Related papers: A Classical $\pi$ Machine and Grover's Algorithm
Grover's algorithm can solve NP-complete problems on quantum computers faster than all the known algorithms on classical computers. However, Grover's algorithm still needs exponential time. Due to the BBBV theorem, Grover's algorithm is…
We simulate Grover's algorithm in a classical computer by means of a stochastic method using the Hubbard-Stratonovich decomposition of n-qubit gates into one-qubit gates integrated over auxiliary fields. The problem reduces to finding the…
Fundamental mathematical constants like $e$ and $\pi$ are ubiquitous in diverse fields of science, from abstract mathematics to physics, biology and chemistry. For centuries, new formulas relating fundamental constants have been scarce and…
Quantum amplitude estimation is a key sub-routine of a number of quantum algorithms with various applications. We propose an adaptive algorithm for interval estimation of amplitudes. The quantum part of the algorithm is based only on…
Classical models of computation traditionally resort to halting schemes in order to enquire about the state of a computation. In such schemes, a computational process is responsible for signalling an end of a calculation by setting a halt…
We present an algorithm for doing Gibbs sampling on a quantum computer. The algorithm combines phase estimation for a Szegedy operator, and Grover's algorithm. For any $\epsilon>0$, the algorithm will sample a probability distribution in…
We discuss classical and quantum computations in terms of corresponding Hamiltonian dynamics. This allows us to introduce quantum computations which involve parallel processing of both: the data and programme instructions. Using mixed…
This paper concerns the Grover algorithm that permits to make amplification of quantum states previously tagged by an Oracle. Grover's algorithm allows searches in an unstructure database of n entries finding a marked element with a…
We describe a simulation method for a quantum spin model of a generic, general purpose quantum computer. The use of this quantum computer simulator is illustrated through several implementations of Grover's database search algorithm. Some…
In this work I describe a classical analog of Grover's quantum searching algorithm, explaining why a quantum algorithm should be able to perform search in O(sqrtN) steps and also acting as a useful pedagogic demonstration.
It is first shown that when the Schr\"{o}dinger equation for a wave function is written in the polar form, complete information about the system's {\em quantum-ness} is separated out in a single term $Q$, the so called `quantum potential'.…
We show how the basic operations of quantum computing can be expressed and manipulated in a clear and concise fashion using a multiparticle version of geometric (aka Clifford) algebra. This algebra encompasses the product operator formalism…
Recent studies have been spurred on by the promise of advanced quantum computing technology, which has led to the development of quantum computer simulations on classical hardware. Grover's quantum search algorithm is one of the well-known…
Quantum algorithms can deliver asymptotic speedups over their classical counterparts. However, there are few cases where a substantial quantum speedup has been worked out in detail for reasonably-sized problems, when compared with the best…
The famous Goldbach conjecture states that any even natural number $N$ greater than $2$ can be written as the sum of two prime numbers $p^{\text{(I)}}$ and $p^{\text{(II)}}$. In this article we propose a quantum analogue device that solves…
The prime-counting function $\pi(x)$ which computes the number of primes smaller or equal to a given real number has a long-standing interest in number theory. The present manuscript proposes a method to compute $\pi(x)$ with time…
The two essential ideas in this paper are, on the one hand, that a considerable amount of the power of quantum computation may be obtained by adding to a classical computer a few specialized quantum modules and, on the other hand, that such…
The application of near-term quantum devices to machine learning (ML) has attracted much attention. In one such attempt, Mitarai et al. (2018) proposed a framework to use a quantum circuit for supervised ML tasks, which is called quantum…
The computational cost of exact methods for quantum simulation using classical computers grows exponentially with system size. As a consequence, these techniques can only be applied to small systems. By contrast, we demonstrate that quantum…
A large spectrum of problems in classical physics and engineering, such as turbulence, is governed by nonlinear differential equations, which typically require high-performance computing to be solved. Over the past decade, however, the…