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Construction of explicit quantum circuits follows the notion of the "standard circuit model" introduced in the solid and profound analysis of elementary gates providing quantum computation. Nevertheless the model is not always optimal (e.g.…

Quantum Physics · Physics 2007-05-23 K. Ch. Chatzisavvas , C. Daskaloyannis , C. P. Panos

CoqQ is a framework for reasoning about quantum programs in the Coq proof assistant. Its main components are: a deeply embedded quantum programming language, in which classic quantum algorithms are easily expressed, and an expressive…

Programming Languages · Computer Science 2022-07-26 Li Zhou , Gilles Barthe , Pierre-Yves Strub , Junyi Liu , Mingsheng Ying

The increasing capabilities of quantum computing hardware and the challenge of realizing deep quantum circuits require fully automated and efficient tools for compiling quantum circuits. To express arbitrary circuits in a sequence of native…

We present the fundamental principles behind quantum key distribution and discuss a few well-known QKD protocols. Bearing in mind that the majority of our readers are from engineering and experimental optics, we focus more on the…

Quantum Physics · Physics 2010-02-23 Bing Qi , Li Qian , Hoi-Kwong Lo

Quantum computing offers the potential to solve certain complex problems, yet, scaling monolithic processors remains a major challenge. Modular and distributed architectures are proposed to build large-scale quantum systems while bringing…

We present a practical course targeting graduate students with prior knowledge of the basics of quantum computing. The practical aims to deepen students' understanding of fundamental concepts in quantum computing by implementing quantum…

Physics Education · Physics 2025-11-24 Florian Krötz , Xiao-Ting Michelle To , Korbinian Staudacher , Dieter Kranzlmüller

In this work, quantum transformers are designed and analysed in detail by extending the state-of-the-art classical transformer neural network architectures known to be very performant in natural language processing and image analysis.…

A quantum circuit is a computational unit that transforms an input quantum state to an output one. A natural way to reason about its behavior is to compute explicitly the unitary matrix implemented by it. However, when the number of qubits…

Programming Languages · Computer Science 2021-12-22 Wenjun Shi , Qinxiang Cao , Yuxin Deng , Hanru Jiang , Yuan Feng

A quantum processor is a programmable quantum circuit in which both the data and the program, which specifies the operation that is carried out on the data, are quantum states. We study the situation in which we want to use such a processor…

Quantum Physics · Physics 2009-11-11 Mark Hillery , Mario Ziman , Vladimir Buzek

With the potential of quantum algorithms to solve intractable classical problems, quantum computing is rapidly evolving and more algorithms are being developed and optimized. Expressing these quantum algorithms using a high-level language…

Quantum Physics · Physics 2020-05-28 N. Khammassi , I. Ashraf , J. v. Someren , R. Nane , A. M. Krol , M. A. Rol , L. Lao , K. Bertels , C. G. Almudever

As quantum computers become real, it is high time we come up with effective techniques that help programmers write correct quantum programs. In classical computing, formal verification and sound static type systems prevent several classes…

Programming Languages · Computer Science 2021-09-10 Kartik Singhal , John Reppy

Quantum computing represents a paradigm shift for computation requiring an entirely new computer architecture. However, there is much that can be learned from traditional classical computer engineering. In this paper, we describe the…

Quantum Physics · Physics 2022-11-03 A. Y. Matsuura , Timothy G. Mattson

Quantum computer programming is emerging as a new subject domain from multidisciplinary research in quantum computing, computer science, mathematics (especially quantum logic, lambda calculi, and linear logic), and engineering attempts to…

Programming Languages · Computer Science 2008-12-18 Donald A. Sofge

Transformers have gained popularity in machine learning due to their application in the field of natural language processing. They manipulate and process text efficiently, capturing long-range dependencies among data and performing the next…

Quantum Physics · Physics 2026-03-06 Michele Banfi , Paolo Zentilini , Sebastiano Corli , Enrico Prati

This tutorial offers a quick, hands-on introduction to solving Quadratic Unconstrained Binary Optimization (QUBO) models on currently available quantum computers and their simulators. We cover both IBM and D-Wave machines: IBM utilizes a…

Quantum Physics · Physics 2025-06-18 Arul Mazumder , Sridhar Tayur

We present the guarded lambda-calculus, an extension of the simply typed lambda-calculus with guarded recursive and coinductive types. The use of guarded recursive types ensures the productivity of well-typed programs. Guarded recursive…

Logic in Computer Science · Computer Science 2019-03-14 Ranald Clouston , Aleš Bizjak , Hans Bugge Grathwohl , Lars Birkedal

The widely held belief that BQP strictly contains BPP raises fundamental questions: if we cannot efficiently compute predictions for the behavior of quantum systems, how can we test their behavior? In other words, is quantum mechanics…

Quantum Physics · Physics 2017-04-17 Dorit Aharonov , Michael Ben-Or , Elad Eban , Urmila Mahadev

Type-level programming is an increasingly popular way to obtain additional type safety. Unfortunately, it remains a second-class citizen in the majority of industrially-used programming languages. We propose a new dependently-typed system…

Programming Languages · Computer Science 2020-11-17 Georg Stefan Schmid , Olivier Blanvillain , Jad Hamza , Viktor Kunčak

As quantum computing evolves, many important questions emerge, such as how best to represent quantum programs, and how to promote interoperability between quantum program analysis tools. These questions arise naturally in the design of…

Quantum Physics · Physics 2024-05-17 Scott Wesley

This tutorial aims at giving an introductory treatment of the circuit analysis of superconducting qubits, i.e., two-level systems in superconducting circuits. It also touches upon couplings between such qubits and how microwave driving and…

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