相关论文: A Lambda Calculus for Quantum Computation

Quantum computing will change the way we tackle certain problems. It promises to dramatically speed-up many chemical, financial, and machine-learning applications. However, to capitalize on those promises, complex design flows composed of…

Quantum computers leverage the unique advantages of quantum mechanics to achieve acceleration over classical computers for certain problems. Currently, various quantum simulators provide powerful tools for researchers, but simulating…

For the last few decades, classical machine learning has allowed us to improve the lives of many through automation, natural language processing, predictive analytics and much more. However, a major concern is the fact that we're fast…

We present a polymorphic linear lambda-calculus as a proof language for second-order intuitionistic linear logic. The calculus includes addition and scalar multiplication, enabling the proof of a linearity result at the syntactic level.

Quantum algorithms are demonstrated to outperform classical algorithms for certain problems and thus are promising candidates for efficient information processing. Herein we aim to provide a brief and popular introduction to quantum…

Quantum computing employs some quantum phenomena to process information. It has been hailed as the future of computing but it is plagued by serious hurdles when it comes to its practical realization. MemComputing is a new paradigm that…

Quantum Computing (QC) claims to improve the efficiency of solving complex problems, compared to classical computing. When QC is integrated with Machine Learning (ML), it creates a Quantum Machine Learning (QML) system. This paper aims to…

For decades, computational chemistry has been posited as one of the areas in which quantum computing would revolutionize. However, the algorithmic advantages that fault-tolerant quantum computers have for chemistry can be overwhelmed by…

We give an adequate, concrete, categorical-based model for Lambda-S, which is a typed version of a linear-algebraic lambda calculus, extended with measurements. Lambda-S is an extension to first-order lambda calculus unifying two approaches…

We apply numerical optimization and linear algebra algorithms for classical computers to the problem of automatically synthesizing algorithms for quantum computers. Using our framework, we apply several common techniques from these…

One perspective on quantum algorithms is that they are classical algorithms having access to a special kind of memory with exotic properties. This perspective suggests that, even in the case of quantum algorithms, the control flow notions…

An outstanding problem in quantum computing is the calculation of entanglement, for which no closed-form algorithm exists. Here we solve that problem, and demonstrate the utility of a quantum neural computer, by showing, in simulation, that…

This course of lectures has been taught for several years at the Lomonosov Moscow State University; its modified version in 2021 is read in the Zhejiang University (Hangzhou), in the framework of summer school on quantum computing. The…

We give a classical algorithm for linear regression analogous to the quantum matrix inversion algorithm [Harrow, Hassidim, and Lloyd, Physical Review Letters'09, arXiv:0811.3171] for low-rank matrices [Wossnig, Zhao, and Prakash, Physical…

We propose a quantum programming language that generalizes the $\lambda$-calculus. The language is non-linear; duplicated variables denote, not cloning of quantum data, but sharing a qubit's state; that is, producing an entangled pair of…

In this note we point out the fact that the proper conceptual setting of quantum computation is the theory of Linear Time Invariant systems. To convince readers of the utility of the approach, we introduce a new model of computation based…

Quantum computers provide a fundamentally new computing paradigm that promises to revolutionize our ability to solve broad classes of problems. Surprisingly, the basic mathematical structures of gate-based quantum computing, such as unitary…

Quantum computing is emerging as a new computing resource that could be superior to conventional computing for certain classes of optimization problems. However, in principle, most existing approaches to quantum optimization are intended to…

Stochastic models are highly relevant tools in science, engineering, and society. Recent work suggests emerging quantum computing technologies can substantially decrease the memory requirements for simulating stochastic models. Here we show…

We introduce and study graphic lambda calculus, a visual language which can be used for representing untyped lambda calculus, but it can also be used for computations in emergent algebras or for representing Reidemeister moves of locally…