The Material World 
Quentin Cooper

Quentin Cooper : Hello, it's long been thought that high quality steel wasn't produced in Europe until the end of the 15th century,today we look at why findings at an 8th century Saxon site near Southampton may dent this previously cast iron argument.

First,pencils ready,your time starts now.

"Steven dives into a pool. The force exerted by the water on his goggles is 160 Newtons. His goggles have a total area of 8cm squared. Calculate the pressure of the water on his goggles and show clearly how you obtain your answer."

If you've ever done any kind of science exam -that question was from a 1998 physics GCSE paper - you may recall those kind of dread questions where reaching the right answer wasn't important as showing the route you took there [Ref: Edge17.rtf {Evolving algorithms}]. It's a principle that runs deep within science,only if you understand every step along the way,can you be sure where you stand. That's why there's big kudos and big cash to be had when a long standing mathematical hypothesis or conjecture is proved. 
But in the strange world of quantum computing [Ref: qcomp1.html and qcomp2.html],which we're about to enter,while the behaviour of matter and particles on the tiny quantum scale can be exploited to solve a problem that's intractable on even the most powerful conventional super computer,the vast amount of parallel data juggling which leads to that result,cannot be scrutinised because...because...well it's just this sort of thing I'm hoping to clear up by talking to quantum computer scientist Dr Tim Spiller,from the Hewlett Packard labs in Bristol,and Professor John Jefferson,from the Defence Evaluation and Research Agency,although perhaps I should start by first repeating this caveat from Nobel Prize winner Richard Feynmann (see www.geocities.com/Omegaman_UK/feynman.html)

"No one understands quantum mechanics. Don't keep saying to yourself 'but how can it possibly be like that?' because you will go down the drain into a blind alley from which nobody has yet escaped."

Down the drain into a blind alley. Tim Spiller,second only to GM,quantum is probably the bit of science terminology that gets banded around most,without ever being,sort of stamped down and defined,so before we get on anything to do with the computing bit,what do we mean by quantum and quantum behaviour?

Tim Spiller : Well quantum behaviour is really what everything that's very very small down at the scales of atoms or electrons or things like that actually does. I mean that's the way nature works [It is the current model of how nature works you mean -LB]- we don't see that in a the big every day world around us,but there are lots of very interesting and strange effects that happen down there,which are just the way nature is when we look at those very very small things.

Quentin Cooper : Right so we need this label because these things at this very very small level at which we cannot see don't behave like things do at our very very big level?

Tim Spiller : Absolutely.

Quentin Cooper :  Okay,and with ordinary computers getting ever faster and as we mentioned on this programme just a couple of weeks ago when we talked about "The Grid" super computers being linked up over the internet to have increased processing power,why even the need to think about going into quantum effects for computing,why not just be happy with the fantastic computing power we've got?

Tim Spiller :  Well,the thing is we've got this effective doubling of computing power about every couple of years,which is Moore's law...

Quentin Cooper :   Which goes back to...right back to the mid 60s? Yeah.

Tim Spiller :  ...that's right,and it still going strong at the moment,but it's not going to go on forever,because the reason we can continue to make computing faster and faster is that we're making the individual devices that go on the chips and so on smaller and smaller. So they work faster and they're closer together,so they can talk to each other more quickly,but if we keep making those devices smaller and smaller,then in about 20 years time,something like that,we are going to get down to those devices being of the order of single atomic or molecular size,and then they are not going to work like they do currently. So Moore's law is going to come into a problem at that point,and in one sense quantum mechanics could almost be the villain there,because if we don't control that quantum behaviour in the way we want,then these things are simply not going to work as ordinary computers anymore.

Quentin Cooper : So you're standing on the watchtower looking into the not too distant future and saying,"Look right now and for the next 10-15 or whatever years,we can keep on and Moore's law will be fine,but pretty soon we're going to run into these problems if we get smaller and smaller where these quantum effects are going to comprehensively muck up computing as we understand it"?

Tim Spiller :  That's right,I mean Moore's law is going to kind of hit a quantum wall and it's something that people are now beginning to worry about.

Quentin Cooper :  So John Jefferson it seems from what Tim's saying,is we get to a point where we either have to go "Well that's it,thank you very much,Moore's law is over,that's as  good as it gets" or we have to...we have to work with the way physics is down there and bring the quantum effects into play?

John Jefferson : Yeah that's absolutely right, I mean as Tim says,quantum effects really become unavoidable as devices get smaller and smaller,and we going to be faced with these quantum problems anyway,so why not take a fresh look at the whole area of  quantum computing,quantum mechanics and computing and see whether we can find some new paradigm for computing.

Quentin Cooper :   But is it just a case of  - we've made it sound so far as if this is a hazard that's on the horizon - it's a quantum barrier...

John Jefferson : Yes.

Quentin Cooper : ...and we need to find a way up it,around it,whatever,but in fact I think it's more a case of there are in fact some good things here that work with?

John Jefferson : Absolutely yes,I mean there are many new opportunities - indeed quantum computing itself - is only one aspect of these new opportunities,I mean there are other quantum effects for other kinds of devices,which one can possibly exploit,but one should look at it as - not as a brick wall - but as an opportunity for investigating new phenomena,and quantum computing is certainly one of the most exciting new phenomena around at the moment.

Quentin Cooper :  Okay,so what are the things that we can maybe take advantage of? Well maybe not all of them,but give me at least an idea here - it's not just a problem - there are things about these quantum properties that can potentially be exploited.

John Jefferson :  Yes indeed.I mean as far as quantum computing is concerned the main thing that can be exploited is this idea of parallelism which really comes from quantum superposition [Ref R.Penrose "ENM"]. I mean quantum superposition is rather a mysterious thing as you said in your introduction,about Feynmann. I mean Feynmann's you know absolutely right - if you try to understand quantum mechanics,then you're doomed to failure,nevertheless you've got to try and have some appreciation of what superposition means in order to really understand quantum computing.

Quentin Cooper :  Well I was with you all the way till you used the word "superposition" but keep on!

John Jefferson :   Okay let me try and give you a simple idea of at least how a superposition manifests itself. Take a single electron for example,the electron has got an intrinsic magnetic moment called its "spin" and if we make a measurement to try and measure this magnetic moment then we get one of two values it either points up or it points down with respect to the magnetic field in our measuring apparatus.

Quentin Cooper :  Right.

John Jefferson :  Now the interesting thing about superposition - or the unusual or mysterious thing about superposition - is that before we make the measurement then this spin can be simultaneously in both these states in some sense.

[This is what Schrodinger's Cat scenario is meant to emphasise by bringing the small scale effects to the macro level of experience for the benefit of the layperson. Note also that there is an idea of an electron as a local single unit here,and also that work done in Japan on "quantum vortices" is related in making use of sub atomic properties in magnetic storage devices [Ref : Video M3 {RI lecture}] -LB]

It's said to be in a mixed state or a superposition state,where it's both up and it's down,and because it's both up and down at the same time,if we think of up and down as 0 and 1,as binary numbers in a computer,then because we can manipulate these states we can essentially manipulate up and down at the same time.

Quentin Cooper :   I had a feeling you were going to make the - if I can use the pun - the quantum leap to 0s and 1s there. But I mean it's a very hard thing to get your head round as you've already hinted...

John Jefferson :  Yeah.

Quentin Cooper :  ..this business of being 0 and 1 at the same time until we make the measurement.

John Jefferson :   Yes.Yes indeed.

Quentin Cooper : And there's almost the implication within it that almost any time we try and take a measurement - ie any time we try and do anything useful,then we muck up the calculation?

John Jefferson :   Absolutely yes.

Tim Spiller :  We do.Yes that's quite right.So..?

Quentin Cooper :  Well I would have thought that would have put it into the "useless file" before we got any further,if every time you take a measurement it mucks up the equation?

Tim Spiller :  Well no the whole idea is that you will only make a measurement at the end,so you've got to prepare this thing very carefully,and then actually not look at it for a while,let it do its stuff,and then you come in at the end and make a measurement and that's going to give you some very interesting and revealing answer. But you absolutely can't look halfway through.
[Ref: seedark.html {Seeing without looking}]

Quentin Cooper :  So you have to have enormous faith in this black box or whatever your quantum computer is that you're getting the right output from your input?

[It's not faith at all,the understanding of the superposition and the idea behind the whole process has as much rigor as any other scientific process,and any answer would be as rigorous as any conventional digital computer,the only sense in which it is different is in making use of the inherent uncertainty - but if this is not understood correctly, then the process won't work,if quantum mechanics is a viable model - then there is no reason to assume that it will be less capable than the Boolean logic that enables digital computers to function with precision. As Roger Penrose points out,for all it's uncertainty,QP is a deterministic theory,since if it was not there would be nothing to be said of it in terms of rules and no use could be made of it. It is not randomness,but a certain kind of statistical variability and the capacity to defeat the usual A and not A mutual exclusion -LB]

Tim Spiller :   Well..

John Jefferson :  Well you can actually manipulate the superposition states providing you prepare the state in the correct way,and you know what the physical system is,then quantum mechanics tells you how this system will evolve in time,before you make the measurement,

[Exactly - it's deterministic and predictive because it has rules,so it is not an act of faith - LB]

and it's the system evolving in time which is in fact the quantum computation.

Quentin Cooper :  But this is the bit Tim,that I alluded to in the introduction isn't it? This is the bit where you cannot show your workings with the answer. You can set it up,you can ...all the conditions are controlled and you can hopefully get this answer you might not have been able to obtain by traditional forms of computation,but seeing exactly how you got there,well that is beyond the wit of man,and beyond the powers of quantum laws?

[Not so - see seedark.html  -LB]

Tim Spiller :    Oh yeah,I mean if you want a really crazy example,then you actually..

Quentin Cooper : Oh please!

Tim Spiller :  ..don't need that many quantum bits so that's these little individual systems that can be both 0 and 1 at the same time - you only need a few hundred of those,until they've got more intrinsic degrees of freedom built into them than there are atoms in the universe. So if you're going to use all of those degrees of freedom,you clearly can't show your working,because you haven't got enough stuff that you can output it onto even if you used the whole universe.

Quentin Cooper : There aren't enough atoms for the paper effectively?

[One would imagine that if that's the case that a QP computer could be as good a model of the universe as the universe is of itself,but somehow I doubt it.Logically any QP computer is a sub part of the universe and can't model something that it is less complex than - or can it? The human brain seems to be able to comprehend far more than it's size would seem to allow for - check out complexity theory - LB]

Tim Spiller :   Exactly, so..so it shows you just how much power there is potentially...potentially in one of these things.

Quentin Cooper :  And there are problems that need that sort of computing power are there?

Tim Spiller : There are some very interesting sort of mathematical problems that can be solved.

[How about weather modelling,that would benefit from massive parallelism -LB]

Some of which sound quite abstract,but some of which actually have some every day uses. I mean a lot of the world's secure communications at the moment [Ref S.Singh "The Codebook"] are actually based on certain mathematical problems being very hard to do one way and very easy to do in reverse, [Ref: I.Petersen "The Mathematical Tourist" - see tour2a/b/c/d/e.html] and the hard bit means that you can actually encrypt something that's because it's hard then cannot be decrypted by most people.

Quentin Cooper :   I think the classic example of this is,isn't it,it's combining two primes to get a much larger number [Ref: largeno.html],and if you've...it's easy enough to  take two primes and get the bigger number,but it's very hard to take the bigger number and work out what the two primes are?
 [Yes,factorising large primes is the secret of decryption and QP computers could chunk through factors like there was no tomorrow causing problems for encryption,but also can yield even safer forms of encryption than large prime numbers -LB]

Tim Spiller :   Exactly, I mean so the thing is we know if we had a sizeable quantum computer we could solve this factoring problem and the dramatic...

Quentin Cooper :   And therefore mess up all the world's cryptography wouldn't you?

Tim Spiller :   ..exactly,we ..you know...most of the current secure communications would run into real problems with that,we'd break them all,so ...so,you know,mathematical problems may sound a bit mundane, but they have some real world consequences.

[A lot of the time the lay public do not understand the relationship between abstract mathematical problems and the consequences that those problems have in real life - solution - understand more maths in the public domain - LB]

There are other applications fro quantum computing as well. I mean people..people have shown that you can search more quickly,if you have a telephone book and you're given the number but not the name,and you wish to search through,then that's a pretty laborious task.We know how to speed that up quite dramatically with a quantum computer as well,and another example,sort of the next one I can think of is - again quite narrow perhaps - but certainly from our perspective - they would be a wonderful research tool. If we had one of these,we could actually use it to simulate all sorts of other things,and then the potential spin-offs for research are dramatic.

John Jefferson :  I mean as Feynmann himself pointed out,classical computers,ordinary computers,are not really very good for simulating quantum problems,but quantum computers are ideal for simulating quantum problems,because behind the scenes of these huge data sets,which as Tim said,more than the atoms in the universe,but that's ..nature is somehow manipulating these large data sets behind the scene and presenting us with the answer which quantum mechanics does quite naturally.

Quentin Cooper :    So not only are they good at doing things in parallel,they work in parallel to existing computers - they're good for their own kind of problems rather than applying them to the sort of things you use your traditional computer for?

John Jefferson :   Yeah absolutely, I think there's all,you know..quantum computers even if they become widely available,will never perform all the operations that ordinary computers do - it really is horses for courses,and one thing of course we need to do is in the future,if we're ever going to have practical quantum computers,is to be able to interface them to ordinary computers as well.

Quentin Cooper :    Okay I want to get on that in a minute,but you've just used the term "if we ever have",there have been a lot of "ifs",and I'm not quite clear,what state are we actually at in terms of quantum computers,is it just theory,or have we begun to make the first sort of abacus equivalents?

John Jefferson :    Well certainly theory is well ahead of experiment here,but there are a few quantum computers that have been made - sort of prototypes with just a few q-bits - atoms in traps for example.

Quentin Cooper :   Q-bits,these are these quantum bits that we've been talking about?

John Jefferson : Quantum bits yes.

Quentin Cooper :  Not cubits as in the medieval form of measurement,right fine.

John Jefferson :   Absolutely not no,just the quantum bits..and so there are a few prototypes but these are...you would hardly call these quantum computers. I mean I think maybe Tim can correct me on this if I'm wrong,but I think it's possible to actually factorise 6,but not 13..14.

Tim Spiller :    Something like that. I mean the point is that we've got some very nice demos at the moment,which you could call very small quantum computers,if you want,but...

Quentin Cooper : But it shows the theory is reasonably sound?

Tim Spiller :  ..it does but that theory is quantum mechanics,and we haven't got any really good reasons yet to doubt that that's the way nature really works,but...

[So we understand - we make use of - and benefit from the understanding,and the experiments prove the theory so it can hardly be described as "haven't the slightest idea what is going on" - LB]

Quentin Cooper :  Again to quote Feynmann "If your theory clashes with quantum mechanics throw it out".

Tim Spiller :  ..yes exactly. The route forward I think is still an open question. We've got a few demos,but I don't think you'll be able to scale those up to very large numbers of quantum bits to do really useful tasks,and it's still an open research problem. You know there are a number of candidates about how we might do this,and it may well be that we haven't actually thought of the best route forward yet.

[Why not ask a genetic algorithm on a traditional computer to solve the "best way forward" problem? -LB]
So it's still very much at the research stage,rather than we know where to go and we just need to do some development there.It's actually still very open.

Quentin Cooper :  So what are the problems that need to be overcome if we are going to make practical machines John?

John Jefferson :   Well I think most people believe that if we're ever going to have practical machines then there's got to be some kind of solid state solution that emerges,and...there are...people are trying,I mean the difficulty of the solid state solution is the so-called coherence problem - that the quantum....the quantum part of the system interacts with the outside world,and this is why one uses atoms in traps,because those interactions are very weak,and they tend to become stronger in solid state solutions,but nevertheless people are trying with solid state solutions,so let me give you an example.
If you take an ordinary transistor and you reduce it in size,eventually it becomes so small that it only contains a single electron,and this would be fairly useless as a conventional transistor. However we can manipulate the spin on that electron,as I described earlier and people have shown that it's - in principle -  possible to have a scaleable array of many of these quantum dots and they would perform like a quantum computer,if only we could solve the coherence problem,and also reproducibility in the technological problems.

Tim Spiller :  I mean this ...this coherence problem is the real problem,I mean the thing to get over is that these superposition states where you can have both - 0 and 1 at the same time are very delicate,and we're big and noisy and clumsy,and we have to be very careful that we don't disturb them while they are doing their quantum stuff,otherwise we will ruin our quantum computation or trash any other quantum behaviour. So that's the tricky thing,it's actually being able to prepare these things and then let them do their stuff without any noise getting in from outside.

Quentin Cooper :  Coherence is often the real problem for me as well! (Tim sniggers) But is there a possibility at this stage,that this coherence problem could be insurmountable? That we could say "Well it was a nice idea,but actually at the end of the day,this is a quantum barrier and that's as far as Moore's law goes,and we are,you know,20 years away from computers being as good as they can be?"

Tim Spiller :  There aren't any fundamental reasons why this coherence problem can't be overcome. There was some very nice work that actually showed that even though it's sort of counter intuitive,correction of errors or the removal of decoherence from quantum system can in fact be done,it's quite tricky,it's more subtle than in the ordinary sort of conventional error correction that's done with ordinary communications [Ref Video A30 : OU:Errors aren't forever;& Mariner 9 code],and so on,but there's not a fundamental problem there,people have shown how to do this,so the point is do it,you will need more quantum resources,you'll need more quantum bits,and that's the problem at the moment.

Quentin Cooper : So almost finally,John by the time this 20 years is up,you would expect quantum computers to be in use,not the subject of research but an actual research tool?

John Jefferson :  I really don't think we can say that at the moment,I mean we're still very much at this research level,and there's many different approaches and you know,for example,the funding agencies are really spreading their funding over all different possible approaches to quantum computing,and no one really knows which will emerge as a winner,if indeed there will be a winner,and so...and we can't say what the time scale is,but what we can say is that if something does emerge,if there does seem to be a viable quantum computing technology,then the development phase could really be quite fast.

Quentin Cooper :  And finally - I say,I say,I say - I've been working on this one -What do you get if you manage to create a computer based on these principles but it comes up with the wrong answers?

Tim Spiller : I haven't a clue! (laughs)

Quentin Cooper :   You get - 

("Juan tanamera" plays)

Quantum - an error! Dr Tim Spiller and Professor John Jefferson (both giggle) many thanks.