Related papers: Complexity Bounds of Constant-Space Quantum Comput…
Let $\mathcal{P}(\Sigma^*)$ be the semiring of languages, and consider its subset $\mathcal{P}(\Sigma)$. In this paper we define the language recognized by a weighted automaton over $\mathcal{P}(\Sigma)$ and a one-letter alphabet.…
We present a number of results related to quantum algorithms with small error probability and quantum algorithms that are zero-error. First, we give a tight analysis of the trade-offs between the number of queries of quantum search…
In this paper, we introduce a new public quantum interactive proof system and the first quantum alternating Turing machine: qAM proof system and qATM, respectively. Both are obtained from their classical counterparts (Arthur-Merlin proof…
We show that one-way quantum one-counter automaton with zero-error is more powerful than its probabilistic counterpart on promise problems. Then, we obtain a similar separation result between Las Vegas one-way probabilistic one-counter…
We have previously (quant-ph/9608012) shown that for quantum memories and quantum communication, a state can be transmitted over arbitrary distances with error $\epsilon$ provided each gate has error at most $c\epsilon$. We discuss a…
Given the Hamiltonian, the evaluation of unitary operators has been at the heart of many quantum algorithms. Motivated by existing deterministic and random methods, we present a hybrid approach, where Hamiltonians with large amplitude are…
Fault-tolerant quantum computations require alternating quantum and classical computations, where the classical computations prove vital in detecting and correcting errors in the quantum computation. Recently, interest in using these…
Random testing approaches work by generating inputs at random, or by selecting inputs randomly from some pre-defined operational profile. One long-standing question that arises in this and other testing contexts is as follows: When can we…
Quantum algorithms for tasks such as factorization, search, and simulation rely on control flow such as branching and iteration that depends on the value of data in superposition. High-level programming abstractions for control flow, such…
This paper studies three classes of cellular automata from a computational point of view: freezing cellular automata where the state of a cell can only decrease according to some order on states, cellular automata where each cell only makes…
Although quantum algorithms realizing an exponential time speed-up over the best known classical algorithms exist, no quantum algorithm is known performing computation using less space resources than classical algorithms. In this paper, we…
There is a fundamental difficulty in generalizing weighted automata to the case of infinite words: in general the infinite sum-of-products from which the weight of a given word is derived will diverge. Many solutions to this problem have…
Finite-turn pushdown automata (PDA) are investigated concerning their descriptional complexity. It is known that they accept exactly the class of ultralinear context-free languages. Furthermore, the increase in size when converting…
To study relationship between quantum finite automata and probabilistic finite automata, we introduce a notion of probabilistic reversible automata (PRA, or doubly stochastic automata). We find that there is a strong relationship between…
Linear quantum cellular automata were introduced recently as one of the models of quantum computing. A basic postulate of quantum mechanics imposes a strong constraint on any quantum machine: it has to be unitary, that is its time evolution…
In this paper we extend both standard fault tolerance theory and Kitaev's model for quantum computation, combining them so as to yield quantitative results that reveal the interplay between the two. Our analysis establishes a methodology…
This paper presents efficient algorithms for testing the finite, polynomial, and exponential ambiguity of finite automata with $\epsilon$-transitions. It gives an algorithm for testing the exponential ambiguity of an automaton $A$ in time…
Automatic differentiation is an invaluable feature of machine learning and quantum machine learning software libraries. In this work it is shown how quantum automatic differentiation can be used to solve the condensed-matter problem of…
The use of quantum computing for machine learning is among the most exciting prospective applications of quantum technologies. However, machine learning tasks where data is provided can be considerably different than commonly studied…
Computation is an input-output process, where a program encoding a problem to be solved is inserted into a machine that outputs a solution. Quantum computation conventionally relies on classical, external control outside the quantum…