quantum finite automata together with classical states (1QFAC for short), is developed, a component of classical states is added, and the choice of unitary evolution of quantum states at each step is closely related to the current classical state.
Succinctness of two-way probabilistic and quantum finite automata
TLDR
It is proved that two-way probabilistic and quantum finite automata (2PFAs and 2QFAs) can be considerably more concise than both their one-way versions, and two- way nondeterministic finite automaton (2NFAs), and it is shown that 2ZFAs with mixed states can support highly efficient probability amplification.
On the power of two-way multihead quantum finite automata
TLDR
It has been proved that a language which cannot be recognizing by any one-way and multi-letter quantum finite automata can be recognized by two-way quantum finite Automata with two heads and it has been investigated that quantum variant of two- way deterministic multihead finite automaton takes less number of heads to recognize a language containing of all words whose length is a prime number.
Two-way Quantum One-counter Automata
TLDR
It is proved that 2Q1CAs are at least as powerful as classical two-way deterministic one-counter automata (2D1C as), that is, every language L recognizable by 2D1 CAs is recognized by 2Q 1CAs with no error.
Determining the equivalence for one-way quantum finite automata
TLDR
This paper first focuses on determining the equivalence for one-way quantum finite automata with control language (CL-1QFAs) defined by Bertoni et al., and then, as an application, addresses the equivalences problem for measure-many one- way quantum finite Automata (MM-1ZFAs), introduced by Kondacs and Watrous.
1-Way Multihead Quantum Finite State Automata
1-way multihead quantum finite state automata (1QFA(k)) can be thought of modified version of 1-way quantum finite state automata (1QFA) and k-letter quantum finite state automata (k-letter QFA)…
The Limitations of Few Qubits: One-way and Two-way Quantum Finite Automata and the Group Word Problem
  • Zachary Remscrim
  • Computer Science, Mathematics
    Electron. Colloquium Comput. Complex.
  • 2019
The two-way finite automaton with quantum and classical states (2QCFA), defined by Ambainis and Watrous, is a model of quantum computation whose quantum part is extremely limited; however, as they…
On the State Complexity of Semi-quantum Finite Automata
TLDR
Three results of such a type that are stronger in some sense than other ones because they deal with models of quantum finite automata with very little quantumness so-called semi-quantum one- and two-way finiteAutomata.
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 33 REFERENCES
On the power of quantum finite state automata
  • Attila Kondacs, J. Watrous
  • Mathematics, Computer Science
    Proceedings 38th Annual Symposium on Foundations of Computer Science
  • 1997
TLDR
It is proved that the class of languages recognizing by linear time, bounded error 2qfa's properly includes the regular languages, and 1-way and 2-way quantum finite state automata are introduced, which are the quantum analogues of deterministic, nondeterministic and probabilistic 1- way and2-way finite state Automata.
1-way quantum finite automata: strengths, weaknesses and generalizations
  • A. Ambainis, R. Freivalds
  • Computer Science, Physics
    Proceedings 39th Annual Symposium on Foundations of Computer Science (Cat. No.98CB36280)
  • 1998
TLDR
This work constructs a 1-way QFA that is exponentially smaller than any equivalent classical (even randomized) finite automaton, and thinks that this construction may be useful for design of other space-efficient quantum algorithms.
A Time Complexity Gap for Two-Way Probabilistic Finite-State Automata
It is shown that if a two-way probabilistic finite-state automaton (2pfa) M recognizes a nonregular language L with error probability bounded below $\frac{1}{2}$, then there is a positive constant b…
Characterizations of 1-Way Quantum Finite Automata
TLDR
This paper characterize the measure-once model when it is restricted to accepting with bounded error and show that, without that restriction, it can solve the word problem over the free group and shows that piecewise testable sets can be accepted with boundederror by a measure-many quantum finite automaton, introducing new construction techniques for quantum automata in the process.
Running Time to Recognize Nonregular Languages by 2-Way Probabilistic Automata
TLDR
The running time for the recognition of nonregular 2-dimensional languages by 4-way pfa can be essentially smaller, namely, linear.
Dense quantum coding and a lower bound for 1-way quantum automata
TLDR
An exponential lower bound on the size of 1-way quantum finite automata for a family of languages accepted by linear sized deterministic finite automaton is proved.
Optimal lower bounds for quantum automata and random access codes
  • A. Nayak
  • Mathematics, Computer Science
    40th Annual Symposium on Foundations of Computer Science (Cat. No.99CB37039)
  • 1999
TLDR
Holevo's theorem is turned to, and it is shown that in typical situations, it may be replaced by a tighter and more transparent in-probability bound.
Quantum automata and quantum grammars
TLDR
This work proposes quantum versions of finite-state and push-down automata, and regular and context-free grammars, and finds analogs of several classical theorems, including pumping lemmas, closure properties, rational and algebraic generating functions, and Greibach normal form.
A Lower Bound for Probabilistic Algorithms for Finite State Machines
TLDR
It is shown that no 2-way probabilistic finite automaton that runs in exp( o ( n )) expected time recognizes { a m b m : m ⩾ 1} with probability of error bounded away from 1 2 .
Finite state verifiers I: the power of interaction
TLDR
An investigation of interactive proof systems (IPSs) where the verifier is a 2-way probabilistic finite state automaton (2pfa) is initiated, and it is shown that IPSs with verifiers in the latter class are as powerful as IPSs where verifiers are polynomial-time Probabilistic Turing machines.
...
1
2
3
4
...