相关论文: And free lunch for all...

This text aims to present and explain quantum machine learning algorithms to a data scientist in an accessible and consistent way. The algorithms and equations presented are not written in rigorous mathematical fashion, instead, the…

These are my published answers to the seventeen questions posed by Max Schlosshauer in his 2011 book "Elegance and Enigma: the Quantum Interviews". I have inserted thirty footnotes into those answers, commenting on them from the perspective…

Ramanujan made many beautiful and elegant discoveries in his short life of 32 years, and one of them that has attracted the attention of several mathematicians over the years is his intriguing formula for $\zeta(2n+1)$. To be sure,…

We provide finite analogs of a pair of two-variable $q$-series identities from Ramanujan's lost notebook and a companion identity.

These notes are a summary of the problem session discussions at various CANT (Combinatorial and Additive Number Theory Conferences). Currently they include all years from 2009 through 2019 (inclusive); the goal is to supplement this file…

We employ an algebraic procedure based on quantum mechanics to propose a `quantum number theory' (QNT) as a possible extension of the `classical number theory'. We built our QNT by defining pure quantum number operators ($q$-numbers) of a…

Quantum walks, the quantum mechanical counterpart of classical random walks, is an advanced tool for building quantum algorithms that has been recently shown to constitute a universal model of quantum computation. Quantum walks is now a…

This article is an attempt to generalize the classical theory of reversible computing, principally developed by Bennet [IBM J. Res. Develop., 17(1973)] and by Fredkin and Toffoli [Internat. J. Theoret. Phys., 21(1982)], to the quantum case.…

In this research notebook in the four-part, quantum computation and applications, quantum computation and algorithms, quantum communication protocol, and universal quantum computation for quantum engineers, researchers, and scientists, we…

Example 7, after Entry 43, in Chapter XII of the first Notebook of Srinivasa Ramanujan is proved and, more generally, a summation theorem for $_3F_2(a,a,x;1+a,1+a+N;1)$, where $N$ is a non-negative integer, is derived.

During his work devoted to Coxeter's friezes, M. Cuntz initiated the study of the notion of $\lambda$-quiddity and raised the problem of the study of this over some subsets of $\mathbb C$. More specifically, $\lambda$-quiddities are the…

This paper investigates Srinivasa Ramanujan's initial intuitive methodology for assigning the finite value -1/12 to the sum of the divergent infinite series of all positive integers. We systematically examine Ramanujan's initial method,…

The concept of absence of opportunities for free lunches is one of the pillars in the economic theory of financial markets. This natural assumption has proved very fruitful and has lead to great mathematical, as well as economical, insights…

We study the $q$-series $F(q) = \sum q^{m(m+1)/2}/(q)_m^2$ and offer some commentary on why Ramanujan may have thought $F(q)$ does not "close."

In this expository article, we discuss the contributions made by several mathematicians with regard to a famous formula of Ramanujan for odd zeta values. The goal is to complement the excellent survey by Berndt and Straub…

The purpose of these lecture notes is to provide readers, who have some mathematical background but little or no exposure to quantum mechanics and quantum computation, with enough material to begin reading the research literature in quantum…

This paper surveys various results in the field of Quantum Learning theory, specifically focusing on learning quantum-encoded classical concepts in the Probably Approximately Correct (PAC) framework. The cornerstone of this work is the…

The Euler product for the Landau--Ramanujan constant could have motivated a curious identity by Ramanujan that appears in his notebooks two times. This observation involves a square root and the first four prime numbers of the form $4n+3$,…

The theory of quantum thermodynamics investigates how the concepts of heat, work, and temperature can be carried over to the quantum realm, where fluctuations and randomness are fundamentally unavoidable. These lecture notes provide an…

Explicit formulas involving a generalized Ramanujan sum are derived. An analogue of the prime number theorem is obtained and equivalences of the Riemann hypothesis are shown. Finally, explicit formulas of Bartz are generalized.