Related papers: Quantum function computation using sublogarithmic …

Quantum information science currently poses a troubling contradiction. It can be summarized as: (1) To factor efficiently, quantum computers must perform exponentially precise energy estimation. (2) Exponentially precise energy estimation…

Foundations of the notion of quantum Turing machines are investigated. According to Deutsch's formulation, the time evolution of a quantum Turing machine is to be determined by the local transition function. In this paper, the local…

In the last couple of decades, the world has seen several stunning instances of quantum algorithms that provably outperform the best classical algorithms. For most problems, however, it is currently unknown whether quantum algorithms can…

It is not currently known if quantum Turing machines can efficiently simulate probabilistic computations in the space-bounded case. In this paper we show that space-bounded quantum Turing machines can efficiently simulate a limited class of…

Quantum computing has emerged as a transformative paradigm, capable of tackling complex computational problems that are infeasible for classical methods within a practical timeframe. At the core of this advancement lies the concept of…

We explore in the framework of Quantum Computation the notion of computability, which holds a central position in Mathematics and Theoretical Computer Science. A quantum algorithm that exploits the quantum adiabatic processes is considered…

We discuss classical and quantum algorithms for solvability testing and finding integer solutions x,y of equations of the form af^x + bg^y = c over finite fields GF(q). A quantum algorithm with time complexity q^(3/8) (log q)^O(1) is…

There is good evidence that quantum computers are more powerful than classical computers, and that various simple modifications of quantum theory yield computational power that is dramatically greater still. However, these modifications…

Machine learning is a fascinating and exciting field within computer science. Recently, this excitement has been transferred to the quantum information realm. Currently, all proposals for the quantum version of machine learning utilize the…

Polynomial--time constant--space quantum Turing machines (QTMs) and logarithmic--space probabilistic Turing machines (PTMs) recognize uncountably many languages with bounded error (Say and Yakary\i lmaz 2014, arXiv:1411.7647). In this…

We study computation of the mean of sequences with values in finite dimensional normed spaces and compare the computational power of classical randomized with that of quantum algorithms for this problem. It turns out that in contrast to the…

The computational abilities of theories within the generalised probabilistic theory framework has been the subject of much recent study. Such investigations aim to gain an understanding of the possible connections between physical…

Quantum computing provides a new way for approaching problem solving, enabling efficient solutions for problems that are hard on classical computers. It is based on leveraging how quantum particles behave. With researchers around the world…

Quantum models of computation are widely believed to be more powerful than classical ones. Efforts center on proving that, for a given problem, quantum algorithms are more resource efficient than any classical one. All this, however,…

Due to common misconceptions about the Church-Turing thesis, it has been widely assumed that the Turing machine provides an upper bound on what is computable. This is not so. The new field of hypercomputation studies models of computation…

The problem of efficient multiplication of large numbers has been a long-standing challenge in classical computation and has been extensively studied for centuries. It appears that the existing classical algorithms are close to their…

Faster algorithms, novel cryptographic mechanisms, and alternative methods of communication become possible when the model underlying information and computation changes from a classical mechanical model to a quantum mechanical one. Quantum…

We present a quantum version of the classical probabilistic algorithms $\grave{a}$ la Rabin. The quantum algorithm is based on the essential use of Grover's operator for the quantum search of a database and of Shor's Fourier transform for…

A theoretical model of a quantum device which can factorize any number N in two steps i.e. by preparing an input state and performing a measurement is discussed. The analysis reveals that the duration of state preparation and measurement is…

Computational complexity characterizes the usage of spatial and temporal resources by computational processes. In the classical theory of computation, e.g. in the Turing Machine model, computational processes employ only local space and…