## Course Specific Stuff

This course uses two sets of notes. There are my own notes (RHB.notes below) for the first part of the course, and the second part of the course will be based on the latter part of Abbas Edalat's excellent notes (AE.notes below), used with the kind permission of Imperial College. Specifically, the course is defined by all of RHB.notes, together with slides 69-123 from AE.notes. The exercises also form an essential part of the course (of course). Although the rest of AE.notes is not officially part of the course, it is very appropriate supplementary reading and you might find it gives you a useful alternative view on some issues. Check out also the supplementary notes on linear algebra provided below.Notes:RHB.notes.ps.gz RHB.notes.pdf AE.notes.ps.gz AE.notes.pdfExercises:Exercises1.ps Exercises1.pdf Exercises2.ps Exercises2.pdf Exercises3.ps Exercises3.pdf Exercises4.ps Exercises4.pdf Exercises5.ps Exercises5.pdfPast Papers:Past Papers (.pdf)Linear Algebra:The linear algebra part of the course is pretty terse, and Computer Science students in particular may appreciate a less frantic treatment. Here are some supplementary notes that cover some of the manipulations most commonly found in quantum computing, and a quick reference sheet of concepts and formulae. Lin.Alg.Suppl.Notes.ps Lin.Alg.Suppl.Notes.pdf Lin.Alg.Quick.Ref.ps Lin.Alg.Quick.Ref.pdf If you type 'linear algebra' into Amazon, you get more than 1300 references. I got bored after about 300. Of these, I've listed some of the more promising below. N.B. There is the unavoidable question of which argument of the inner product is linear and which is conjugate linear; call the two possibilities the Maths convention and the Physics convention.Maths: linear in first argument, conjugate linear in second argument. Physics: conjugate linear in first argument, linear in second argument.Most of the 'purely linear algebra' books below, being primarily for mathematicians, use the Maths convention, though all the quantum computing literature and thus also COMP30222 uses the Physics convention. Of late however there is an increasing supply of physics and quantum computing books that do linear algebra in a manner suitable for COMP30222 revision. By and large these now take precedence over the 'purely linear algebra' books because they deal with the more specialised concepts like functions of operators and (especially) tensor products, which the 'purely linear algebra' books tend not to do. Griffiths R. Consistent Quantum Theory Cambridge University Press; ISBN: 021539293 (2002)Physics convention(No there's no mistake, this book really does belong here. Chapter 3 on linear algebra and Chapter 6 on tensor products are fairly brief, but so close to the treatment in RHB.notes that it's creepy. Definitely the first port of call for supplementary reading on linear algebra. No worked examples or exercises though.) Benenti G., Casati G., Strini G. Principles of Quantum Computation and Information Volume I: Basic Concepts World Scientific Publishing; ISBN: 9812388583 (2004)Physics convention(Contains a perfectly reasonable survey of linear algebra concepts from the quantum computing point of view. Neck and neck with Griffiths. Like Griffiths, no worked examples or exercises.) Steeb W-H., Hardy Y. Problems and Solutions in Quantum Computing and Quantum Information World Scientific Publishing; ISBN: 9812387900 (2004)Physics convention(Contains lots of worked examples of advanced quantum physics concepts. Some reasonable coverage of the more advanced linear algebra concepts for quantum computing; but you have to dig to find them.) Anton H. Elementary Linear Algebra John Wiley & Sons Inc.; ISBN: 0471230928 (2001) (also Anton H., Rorres C.; Elementary Linear Algebra with Applications John Wiley & Sons Inc.; ISBN: 0471170526 (2000))Maths convention(Chapter 10 gives a nice overview of complex numbers and complex inner product spaces. Lots of examples etc. Not too longwinded, not too terse. Recommended if you need a gentle coverage of the basics.) Kaye R., Wilson R. Linear Algebra Oxford University Press; ISBN: 0198502370 (1998)Physics convention(A maths book (definitely a maths book) that uses the Physics convention! Startling in itself. Also surprising is the close resemblance to the linear algebra part of COMP30222 which is quite accidental. Recommended.) Fraleigh J., Beauregard, R. Linear Algebra Addison Wesley; ISBN: 0201839997 (1995)Physics convention(Another maths book that uses the Physics convention. Chapter 9 covers complex numbers and the basics of complex linear algebra, while refering back to earlier material done with just the reals. The chapter is somewhat briefer than Anton's Chapter 10, and is not as self contained.) Lipschutz S., Lipson M. Schaum's Outline of Linear Algebra (Schaum's Outlines) Schaum; ISBN: 0071362002 (2001)Maths convention(Ancient warhorse of linear algebra revision. Still going strong after all these years. God only knows which edition/reprinting it's in now.) Lay D. Linear Algebra and Its Applications Addison Wesley; ISBN: 0201709708 (2002)Maths convention(It hardly matters that it uses the Maths convention since there seems to be no trace ofcomplexvector spaces. If you're desperate and can't find any of the preceding books, it might be worth a look provided you keep a mental note of where complex conjugations are required yourself. (But if you're confident about that, would you be looking here?? :-/) Lots of pretty pictures, colour diagrams, biographical details, and other distractions.) Strang G. Introduction to Linear Algebra (6th ed.) Wellesley-Cambridge; ISBN: 9781733146678 (2023) (Very 'in your face' treatment of matrix mathematics. Gets to the essentials of what is needed for many modern applications without wasting words. Focused on the real theory, so not much complex material included, but what there is uses thePhysics convention. Very readable and very immediate. I rather like it. Evolved from the older book below.) Strang G. Linear Algebra and Its Applications Thomson Learning; ISBN: 0030105676 (2006) (Unreconstituted headbanging matrix mathematics, now in its fourth edition, and suitably 'friendliness-enhanced' to cater for today's more demanding tastes. Definitely for the determined, but it's the only 'purely linear algebra' book in this bunch that mentions the exponential of a matrix. I'm confident it uses thePhysics conventionthough you have to look hard to find the actualdefinitionof the complex inner product.)Course Texts and Similar:Yanofsky N., Mannucci M. Quantum Computing for Computer Scientists Cambridge University Press; ISBN: 0521879965 (2008) (A book that says it's written for computer science students, and means it. Very careful and gently paced intro to the basic machinery in the first couple of chapters. Then it covers (almost all of) the COMP30222 syllabus with equal tenderness up to chapter 6. Most of the rest is not needed for COMP30222, though teleportation is done near the end. Definitely recommended for computer scientists. Others may well enjoy it too, if they prefer a gentler, minimalist approach to the subject. If you want the real deal on quantum computing then you have to read Nielsen and Chuang, but this one will do for the COMP30222 exam. Cherry-picked literature guide in Appendix A.) Benenti G., Casati G., Rossini, D., Strini G. Principles of Quantum Computation and Information A Comprehensive Textbook World Scientific Publishing; ISBN: 9789813237223 (2019) (A particularly nice combination of, on the one one hand, a fairly gentle and readable approach, with, comprehensive coverage of both intoductory material and advanced material including stuff too recent for any other text (e.g. Nielsen and Chuang), all covered in as accessible a manner as the material permits. The coverage of the COMP30222 syllabus is not always exactly as in the notes, but it's nevertheless an extremely good treatement. It supersedes the predecessor two volume edition (Vol I, ISBN: 9812388583, Vol II, ISBN: 9812565280), of which Vol I is still good for COMP30222.) Nielsen M., Chuang I. Quantum Computation and Quantum Information Cambridge University Press; ISBN: 0521635039 (2000) (This remarkable volume set the standard for books about quantum computing, and immediately became the de facto set text for any decent course on the subject. It strives valiantly to not be a physics book for six chapters and pretty much succeeds. After that it's a physics book. For COMP30222, the part you need is those first six chapters, which cover all the course material and some more.) Mermin N.D. Quantum Computer Science Cambridge University Press; ISBN: 9780521876582 (2007) (Written by the 'M' of the GHZ argument in RHB.notes, it features a unique operator-led approach to the subject quite unlike the mainstream account. The clearest treatment of error correction that I've seen. A small number of bugs in the latter parts do not detract from the fact that this is a thoroughly mind-expanding read. Recommended.) Rieffel E., Polak W. Quantum Computing: A Gentle Introduction MIT Press; ISBN: 0262015064 (2011) (Written by non-physicists for non-physicists, the book covers all the basic stuff pretty thoroughly. A pity it uses non-standard notation for quantum circuit diagrams though. It goes into fair technical detail about a number of more advanced topics, and, given its relatively recent vintage, has a brief, up to date survey of more recent advances. I don't see what's especially "gentle" about all of that.) Kaye P., Laflamme R., Mosca M. An Introduction to Quantum Computing Oxford University Press; ISBN: 019857049X (2006) (Starts off in a rush, skimping a bit on the introductory topics. Shame, because with another 20 or so pages, distributed where needed in the first four chapters, it would have made an ideal course text. Much material presented well: e.g. it's the only book that reallyexplainswhat needs to be explained about the quantum Fourier tansform. Some typos here and there, some latter parts rather terse; but a real shame about those 20pp.) Lo H-K., Spiller T. Introduction to Quantum Computation and Information World Scientific Publishing; ISBN: 981024410X (1998) (Despite its age(!) it still gives decent approachable accounts of many aspects of quantum computing.) Gruska J. Quantum Computing Osborne McGraw-Hill; ISBN: 0077095030 (1999) (Eclipsed by Nielsen and Chuang's book almost immediately after publication, it betrays its roots as a review article that got out of hand. Generally not bad, there's some unevenness of treatment, appearance, language. But it's still the text of choice for some aspects that Nielsen and Chuang neglect.) Hirvensalo M. Quantum Computing (2nd ed.) Springer-Verlag Berlin; ISBN: 3540407049 (2003) (Short, fairly mathematical book on the main aspects of quantum computing, written by a PhD student at Turku(!). Not bad if you're mathematically inclined. If you look at this one, make sure it's the second edition, in which the introductory chapters have been improved.) Pittenger A. An Introduction to Quantum Computing Algorithms Birkhauser Verlag AG; ISBN: 0817641270 (1999) (Another short book on the main aspects of quantum computing. Slightly less mathematical than Hirvensalo.) Griffiths R. Consistent Quantum Theory Cambridge University Press; ISBN: 021539293 (2002) (A book on quantum theory very much in the spirit of COMP30222, though the material relevant to COMP30222 (say the first nine chapters) isn't covered in the same order, and those nine chapters cover other material too. Concentrates on fundamental concepts and toy models, and avoids heavy duty physics calculations. Contains much material on the consistent histories approach to quantum paradoxes and dilemmas. No exercises etc. so it's not really a textbook, but gives great insight into the wierd aspects of quantum theory. Also good for its COMP30222-like treatment of linear algebra.) Styer D. The Strange World of Quantum Mechanics Cambridge University Press; ISBN: 0521667801 (2000) (Gentle introduction to the principal ideas of quantum mechanics. Almost coffee table reading, but written with care, so no bullshit.) Isham C. Lectures on Quantum Theory: Mathematical and Structural Foundations Imperial College Press (World Scientific); ISBN: 1860940013 (1995) (Solid treatment of foundational issues of quantum mechanics at advanced undergraduate level. Tends to rely a bit on preexisting physics knowledge, but not excessively so.) Berman K., Paul J. Algorithms: Sequential, Parallel, and Distributed Thomson Course Technology; ISBN: 0534420575 (2004) (A nice, modern, thorough, and pedagogic account of algorithms. Analysis of algorithms is in Chapter 3, if that's what you need.) Brassard G., Bratley P. Fundamentals of Algorithmics Prentice-Hall; ISBN: 0133350681 (1996) (Quite good but quite verbose treatment of algorithmic issues. Chapter 4 on analysis of algorithms is the key one for those lacking computing experience.) Hardy Y., Steeb W.-H. Classical and Quantum Computing with C++ and Java Simulations Birkhauser Verlag AG; ISBN: 3764366109 (2001) (Not a course text, but of the same ilk. A somewhat strange book, featuring descriptions of all sorts of computing paradigms, with lots of sample C++ and Java code bulking it out. The last 200pp. are a relatively terse but competent summary of quantum computing, along with the requisite results in linear algebra.) Steeb W-H., Hardy Y. Problems and Solutions in Quantum Computing and Quantum Information World Scientific Publishing; ISBN: 9812567402 (2006) (Absolute goldmine for the lazy quantum physicist! Here you will find lots of worked out calculations about all sorts of advanced quantum models, both central and peripheral to the quantum computing enterprise. Loads of stuff that the advanced texts and research papers just leave you to do for yourself. Great! A proportion of this is relevant to COMP30222, but it's buried in a much larger quantity of much more advanced stuff, so you have dig quite a bit to find it. Bring a shovel. Like the previous book, the authors are unable to resist including a (mercifully small) amount of C++ code. Why in heaven's name? Endearingly egocentric book selection in the bibliography.) Marinescu D., Marinescu G. Approaching Quantum Computing Prentice Hall; ISBN: 013145224X (2004) (Intended as an introductory text, the writing style is however rather too uncontrolled to rely on as sole main reference. Still, the calculations relating to many specific course topics are treated in a lot of detail, so worth dipping into for backup info.) Bez H., Croft T. Quantum Computation CRC Press; ISBN: 1032206489 (2023) (Very gentle and detailed coverage of the required mathematics. The actual quantum computation part doesn't cover Grover or Shor.)## Background reading

These days books and articles on quantum computing are coming out seemingly as if out of a firehose. Essentially none are exactly at the level of COMP30222, basically because COMP30222 treads a carefully navigated path between the most elementary results and more advanced material. (And this mismatch is is even largely true of the course texts.) So the following selection from among stuff worth looking at beyond the course reading list, falls into two camps. The coffee table stuff is wide ranging, not too technical, and certainly not detailed enough on the COMP30222 syllabus topics to get you through the COMP30222 exam. The advanced stuff invariably assumes more than covered in COMP30222. At the very least you have to learn to love density matrices. Nevertheless it may also not be detailed enough on the COMP30222 syllabus topics to get you through the COMP30222 exam because of different emphasis. Then there's the online stuff ...Coffee Table and Introductory Reading:Bernhardt C. Quantum Computing for Everyone MIT Press; ISBN: 9780262039253 (2019) (Written by a mathematician motivated to learn about this topic, it is a nice and careful introduction to many of the main ideas in the subject. ) Siegfried T. The Bit and the Pendulum John Wiley & Sons Inc; ISBN: 0471399744 (2001) (Can you believe that title? Chapters like 'Beam up the Goulash' ... and it uses the word 'klutz'. A very American, informal, entertaining, (and for all that, surprisingly cogent) excursion into the role of information in physics and other sciences today, by a well informed science journalist. It's also where I found the Gell-Mann quote. :-) Williams C., Clearwater S. Ultimate Zero and One Springer-Verlag New York Inc.; ISBN: 0387947698 (1999) (An informal account of quantum computing. Not perfect but not at all bad.) Berman G., Doolen G., Mainieri R., Tsifrinovich V. Introduction to Quantum Computers World Scientific Publishing; ISBN: 9810235496 (1998) (Many authors make patchy coverage. Veers between very elementary and fairly detailed. Some nice accessible calculations of experimental phenomena in the later chapters.) Le Bellac M. A Short Introduction to Quantum Information and Quantum Computation Cambridge University Press; ISBN: 0521860563 (2006) (It assumes you're a physicist and already know a reasonable amount about optics and quantum theory, despite trying not to rely on this too much. Not recommeded if you're a quantum computing novice, as there are too many potential red herrings in the writing.) Imre S., Balazs F. Quantum Computing and Communications: An Engineering Approach John Wiley & Sons Inc; ISBN: 047086902X (2005) (The usual quantum computing topics, flavoured with a notably East-European style of English and humour. Add an unconventional layout for matrix calculations, and it starts to get a bit unhelpful. Little to do with engineering.) Darling D. Teleportation: The Impossible Leap John Wiley & Sons Inc; ISBN: 0471470953 (2005) (Chapters 1-9 are a nicely written informal account of the physics relevant to modern teleportation. The remaining bits are pure SF froth.) [N.B. These days (2020 onwards let's say), a huge number of 'popular' and 'semi-popular' books about Quantum Computing, written by non-physicists, have been published. The ones I've seen are basically garbage, or close to garbage. Best Avoided.]Advanced:Vidick T., Wehner S. Introduction to Quantum Cryptography Cambridge U.P.; ISBN: 9781316515655 (2024) (An excellent book about quantum cryptography, which is, perhaps the most practical area of the quantum computing and communication world. It's serious about both the quantum theory, which goes well beyond this course, and about the cryptography, which is done properly.) Garcia Ripoll, J. Quantum Information and Quantum Optics with Superconducting Circuits Cambridge University Press; ISBN: 9781107172913 (2022) (An excellent book on the experimental physics that underpins one of the most prominent approaches to quantum computing technology today. It treads a well judged line between the necessary theory, and the facts in the lab, and discusses the experimental world in enough detail to show its ups and downs. Includes a very decent teatment of the D-Wave approach.) Fabre C. Quantum Processes and Measurement: Theory and Experiment Cambridge University Press; ISBN: 9781108477772 (2023) (A survey of up to date experimental techniques and the theory behind them. However, it's a book that summarises rather than expounds. So the theory jumps between the main account, appendices (which occupy a third of the book) and external references. Easiest to read if you already know most of the underlying physics.) Bruss D., Leuchs G. Lectures on Quantum Information Wiley-VCH; ISBN: 3527405275 (2006) (Lectures, from a large number of presenters at a 2000 summer school, written up, extended, and brought up to date; so the style from chapter to chapter is a bit variable. Despite this, it gives the broadest coverage of 'beyond basic textbook' material that I have seen in a single book, and gives a very thorough impression of the state of the art at the time of publication.) Stolze J., Suter D. Quantum Computing: A Short Course from Theory to Experiment Wiley-VCH; ISBN: 3527404384 (2004) (Leans a little bit too heavily towards physics generally and experimental physics in particular to make it as a course text. Pity. Then again it suffers from the wrong-blob problem. Despite this it's quite a nice account. Experimental physicists will get a nice warm feeling; others can enjoy it too if they just take the experimental stuff at face value and go along for the ride. The only textbook with a more than cursory account of the IBM 15 factorisation.) Nakahara M., Ohmi T. Quantum Computing: From Linear Algebra to Physical Realizations Taylor & Francis; ISBN: 0750309830 (2008) (A workmanlike account of all the basic material, moving on to a number of more advanced topics. A slightly non-standard treatment (from the COMP30222 perspective) of the Shor factorization, is balanced by a careful account of the arithmetic circuit required, (the part that most others discuss superficially). The second half of the book gives the most detailed textbook account of the standard experimental approaches that I've seen.) Audretsch J. Entangled Systems: New Directions in Quantum Physics Wiley-VCH; ISBN: 3527406840 (2007) (A quite gently paced account of all things to do with entanglement. The unhurried pace extends to a considerably less rushed treatment of POVMs (and related topics) than is usually found in textbooks.) Barnett S. Quantum Information Oxford University Press; ISBN: 0198527632 (2009) (Although a bit skimpy on mathematical detail in places (with several topics relegated to the appendices), this is basically a pretty solid treatment of topics connected with quantum informatiom. Well worth a look.) Bouwmeester D., Ekert A., Zeilinger A. (eds.) The Physics of Quantum Information Springer-Verlag Berlin; ISBN: 3540667784 (2000) (Quite readable if non-elementary accounts of a selection of relevant topics.) Alber G., Beth T., Horodecki M., Horodecki P., Horodecki R., Rotteler M., Weinfurter H., Werner R., Zeilinger A. Quantum Information Springer-Verlag Berlin; ISBN: 3540416668 (2001) (Not for the faint hearted. As expensive in its material incarnation as its author list is long. Contents freely downloadable (at this university).) Heiss D. (ed.) Fundamentals of Quantum Information: Quantum Computation, Communication, Decoherence and All That Springer-Verlag Berlin; ISBN: 3540433678 (2002) (Intended for a sophisticated physics audience. Contains a broad range of articles, including surveys of a range of experimental investigations.) Kitaev A., Shen A., Vyalyi M. Classical and Quantum Computation American Mathematical Society; ISBN: 0821832298 (2002) (Excellent leading edge treatment of quantum computing. Advanced and mathematical, it casually assumes familiarity with many a nontrivial topic, e.g. Lie groups, cohomology. Focuses on complexity issues from an up to date perspective. And it's terse, very terse. Many key topics, e.g. the halting problem, universal properties of tensor products, Fourier transforms, quantum teleportation, are relegated to exercises, though with solutions provided. Very good if you can take the pace. Very, very terse.) Jaeger G. Quantum Information: An Overview Springer; ISBN: 0387357254 (2006) (The 'Overview' in the title is right. The author mentions a large number of topics in the quantum information/computing field in a relatively small space (albeit with a noticeable bias towards quantum optics on the experimental side). Hence 'mentions' rather than 'discusses in depth'. Good bibliography.) Vedral V. Introduction to Quantum Information Science Oxford University Press; ISBN: 0199215707 (2006) (Spuriously opinionated, somewhat buggy and mathematically sloppy, this is a rather disorganised treatment of a broad and interesting range of topics, marred by poor execution. Pity. Read Benenti et al. Vols II and I, or Nielsen and Chuang, or Alber et al., or Jaeger, or Bruss and Leuchs, or especially Barnett, instead.) Lomonaco S. (ed.) Quantum Computation American Mathematical Society; ISBN: 0821820842 (2002) (Hastily thrown together proceedings of an AMS Short Course that took place in 2000. Much flippant writing, and many interesting topics touched on but not presented properly. Many careless bugs. Some good bits, but you have to be able to tell them apart from the ... less good bits. Beautifully embossed hard cover.) Brylinski R., Chen G. (eds.) Mathematics of Quantum Computation CRC Press; ISBN: 1584882824 (2002) (Rather mixed bag of papers on various aspects of quantum computing, but no Shor's algorithm! Many of the papers give a more pure-mathematical treatment than usual, centred around algebraic geometry techniques. Not an easy read for people who are not algebraic geometers.) Stenholm S., Suominen K-A. Quantum Approach to Informatics John Wiley & Sons Inc; ISBN: 0471736104 (2005) (Don't be fooled by the title, it's a physics book! An interesting choice of topics at the physics end of the subject is sadly marred by writing that is too often unclear. The authors know their stuff, but don't explain it well for the novice.) Meglicki Z. Quantum Computing Without Magic: Devices MIT Press; ISBN: 026213506X (2008) (Could have been called "Quantum Theory isn't very Quantum Really". After an enticing Preface, the text gets rather lost in a lot of low level detail and chatty asides, and the attempts to motivate quantum structure via essentially non-quantum means don't seem to persuade as well as the reader had been seduced into hoping. An interesting idea that somehow doesn't quite come off.) McMahon D. Quantum Computing Explained John Wiley & Sons Inc; ISBN: 0470096993 (2008) (Really buggy. Lots of typos, small mistakes, slightly misleading text, the odd broken sentence. A real pity, because done properly, it would be right up there as an excellent supplement to any main text due to its wealth of examples worked out in great detail.) Perry R. Quantum Computing from the Ground Up World Scientific; ISBN: 9789814412117 (2012) (Like the book above, a book which could have served a useful purpose by gently leading the reader into the basics via lots of carefully worked out detail. But again, it gets very buggy as soon as you get beyond the most elementary level. Avoid.) Lipton R., Regan K. Quantum Algorithms via Linear Algebra. A Primer MIT press; ISBN: 9780262028394 (2014) (Another 'quantum computing done a different way' book, this one's USP is to leave out the quantum physics. Thus, instead of clearly presenting the relevant facts, they tend to be sneaked in here and there. A similar attitude affects many other aspects. Simple things are slipped in, yet many complex things are plunged into without hesitation. To get anything out of it you have to read it rather more carefully than the authors have written it. It's not what I would call a primer.) Hundt R. Quantum Computing for Programmers Cambridge University Press; ISBN: 9781009098175 (2022) (Unfortunately, most of the explanations here are any of: imprecise, incoherent, incomplete, and thus quite likely to lead the newcomer astray. On the plus side, many very recent topics are discussed, with good contemporary references.) Donohoe J., Sorbi L. A Prelude to Quantum Field Theory Princeton University Press; ISBN: 9780691223483 (2022) (OK, it's pushing it a bit to include a book on Quantum Field Theory here. Almost any self-respecting book on QFT is at least 700pp long (Weinberg, Coleman, Fradkin, Peskin/Schroeder, Schwartz, Kaku, Itzykson/Zuber, Kleinert, Hatfield, Nastase, Baulieu/Iliopoulos/Seneor, the awesome Zinn-Justin, and many others), so getting into it is a non-trivial undertaking. The present authors do a stunning job of bringing the essence of the subject to the reader in a manner as clear and economical as is humanly possible, mainly by kicking the more complicated group theory stuff into the long grass and focusing on scalar theory and tree level. The go-to entry point for the uninitiated. I wish it had been around when I was a grad student.)Online Stuff:Here you can find copies of the articles mentioned in AE.notes and other similar material. Aharonov.ps.gz Ekert.ps.gz Rieffel.ps.gz Steane.ps.gz The above are shadowed here on our site. This link leads to a miscellany of stuff out there on the web.Other StuffAside from quantum computingper se, there is much readable stuff on the physical background and asociated topics. Here are some selected items categorised by topic. For each topic, they are listed in roughly increasing order of muscularity, the later ones being essentially research references.Cryptography:(see also the Info page for COMP61411) Harmin.slides.pdf (A set of slides for a telelecture delivered here by Prof. Harmin from Kentucky, and including a nice overview of RSA and how Shor's algorithm relates to it.) Singh S. The Code Book Fourth Estate; ISBN: 1857028899 (2000) (A popular account of cryptography, and a lot better than most popular accounts of anything.) Stinson D. Cryptography CRC Press; ISBN: 1584885084 (2006) (A very solid account of cryptography techniques.) Bauer F. Decrypted Secrets Springer-Verlag Berlin; ISBN: 3540426744 (2002) (A nice mixture of solid theory, stories, and entertaining anecdotes. More entertaining than was perhaps intended. Some of it reads like a MontyPythonesque excoriation of a book on German cryptography ... except that itISa book on German cryptography :) Look at the stuff on Enigma.) Schneier B. Applied Cryptography John Wiley & Sons Inc; ISBN: 0471117099 (1996) (Encyclopaedic survey of the field from a practical point of view. Commenting on key escrow (in 1996), it contains the chillingly prophetic: 'Imagine a major terrorist attack on New York; what sorts of limits on the police would be thrown aside in the aftermath?') Koblitz N. A Course in Number Theory and Cryptography Springer-Verlag New York; ISBN: 0387942939 (1994) (Does what it says on the tin.) Yan S. An Introduction to Formal Languages and Machine Computation World Scientific Publishing; ISBN: 9810234228 (1997) (Despite its title it contains an extensive account of the number theory used in cryptographic applications.)Approximate and Randomised Algorithms:There aren't any 'elementary' treatments that deal exclusively with these topics. Introductory texts on algorithms sometimes contain a chapter or so on the basic results in this area. The following are all specialised and thoroughgoing. Motwani R., Raghavan P. Randomized Algorithms Cambridge University Press; ISBN: 0521474655 (1995) Ausiello G., Crescenzi P., Gambosi G., Kann V., Marchetti-Spaccamela A., Protasi M. Complexity and Approximation Springer-Verlag Berlin; ISBN: 3540654313 (1999) Vazirani V. Approximation Algorithms Springer-Verlag Berlin; ISBN: 3540653678 (1999) Hromkovic J. Algorithmics for Hard Problems Springer-Verlag Berlin; ISBN: 3540668608 (2000)Optics:Smith F.G., King T. Optics and Photonics: an Introduction John Wiley and Sons Ltd; ISBN: 0471489255 (2000) (Standard introduction, written by experimentalists.) Hecht E. Optics Addison Wesley; ISBN: 0805385665 (2001) (More comprehensive alternative to above.) Born M., Wolf E. Principles of Optics (7th ed.) Cambridge University Press; ISBN: 0521642221 (1999) (Venerable Classic.) Walls D., Milburn G. Quantum Optics Springer-Verlag Berlin; ISBN: 3540588310 (1995) (Quantises the electromagnetic field on p.7 and goes on from there.) Scully M., Zubairy M., Quantum Optics Cambridge University Press; ISBN: 0521435951 (1997) (Even more solid than Walls and Milburn.) Mandel L., Wolf E. Optical Coherence and Quantum Optics Cambridge University Press; ISBN: 0521417112 (1995) (Son of Venerable Classic.) Puri R. Mathematical Methods of Quantum Optics Springer-Verlag Berlin; ISBN: 3540678026 (2000) (Robust treatment of theoretical topics.)Quantum Theory:Rae A. Quantum Mechanics The Institute of Physics; ISBN: 0750308397 (2002) (Up to date introduction.) Griffiths D., Schroeter D. Introduction to Quantum Mechanics (3rd ed.) Cambridge University Press; ISBN: 0521417112 (2018) (Writes down the Schrodinger equation on the first page and never looks back. An excellent pedagogical presentation of wave mechanics, done carefully and including plenty of detail.) Gasiorowicz S. Quantum Physics John Wiley and Sons (WIE); ISBN: 0471857378 (1995), ISBN: 0471429457 (2002) (Standard textbook, now in it's third edition. Following a trend started earlier in engineering texts, it contains*less*material than the second edition ... end of the world as we know it, etc. etc.) Merzbacher E. Quantum Mechanics John Wiley and Sons (WIE); ISBN: 0471887021 (1998) (Considerably more advanced standard text.) Sakurai J., Napolitano J. Modern Quantum Mechanics Cambridge University Press; ISBN: 9781108473224 (2021) (Venerable Classic updated with references to recent experiments and similar. The fussy reader will feel some mathematical details are a bit clumsy, but the physics is totally eloquent.) Schiff, L. Quantum Mechanics McGraw-Hill (1955, 1968) (Venerable Classic from long before ISBNs. A grown up presentation of 20th century QM. Difficult to get hold of nowadays (Dover should do a reprint). It's where I learned the subject. Included here for reasons of nostalgia.) Auletta G, Fortunato M., Parisi G. Quantum Mechanics Cambridge University Press; ISBN: 0521869633 (2009) (Intended as a textbook for a solid grounding in quantum mechanics, it nevertheless (to its great credit) features considerably more engagement with issues of contemporary conceptual interest, such as measurement, entanglement etc., than is usually found in such texts.) Townsend J. A Modern Approach to Quantum Mechanics University Science Books; ISBN: 1891389130 (2000) (Inspired by the legendary Feynman Lectures Vol III, this is the quantum mechanics text nearest in spirit to COMP30222. Perhaps the kind of thing that Feynman might have produced if he had set out to write a textbook, instead of just to enjoy himself.) Ballentine L. Quantum Mechanics: A Modern Development (2nd ed.) World Scientific; ISBN: 9789814578585 (2015) (Avoiding all 'by analogy with classical mechanics' temptations, it takes 100 pages to get to Schrodinger's equation. But by then, you really believe it. As well as a having good selection of the standard applications, the account is underpinned with substantial discussions of foundational topics, and with the dispelling of many established misapprehensions. Excellent, if you can afford the time to devote to it.) Bohm A. Quantum Mechanics Springer Verlag; ISBN: 0387953302 (2001) (Not for beginners, though excellent if you already know quantum mechanics. Thorough and uncompromising. Interestingly idiosyncratic, e.g. the hydrogen atom is done via the Pauli-Bargmann SO(4) technique. Rigged Hilbert space, Gamow vectors, Berry phase ... the works.) The preceding all tell you with varying degrees of thoroughness how to*do*quantum mechanics. However if you want to know what quantum mechanics*is*, you must read Peres A. Quantum Theory: Concepts and Methods Kluwer Academic Publishers; ISBN: 0792336321 (1998) (Not for beginners. A truly excellent account of the nontrivial aspects of nonrelativistic quantum theory from one who knows.) Aharonov Y., Rohrlich D. Quantum Paradoxes: Quantum Theory for the Perplexed Wiley VCH; ISBN: 3527403914 (2005) (A physics book for physicists, it goes a long way towards showing that in quantum theory you can get almost anything you like if you are ingenious enough. Negative kinetic energy? No problem at all, Sir. As the authors so eloquently put it: In Hilbert space no one can hear you scream.) Laloe F. Do We Really Understand Quantum Mechanics Cambridge University Press; ISBN: 9781107025011 (2012) (With a remit broadly similar to the voluminous Auletta tome below, this is a nice, readable, much more compact treatment, written at an intermediate level. Also, there's a perspective that is more up to date and in touch with quantum computing concerns.) ... and if you want to know everything that anyone ever thought quantum theory may or may not have been, there is Auletta G. Foundations and Interpretation of Quantum Mechanics: In the Light of a Critical-Historical Analysis of the Problems and of a Synthesis of the Results World Scientific Pub Co; ISBN: 9810246145 (2000) (Length of text in proportion to length of title. Reads like a contender for the longest review article ever written, so it's pretty terse and rarely comes across like a source that you could conveniently learn from. But it's astonishing for its comprehensiveness of coverage and analysis of important and subtle philosophical issues. You have to watch out for the bugs and for the Italian English, e.g. the absolutely delightful 'quantum bats' :-) .)Classical Stuff:Quantum theory did not spring fully formed from nowhere of course, though it is often presented that way these days (especially in COMP30222). The following are some of my favourite accounts of the prequel. Goldstein H., Poole C., Safko J. Classical Mechanics Addison Wesley; ISBN: 0201657023 (2001) (Venerable Classic relatively recently updated. To get to the frontier of quantum theory, you need to read as far as Poisson Brackets (for operator mechanics), and Action-Angle Variables (for wave mechanics and the Schrodinger equation).) Rajeev S. Advanced Mechanics Oxford University Press; ISBN: 9780199670864 (2013) (A very rapid survey of advanced topics in mechanics, and of their connections to all sorts of areas of modern physics. Great fun to read.) Fasano A., Marmi S. Analytical Mechanics Oxford University Press; ISBN: 9780199673858 (2013) (Translated from a recently written Italian text, this new kid on the block is an up to date and very thorough treatment of the subject.) Jackson J. Classical Electrodynamics John Wiley and Sons (WIE); ISBN: 047130932X (1998) (Venerable Classic relatively recently updated. This gets you to p.7 of Walls and Milburn.) Stratton J. Electromagnetic Theory McGraw Hill (1941) (Venerable Classic from the days before ISBNs, not updated at all. Style is of its age, but it's still a rock solid treatment of electrodynamics. The reference they all use but never cite. Available in various reprint formats.) Vanderlinde J. Classical Electromagnetic Theory Springer Verlag; ISBN: 1402026994 (2005) (Sadly out of print, what I particularly like about this book is the huge number of nontrivial examples worked out in detail.) Muller-Kirsten H. Electrodynamics World Scientific; ISBN: 9789814412117 (2011) (New kid on the block offering a treatment of electrodynamics that stands up well in comparison to venerable predecessors.) Zangwill A. Modern Electrodynamics Cambridge University Press; ISBN: 9780521896979 (2013) (New kid on the block offering a treatment of electrodynamics that stands up well in comparison to venerable predecessors. The 'modern' refers more to publication date than subject matter :-) .)Finally ...That 'Snapshots of Innovation' article in full.