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- Herausgeber: John Wiley & Sons
- Kategorie: Wissenschaft und neue Technologien
- Sprache: Englisch
From Distributed Quantum Computing to Quantum Internet Computing Understand the future of the internet with this accessible guide Quantum computing, which draws upon the principles of quantum mechanics to perform computing functions unrestricted by the binary language of ordinary computing, has developed with extraordinary speed in recent years. Progress in quantum computing and its related technological subfields, including quantum internet, has been rapid enough to suggest that we are living in a "new Quantum Age." To understand the future of the internet, it's now essential to understand the present and future of quantum computing and quantum internet computing. This book provides a groundbreaking overview of this field of technology and its latest developments. It provides readers with a working knowledge of the key topics required to connect quantum computing to the future of distributed computing and the internet, including important issues like quantum protocols, distributed quantum computations, fundamental computations in the quantum internet architecture, and more. The result is an accessible and essential reference for any reader looking to better understand quantum technologies. From Distributed Quantum Computing to Quantum Internet Computing readers will also find: * Detailed discussion of topics including qubit states, entanglement, quantum gates, and more. * Mathematical background for underlying key concepts. * Worked out examples that aim to initiate readers into the emerging area of quantum internet computing. This book is ideal for researchers and graduate students in quantum computing, quantum internet, quantum communications, and related fields, as well as Computer Scientists and Information Technology students and researchers who want an introductory overview to quantum internet computing.
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Veröffentlichungsjahr: 2023
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Table of Contents
Cover
Table of Contents
Title Page
Copyright
Dedication
About the Author
Preface
Note
Acknowledgments
1 Introduction
1.1 The New Quantum Age and the Second Quantum Revolution
1.2 Distributed Quantum Computing and the Rise of Quantum Internet Computing
1.3 Aim and Scope of the Book
1.4 Outline of this Book
1.5 Related Books and Resources
References
Notes
2 Preliminaries
2.1 Qubit and Qubit States
2.2 Quantum Gates and Quantum Circuits
2.3 Entanglement
2.4 Teleportation and Superdense Coding
2.5 Summary
2.6 Further Reading and Resources on Quantum Computing
References
Notes
3 Distributed Quantum Computing – Classical and Quantum
3.1 The Power of Entanglement for Distributed Computing
3.2 Other Quantum Protocols
3.3 Summary
References
Notes
4 Distributed Quantum Computing – Distributed Control of Quantum Gates
4.1 Performing a Distributed CNOT
4.2 Beyond the Distributed CNOT
4.3 Distributing Quantum Circuits and Compilation for Distributed Quantum Programs
4.4 Control and Scheduling for Distributed Quantum Computers
4.5 Distributed Quantum Computing Without Internode Entanglement
4.6 Summary
References
Notes
5 Delegating Quantum Computations
5.1 Delegating Private Quantum Computations
5.2 How to Verify Delegated Private Quantum Computations
5.3 Quantum Computing‐as‐a‐Service
5.4 Summary
References
Notes
6 The Quantum Internet
6.1 Entanglement Over Longer Distances
6.2 Entanglement with Higher Fidelity
6.3 Distributed Quantum Computation Over the Quantum Internet – Challenges
6.4 Summary
References
Notes
7 Conclusion
References
Note
Index
End User License Agreement
List of Tables
Chapter 5
Table 5.1 Table summarizing the protocol for computing with encrypted data ...
List of Illustrations
Chapter 1
Figure 1.1 An illustration of a distributed quantum computer with multiple q...
Figure 1.2 A simple architecture of quantum Internet computing: distributed ...
Chapter 2
Figure 2.1 A beamsplitter, with detectors d1 and d2 for the transmitted and ...
Figure 2.2 An interferometer configuration with two 50/50 beamsplitters. One...
Figure 2.3 Symbols and matrices for single qubit gates...
Figure 2.4 Symbol for a quantum measurement operation, where the input is a ...
Figure 2.5 Symbols for the CNOT gate and controlled‐...
Figure 2.6 An example circuit with two wires for two qubits.
Figure 2.7 An example of a two‐qubit circuit. (a) An example circuit with tw...
Figure 2.8 An example circuit with three wires for three qubits.
Figure 2.9 An example circuit which
looks like
a copying operation.
Figure 2.10 A circuit to generate the entangled state...
Figure 2.11 Simplified diagram for entangling a pair of qubits.
Figure 2.12 Simplified diagram for entangling three qubits.
Figure 2.13 Circuit for generating the cat‐like state:...
Figure 2.14 Circuits to generate the generalized GHZ state. (a) Circuit to g...
Figure 2.15 A circuit for teleporting a quantum state from...
Figure 2.16 A circuit for transmitting two classical bits of information by ...
Chapter 3
Figure 3.1 The GHZ&M problem is for...
Figure 3.2 The CHSH game. The referee produces a pair of inputs...
Figure 3.3 A solution to the coin flipping protocol without a trusted mediat...
Figure 3.4 A generic bit commitment protocol.
Figure 3.5 Coin flipping protocol using the bit commitment protocol – note t...
Figure 3.6 Leader election where the winner of each pair is decided using a ...
Figure 3.7 Illustration of a scenario where...
Figure 3.8 Illustration of a scenario where...
Figure 3.9 Illustration of a graphical representation of the Dining Cryptogr...
Figure 3.10 Illustration of a graphical representation of the Dining Cryptog...
Figure 3.11 (a) An illustration of the metaphor of three generals (with thei...
Chapter 4
Figure 4.1 Distributed CNOT using teleportation.
Figure 4.2 Distributed CNOT by Eisert et al.
Figure 4.3 Distributed CNOT with single control qubit (on...
Figure 4.4 Distributed CNOT with single control qubit (on...
Figure 4.5 An efficient way to perform a distributed multiqubit control on a...
Figure 4.6 The circuits from Figures 4.2–4.5 marked with cat‐entanglers and ...
Figure 4.7 An illustration of execution of a four‐qubit circuit for the dist...
Chapter 5
Figure 5.1 Protocol for an...
Figure 5.2 A slightly modified protocol for an...
Figure 5.3 The ‐gate gadget in an...
Figure 5.4 The ‐gate gadget in a ...
Chapter 6
Figure 6.1 Illustration of entanglement swapping, from (1) entangled pairs b...
Figure 6.2 Illustration of repeated application of entanglement swapping to ...
Figure 6.3 Graph of ...
Figure 6.4 An illustration of three nodes QC1, QC2, and QC3, involved in a d...
Figure 6.5 A circuit implementing a distributed‐CNOT between qubits ...
Guide
Cover
Table of Contents
Series Page
Title Page
Copyright
Dedication
About the Author
Acknowledgments
Begin Reading
Index
End User License Agreement
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From Distributed Quantum Computing to Quantum Internet Computing
An Introduction
Seng W. Loke
Deakin UniversityAustralia
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To my Princess YC
About the Author
Professor Seng W. Loke (Member, IEEE) received the BSc degree (Hons.) in Computer Science from the Australian National University in 1994 and the PhD degree in Computer Science from the University of Melbourne, Australia, in 1998. He is a Professor of computer science at the School of Information Technology, Deakin University, Australia. He currently co‐leads the IoT Platforms and Applications Laboratory and directs the Centre for Software, Systems and Society, within Deakin's School of Information Technology. His research interests include the Internet of Things, quantum Internet computing, cooperative vehicles, distributed and mobile systems, and smart cities.
Preface
The book is an outcome of my own journey, in recent years, into quantum computing and into a number of topics (detailed later), which can be considered to come under the theme of quantum Internet computing. This seems to be rather timely, since recent years have also seen important developments in quantum computing, including companies successfully building (though small/intermediate scale) quantum computers and offering access to them over the Cloud, and some momentum toward building the quantum Internet, making these topics almost too important to ignore. The developments in quantum computing, quantum cryptography, quantum information theory, quantum networking, and the quantum Internet in the recent decades have led to what has been called “the new quantum age” (to borrow the title from Andrew Whitaker's book) and the “second quantum revolution,” which we are living in today.1
This book is an attempt to provide an introductory overview of work leading toward what I call quantum Internet computing at the intersection of work in distributed quantum computing and the quantum Internet, where one does distributed computing but over Internet‐scale distances and systems involving nodes connected via the Internet. The notion of quantum Internet computing is based loosely on an analogy to Internet computing at the intersection of work in distributed computing and the Internet. While the quantum Internet and distributed quantum computing can be considered nascent, the book attempts a selective introduction to the following four key topics which I identify as coming under quantum Internet computing: (i) distributed quantum computing, including quantum protocols and theoretical perspectives, (ii) distributed quantum computing via nonlocal or distributed quantum gates, (iii) delegating quantum computations, blind quantum computing, and verifying delegated quantum computations, and (iv) the quantum Internet, including the concept, and key ideas, such as quantum entanglement distillation, and entanglement swapping (where this book focuses on the computational aspects, instead of the underlying physics, if one accepts such a separation of focus). At the time of writing, distributed quantum computers over the quantum Internet can be considered “under construction,” though experiments on fundamental concepts have been realized as well as prototypes of software working over simulations, and demonstrations of quantum networking – so, this book is rather optimistic toward the future.
The book, in a way, empathizes with newcomers to the subject and attempts to explain the concepts for the newcomer to quantum (Internet) computing, having been there myself. In short, the book is what I would have liked to have had when starting my own journey into these areas, at least to gain an overview of the area. Knowledge in the four topics above exists though mainly distributed in the research literature and in a range of (very good) online resources (which the book will also point out) – this book is an attempt (to the author's knowledge, the first book) to discuss the above four topics under one “umbrella paradigm,” here called quantum Internet computing.
Each of the above four topics is emerging as active areas of research, and this book, as well, does not attempt a full coverage. The book aims to highlight and discuss a selection of key (at least in my opinion) ideas and concepts in the literature within those four topics above, and hence, the word “introduction” in the title, and given the vastness of the literature on the above topics, one might consider this introduction “short”! As a result, the book might appear to lack novelty and sophistication since it might not be a complete guide about the state of the art in all the above topics (multiple books would be likely needed to do so!), but the aim of this book is to introduce readers to certain key (and one might say fundamental) ideas that have emerged in the above topics, and perhaps “whet the appetite” of readers to go further. Even with the relatively “small” sampling of algorithms, protocols, and ideas discussed in this book, one can already observe their beauty and ingenuity – which is also partly a reason for the choice of topics included. One might consider the book as a “teaser” for a vast area of exciting research.
The book's approach is to select a range of key ideas and discuss them in depth, including detailed calculations often needed in seeing how a protocol or concept actually works – this is partly inspired by David McMahon's book Quantum Computing Explained which helps readers by detailing calculations. The details are given to allow someone fairly new to quantum computing (and not the expert who does such calculations every day!) to be able to see why certain ideas, algorithms, or protocols work; hence, it is an attempt to be pedagogical, providing a “gentle” introduction for those who might not have read the research papers upon which the book's material is based – we refer to and point out the original papers and resources for further reading.
The book is intended for advanced undergraduate and graduate students, researchers and practitioners in industry and academia, across different disciplines who might be interested in the area of quantum Internet computing and just wanted an introduction to the area, or before possibly moving on to technical papers and the research literature. However, given my own background in computing, and the style of the book, the book should appeal to students and researchers in Computer Science, or Information Technology (though it is hoped it might be useful to some physicists and mathematicians as well).
Often, the mathematics and quantum physics knowledge are hurdles to one, who does not have such background, trying to learn quantum computing for the first time. So, the book does not use a mathematical monograph style with theorems and proofs, but attempts a narrative style without sacrificing the mathematical rigour and technical details; in so doing, the theoretical Computer Scientist, physicist, or mathematician (or student thereof) might find the style of the book rather “informal,” and there is little focus on exercises – but the aim is to make the book “readable” (perhaps an exercise for the reader is to follow the calculations and find errors (if any)!). The main prerequisites for readers would be mainly basic linear algebra and probability (and perhaps some perseverance to follow calculations!) and some basic background in computing, and though some basic knowledge in quantum computing would be helpful, we attempt to provide sufficient background for the assiduous reader relatively new to quantum computing (and provide pointers to good resources for learning quantum computing for the first time). The book can be used as a reference for a first course on quantum Internet computing (though perhaps not as a first course on quantum computing), supplemented by selected research literature.
The expert reader might notice that there are some topics missing, e.g. measurement‐based quantum computation or one‐way quantum computing, and quantum error correction (each of these topics probably deserves books of its own). The book also does not discuss distributed quantum sensing.
Additional explanations and calculations that could be useful to readers are in footnotes as well as marked as Aside. Lastly, the reader is invited to email me any inaccuracies or errors found in the book. With the above, let's get on with it!
October 2023
Seng W. Loke
Deakin University, Melbourne, Australia
Note
1
This phrase “second quantum revolution” has been used at the NIST website
https://www.nist.gov/physics/introduction-new-quantum-revolution/second-quantum-revolution
, and in association with developments which the contributions, recognized by the 2022 Nobel Prize in Physics, drove:
https://www.nobelprize.org/uploads/2022/10/advanced-physicsprize2022.pdf
[last accessed: 7/10/2022].
Acknowledgments
The author would like to thank the School of Information Technology at Deakin University and the publisher (and the wonderful editorial team) for the tremendous support toward the writing of this book (any errors would be my own fault!). The quantum computing enthusiasts and colleagues at the School have also helped (implicitly) nudge me toward the subject and provided a vibrant environment for sustaining my interest in the subject. Finally, my gratitude to YC for her continual support.
Seng W. Loke
1Introduction
For the Stoics, living in accordance with nature required a knowledge of nature and its operations. One reason for this was that the study of nature was thought to offer the best way of establishing what lay within one's own power, and what in the power of nature.
— Peter Harrison, The Territories of Science and Religion
1.1 The New Quantum Age and the Second Quantum Revolution
Andrew Whitaker's book The New Quantum Age: From Bell's Theorem to Quantum Computation and Teleportation speaks of the First Quantum Age marked by the pioneers of quantum theory (or quantum mechanics), such as the physicists Max Planck, Albert Einstein, Niels Bohr, and others, in the first quarter of the 20th century, and the New Quantum Age ushered in by the work of the physicist John Stewart Bell in the 1960s and others, some later winning the Nobel Prize in Physics, in the area of quantum information science (a term we will come back to later).
The 2022 Nobel Prize in Physics went to three outstanding physicists, Alain Aspect, John F. Clauser, and Anton Zeilinger, for “experiments with entangled photons, establishing the violation of Bell inequalities and pioneering quantum information science.”1 Some readers might already be familiar with the many ideas and concepts mentioned in that one sentence, but some not so – we will in this book unpack some of the above concepts such as “entanglement,” “quantum information,” and “Bell inequalities” (and the associated concepts of “Bell pairs” and “Bell states,” named after John Bell mentioned above). Some of the experiments conducted by the Nobel prize winners investigated and demonstrated a key concept in quantum mechanics called entanglement, a term due to physicist Erwin Schrödinger in 19352 – informally, a type of “quantum link.”3 One could also think of such entanglement between particles (e.g. photons of light) as a type of “resource” that will enable the transfer of quantum information over geographical distances (a phenomenon called quantum teleportation). We will see that such a resource is central to distributed quantum computing and is a key concept in quantum networks.
As mentioned in the document on the scientific contributions of the 2022 Nobel Prize in Physics:
This year's Nobel prize is for experimental work. Apart from the disparities in philosophical interpretation, the early Bell experiments drove the development of what is often referred to as the ‘Second Quantum Revolution’. Two of this year's laureates, John Clauser and Alain Aspect, are honoured for work that initiated a new era, opening the eyes of the physics community to the importance of entanglement, and providing techniques for creating, processing and measuring Bell pairs in ever more complex and mind‐boggling scenarios. The experimental work of the third Laureate, Anton Zeilinger, stands out for its innovative use of entanglement and Bell pairs, both in curiosity driven fundamental research and in applications such as quantum cryptography. [https://www.nobelprize.org/uploads/2022/10/advanced-physicsprize2022.pdf, p. 15, accessed: 7/10/2022]
The Nobel Prize also recognized Anton Zeilinger's work on entanglement swapping and multipartite entanglement, concepts which we will discuss later in the book.
Since the early experimental work by the Nobel prize winners dating back to the early 1970s and 1980s, much has happened in the areas of experimental demonstrations of quantum entanglement (over larger geographical scales) and quantum teleportation, quantum cryptographic protocols, quantum communications, quantum networking, quantum computing, quantum distributed computing, as well as quantum information theory. For example, in 1984, Charles Bennett and Gilles Brassard came up with the first quantum key distribution (QKD) protocol, a secure way to share keys used for encryption and decryption, called BB84,4 which was later demonstrated experimentally in 1989 [Bennett et al., [1992]]. A brief history of quantum cryptography is given by Brassard [[2005]]. In 1991, Artur Ekert came up with the E91 protocol for QKD [Ekert, [1991]]. We will come back to the topic of QKD later in the book. Further experimental demonstrations were then conducted over the years. In the early 2000s, ID Quantique5 became one of the first companies to bring a QKD product to the commercial market. Going beyond just two nodes, the world's first quantum network became operational between 2004 and 2007, demonstrating QKD, i.e. the DARPA Quantum Network.6 Today, a Quantum Network architecture standard is being developed with the creation of the Quantum Internet Research Group (an Internet Research Task Force [IRTF]).7 Recent work has continued to conceptualize and develop architectures and applications of the quantum Internet, as reviewed in Gyongyosi and Imre [[2022]], Illiano et al. [[2022]], Wehner et al. [[2018]], and Rohde [[2021]]. Quantum‐enabled 6G wireless networking has been discussed in Wang and Rahman [[2022]]. We discuss quantum networking and the quantum Internet further in Chapter 6.
At the same time, developments in quantum computing have progressed with (i) important work in the 1980s and 1990s, e.g. with the foundational thinking of Deutsch [[1985]] and the invention of quantum algorithms for factoring numbers by Shor [[1994], [1999]] and for quantum search by Grover [[1996]] and (ii) many other developments in the more recent decades, including in the areas of quantum computing applications such as quantum simulation [Smith et al., [2019]] and quantum machine learning [Biamonte et al., [2017]; Ramezani et al., [2020]; Schuld and Petruccione, [2021]]. Several companies (big tech and startups)8 and a number of universities have built quantum computers or are experimenting with quantum hardware concepts,9 research continues into building even larger scale quantum computers, and developing tools and software for programming quantum computers toward full quantum computer systems [Ding and Chong, [2020]] for at least, what John Preskill has called, Noisy Intermediate‐Scale Quantum (NISQ) computers [Preskill, [2018]].10 Also emerged is what has been called quantum software engineering [Piattini and Murillo, [2022]; De Stefano et al., [2022]; Ali et al., [2022]], concerned with processes, tools, and methodologies for developing software that runs on quantum computer systems. A number of companies are also providing access to quantum computers via a cloud service model.11 Government investments into quantum computing and networking have increased in many countries.12
Hence, one can see the increasing developments at the intersection of Information and Communication Technologies (ICT) and quantum theory, yielding quantum information science, which can be described as
an emerging field with the potential to cause revolutionary advances in fields of science and engineering involving computation, communication, precision measurement, and fundamental quantum science. [https://www.nsf.gov/pubs/2000/nsf00101/nsf00101.htm, accessed: 8/10/2022]
And more recently, research into quantum software development, from the information technology or computing perspective.
1.2 Distributed Quantum Computing and the Rise of Quantum Internet Computing
We have been in the Internet or Web Age for some decades now since the early days of the Web in the 1990s and the invention of email even earlier. With networked computers (wired or wireless) around the world, and computers being pervasive, we then have the field of distributed computing, looking into computations (and communication protocols) over distributed networked or connected nodes, and the Internet of Things, which is concerned with all sorts of things (including everyday objects with embedded computers), people and places, becoming connected to the Internet. Distributed computing might be over computers (or nodes) within the same room, or the same geographical area, or might utilize nodes geographically far apart but connected over the Internet. The latter involves a number of issues perhaps not as apparent or on the same scale as when the nodes are local, such as increased latency in communications, fault tolerance, heterogeneity, and scalability. Distributed computing can go beyond geographically local nodes and involve nodes distributed over vast geographical (Internet size) scales (perhaps even interplanetary in the future!), and hence, the often used term Internet computing in such cases.
1.2.1 Distributed Quantum Computing
While work on distributed computing (including mobile and pervasive computing) in the recent decades have been mostly on classical (one might call traditional) distributed computing, there has been a lot of thinking since the 1990s about how quantum mechanics might have an impact on distributed computing.
Lov Grover proposed the idea of computations with distributed quantum processors [Grover, [1997]], which he called quantum telecomputation, with respect to the problem of finding the average of real numbers to a given precision, where each node has one or more pieces of the data.
Others studied the communication complexity of quantum distributed system protocols, where some computation is to be computed by two or more parties which need to send messages to each other, including how having entanglement between nodes might help reduce the communications required between the nodes, compared with classical versions of the distributed system protocols, and how entanglement might make possible some distributed computations not possible classically, e.g. the work by Buhrman and Röhrig [[2003]], Buhrman et al. [[2010]], Broadbent and Tapp [[2008]], and Cleve and Buhrman [[1997]] – such work has been called distributed quantum computing, dating back to late 1990s and early 2000s. Cirac et al. [[1999]] studied considerations of noisy channels on distributed quantum computations.
At around the same time, there has been work on non‐local quantum gates (viewing quantum gates as the quantum analogue of digital logic gates), where quantum computations are distributed over two or more nodes [Yimsiriwattana and Lomonaco, [2005]; Eisert et al., [2000]], including a distributed version of Shor's algorithm mentioned earlier [Yimsiriwattana and Lomonaco, [2004]], also called distributed quantum computing.
Since then, more recent work on what might be considered as “(classical) distributed computing inspired” distributed quantum computing have taken place, e.g. the work by Parekh et al. [[2021]], Sundaram et al. [[2022]], Denchev and Pandurangan [[2008]], Andrés‐Martínez and Heunen [[2019]], and Häner et al. [[2021]], many of which involve work on distributing quantum computations (represented as quantum circuits, analogous to digital circuits) over multiple nodes.
Indeed, apart from theoretical studies into quantum communication complexity, a key motivation for distributed quantum computing is the ability to utilize multiple quantum computers for a given application:
By connecting a network of limited capacity quantum computers via classical and quantum channels, a group of small quantum computers can simulate a quantum computer with a large number of qubits. This approach is useful for the development of quantum computers because the earliest useful quantum computers will most likely hold only a small number of qubits. [Yimsiriwattana and Lomonaco, [2005], p. 131]
Of course, what “small” meant at that time might be different today, or in the NISQ era.
For a collection of quantum computers to collaboratively perform computations, the computers might not just exchange classical information but also quantum information. Connecting multiple quantum computers together to perform computations is non‐trivial and requires not just classical communication (via classical channels) between these computers but also quantum communication (via quantum channels) between these computers so that quantum information can be transferred between these computers, not just classical information. In particular, we will see that two (or more) computers can use shared entanglement in order to exchange quantum information. An excellent depiction of such a connected set of quantum computers (or one might say quantum processing units (QPUs) perhaps analogous to GPUs) is given in DiAdamo et al. [[2021]] and redrawn slightly differently in Figure 1.1. One can observe that both types of networks, classical and quantum, are required and when the computers are connected not just via a local network but the Internet, the classical network becomes the classical Internet and the quantum network becomes the quantum Internet. Also needed is a way to manage the programs that will run across multiple computers, such as scheduling the (sub)programs on each computer, managing the program execution and communications, and coordinating and combining the results and so on, i.e. some sort of controller is required though decentralized controllers are also discussed in DiAdamo et al. [[2021]]. There would be greater complexity if resources (e.g. QPUs, entanglement generation, and network access) are shared by multiple programs and clients wanting to execute their programs.
Figure 1.1 An illustration of a distributed quantum computer with multiple quantum computers (or quantum processing units, or QPUs) connected using quantum channels (i.e. via entanglement) and classical channels, so that both quantum and classical information can be communicated. The controller manages the execution of computations, classical and quantum parts, across the computers (QPUs).
Source: Adapted from the diagram by DiAdamo et al. [[2021]].
We note that there has also been work on the quantum parallel RAM model, analogous to the classical parallel RAM model for representing parallel and distributed computations [Beals et al., [2013]], and work on quantum arithmetic algorithms running on a distributed quantum computer (called a quantum multicomputer) in Van Meter et al. [[2008]]. Based on the measurement‐based model of quantum computing by Raussendorf et al. [[2003]], a model for distributed measurement‐based quantum computations has been developed [Danos et al., [2007]]. A formal model for reasoning about distributed quantum computing has been developed by Ying and Feng [[2009]]. Interestingly, the quantum Message Passing Interface [Häner et al., [2021]] provides an Application Programming Interface (API) for distributed quantum computing, analogous to the Message Passing Interface (MPI) developed as a standardized API for (classical) distributed computing [Nielsen, [2016]]; by writing programs using such a standardized API, such programs become portable, and can, by and large, be independent of the underlying computer architecture or specific implementations.
There have also been studies on “quantum versions” of classical distributed computing protocols, though fundamentally, these are quite different from the classical analogues since quantum entanglement is employed, including quantum oblivious transfer, QKD, quantum coin flipping, quantum electronic voting, quantum leader election, quantum anonymous broadcasting, quantum secret sharing, and quantum Byzantine Generals.13 We will look at some of these protocols later in the book.
Hence, drawing inspiration partly from the decades of work in (classical) distributed computing and other innovations, developments have emerged in distributed quantum computing, including new concepts, models, abstractions, protocols, tools and software. We have not provided a comprehensive account of distributed quantum computing here, but a brief overview, and we will come back to many of the topics above in the rest of the book. A recent survey on distributed quantum computing is by Caleffi et al. [[2022]].
1.2.2 Quantum Internet Computing
With developments in the coming decades in quantum networking (and the quantum Internet), quantum computing hardware and software, and distributed quantum computing, we can conceptualise quantum Internet computing, analogous to (classical) Internet computing mentioned above, referring to distributed quantum computing over the emerging quantum Internet, potentially over vast geographical distances, or roughly put:
Inspired by Cuomo et al. [[2020]] who noted that the quantum Internet will become the “underlying infrastructure of the Distributed Quantum Computing ecosystem,” Figure 1.2 illustrates a layered conceptualization of the idea of distributed quantum computing over the quantum Internet, where
the Distributed Quantum Computing Layer contains the
the Distributed Quantum Computing Applications sublayer, which comprises the end‐user applications built using the tools and abstractions from the Distributed Quantum Computing Tools, Abstractions, Libraries, Environment layer, and
the Distributed Quantum Computing Tools, Abstractions, Libraries, Environment sublayer, which provides a range of tools and abstractions, and environments for executing and managing programs.
the Networking Layer realizes quantum networking services used by the programs at the Distributed Quantum Computing Layer, supported by the classical Internet, including preparation of quantum entanglement and transmission of qubits; at least for the foreseeable future, the quantum Internet is expected to coexist with the classical Internet.
Figure 1.2 A simple architecture of quantum Internet computing: distributed quantum computing over the quantum Internet.
Later in the book, we will come back to discussing this architecture in further detail, but here, it suffices to convey the idea of quantum Internet computing.
1.3 Aim and Scope of the Book
As mentioned, Internet computing, where one does distributed computing but over Internet scale distances and distributed systems involve nodes connected via the Internet, is at the intersection of work in (classical) distributed computing and the (classical) Internet. By an analogy to Internet computing, one could ask the question of what would be at the intersection of distributed quantum computing and the quantum Internet. This book provides an introductory overview of selected topics in distributed quantum computing and the quantum Internet, and then attempts to answer this question, proposing the notion of quantum Internet computing, a proposed “umbrella paradigm” for a collection of topics (listed below), from an analogy to (classical) Internet computing:
distributed quantum computing, including theoretical studies of quantum protocols which are often quantum versions of classical quantum distributed computing protocols, and perspectives on communication complexity including gains from the use of entanglement,
distributed quantum computing using non‐local (or distributed) quantum gates and circuits, where we focus on how large quantum computation represented by a quantum circuit can be distributed over multiple nodes,
delegating quantum computations to a server, including delegating in such a way that the server has limited or no knowledge of the computations for the purposes of privacy of the client (who is delegating the computations to the server) or sometimes called
blind quantum computing
, and verifying delegated quantum computations so that the client is assured that the server did do the required computations; delegating quantum computations (on a pay‐per‐use basis) might come under what has been called
quantum cloud computing
given the cloud model of providing computing‐as‐a‐service (typically, in classical cloud computing, including software, computer servers, memory and so on, provided on a pay‐as‐you‐use service over the Internet), and
quantum Internet, where we introduce the concept, key ideas such as quantum entanglement distillation, and entanglement swapping, and possible architectures.
With respect to Figure 1.2, the first three topics might be considered as falling within the Distributed Quantum Computing Layer, while the last topic, clearly, is in the Networking layer. In a way, “quantum Internet computing” is yet another label, but the label aims to (i) capture the scale of distributed quantum computing envisioned, and the associated challenges with that, as well as (ii) attempts to “bundle” the topics above with the issues they address, at least for the purposes of this book. There are a number of topics mentioned in Section 1.2.1, which we do not cover in detail in this book – some are covered in the books we will mention later in Section 1.5 and others are perhaps left to other books to come! The range of topics under quantum Internet computing may yet grow and evolve in the coming years.
1.4 Outline of this Book
The rest of this book is organized as follows.
Chapter 2
discusses the mathematical and quantum computing background required for the rest of the book, including a brief introduction to quantum computing and related concepts, including qubit and qubit states, measurement, quantum gates and circuits, entanglement, and teleportation.
Chapter 3
