AUSTRALIAN FRONTIERS OF SCIENCE, 2003
Canberra, 31 July to 1 August 2003
Solid-state quantum
computing and quantum electronic devices
by Dr Alex Hamilton
 |
Alex Hamilton is an Associate Professor in the School of Physics at the University of New South Wales, and manager of the quantum measurement program in the ARC Centre of Excellence for Quantum Computer Technology. Alex's expertise lies in the field of Experimental Condensed Matter Physics, having worked on semiconductor nanofabrication and the study of quantum effects in nanometer scale electronic devices at ultra-low temperatures for over 15 years. He obtained his BSc in Physics from the University of London in 1988, and a PhD from the University of Cambridge in 1993. He was awarded a highly competitive EPSRC postdoctoral fellowship to continue his work at the Cavendish Laboratory, which led to new understandings of electrical conduction in highly correlated low-dimensional quantum systems. Alex moved to UNSW in 1999, where his team is developing techniques for controlling and reading out quantum information in silicon quantum computer devices. He has published over 50 research papers, and is Australasian editor of the international journal Solid State Communications. |
I am going to be talking today about a brief summary of experimental approaches, and then specifically silicon quantum computing. I have to say that this is the work of an enormous team that has been assembled in Australia. I am very proud to be presenting the results of a very talented team of individuals from New South Wales, with our colleagues from the University of Melbourne, and particularly some of these young postdocs and students who have been working almost non-stop for months now. And we have got some very exciting late-breaking news.
I will give a little bit of introduction in terms of how, having heard about the theory behind quantum computation, you might experimentally realise a quantum computer, and then talk a little bit about silicon based quantum computer architectures and give two examples of slightly different architectures. I will briefly mention how those might be built.
Then I come onto the area that I have been working on: if you could build it, how can you measure it and demonstrate that it is working correctly? I will talk about some measurement technology we have developed for that, and some very recent results from buried phosphorus donor [P-donor] clusters in silicon.
Click on image for a larger version of figure 1
As Howard said, the difference between a quantum computer and a classical computer is really that in a quantum computer you replace the bits with qubits, and a qubit is just the quantum state of a two-level system. So if we imagine here is an atom, there is the ground state and there is the excited state, we could say, 'If the atom is in the ground state we will call it a 0, if it is in the excited state we will call it a 1.' That is our qubit. Or it could be the spin of an electron. If it is spinning clockwise we will call that a 1, and if it is spinning anticlockwise we will call that a 0. Any two-level quantum system that is well defined will do.
So there is your quantum bit. How do you make a quantum computer out of them? It turns out that any classical computation can be performed by a combination of one- and two-bit gates. So if you can take classical bits and do a NOT gate, and classical bits and do an AND gate, that is enough to do any arbitrary classical computation, from working out the factors of a number through to word processing. And exactly the same results apply for quantum computing. If you have a combination of one- and two-qubit gates, you can do any arbitrary quantum computation. For example, for quantum operations you might choose the quantum NOT gate and the quantum CTRL NOT [CNOT] gate, which are the analogues of the NOT and the NAND gate, or close to the NAND gate, in conventional electronics.
So really to build a quantum computer we just need quantum bits, we need to be able to do one-qubit operations, and we need to be able to do two-qubit operations.
This has led almost everyone in physics to say, 'My particular area of physics is very good for building a quantum computer.' And here is just a small subset of the number of proposals for building a quantum computer. Howard has mentioned the liquid-state nuclear magnetic resonance; there are experiments done with neutral atom optic-traps, linear ion-traps, cavity quantum electron dynamics, electrons on liquid helium that is just some of them. Solid state is particularly interesting because it potentially offers great scalability to large numbers of qubits. And there is a lot of effort going on around the world in superconducting Josephson junctions, quantum Hall qubits, et cetera, coupled quantum dots, and what we are particularly interested in donor atoms and semiconductors, really the ultimate limit of nanotechnology.
So, of all these different architectures, what is the state of play at the moment? How well are we doing? It is comparatively easy to come up with an idea for a quantum computer; it is somewhat harder to actually build it and demonstrate that it does something useful.
This is the state of play. Of the two most developed quantum computer architectures, liquid nuclear magnetic resonance uses the nuclear spins of individual atoms in a molecule that is floating around in a liquid, and there one-qubit operations have been demonstrated, two-qubit operations have been demonstrated, and even small quantum algorithms have been run and demonstrated to work. That bodes really well for quantum computation. The only problem is that it turns out that it is almost impossible to scale a liquid nuclear magnetic resonance computer beyond about 10 qubits. So for a large-scale quantum computer, liquid NMR doesn't look to be terribly useful.
Solid state qubits, like superconductors and semiconductors, have not done so well yet on the one-qubit operation and the two-qubit operation, although one-qubit operation has now been demonstrated in superconductors, with great promise for two-qubit operation, and there are indications of one-qubit operation in semiconductors. But solid state qubits scale really well. That is what the silicon industry and the microelectronics industry is very good at doing. Give them one transistor, and they will sell you a Pentium with 40 million transistors. It will take them a little while, but they can do it. That is why, although it is harder to show the basic operation for solid state qubits, because they scale more easily there is a lot of interest. For the solid state component of the Centre for Quantum Computer Technology, we are concentrating on silicon qubits, partly because of physical advantages that silicon has and also because there is an enormous silicon industry there to interact with.
Click on image for a larger version of figure 2
Let me give two examples of silicon based qubits. The first one is a very simple qubit, just so that we can picture what is going on. What we have here is two phosphorus atoms, and they are donors in silicon: each of them has one excess electron. We are going to rip one of the electrons off this phosphorus atom so that it is a P+, and this one is just a P. So we have got a double well potential here, with one electron shared between the two. That is sitting in the silicon and we have some sort of oxide on top, a barrier, and then surface control electrodes, which control what is happening inside the chip.
If the electron is in this right-hand potential well, we will call that a 1, if it is in the left-hand potential well we can define that as a 0. But if we use these surface gates to make the potential symmetric, then it will sit both in the left and in the right simultaneously unless, as Howard pointed out, you look at it, in which case it is either in the left or the right. So immediately we have superposition and a 0 and a 1. It is a very simple qubit.
Because the coulomb interaction of this electron with the outside world is very well defined, it couples strongly. That means it is easy to tell whether the electron is over here or over here [in one well or the other]. But because it couples very strongly to the environment, the environment keeps messing up your quantum computer all the time. It keeps doing measurements on it while you don't want it do. That means it decoheres relatively quickly.
Nevertheless, we have proposals for doing one-qubit gates, using these surface gates and changing the potential, and two-qubit gates, allowing us to couple one charge qubit to another charge qubit and then scale this thing up to large numbers of qubits.
Click on image for a larger version of figure 3
If you want to have longer coherence times and coherence is very important for computing, because if you lose coherence the computer just basically crashes one of the longest coherence times is in the nuclear spins of donor atoms in silicon. The reason is that there is very weak coupling between the nuclear spin and the external environment. In fact, the relaxation time is incredibly long, about 1018 seconds. If you have a nuclear spin in a given state, it will stay like that almost indefinitely while you perform operations.
So here we have again an array of phosphorus atoms buried in silicon. They are spaced about 20 nm apart, with control electrodes on the top and some sort of a barrier. There is an external magnetic field. And then if we say the electron spin is aligned with the field we will call that a 1, if it is anti-aligned we will call that a 0. So that is our qubit, the nuclear spin.
Because it does not interact with the environment, we couple it, using the electron that surrounds this phosphorus atom, to the outside world. And that electron cloud we control with these gates. That is the ingenious part of it. And there are one- and two-qubit gates to allow you to do one- and two-qubit operations, to flip individual spins of these phosphorus nuclei or to couple two phosphorus nuclei via the combined electron cloud.
All one has to do then is just to read out. We can do the operations; we know how to couple them. Once we have done the calculation, we just want to read the answer out. That is a little bit tricky, because you need to read out whether a single nuclear spin is pointing up or pointing down. That is hard. No-one has ever measured a single spin in a solid state.
One idea is to transfer that nuclear spin onto the state of the electron spin the electron that is going round and round that phosphorus atom and then we just measure whether that electron spin is up or down. That is much easier, but still very, very hard.
So, in principle, we can build scalable quantum computers in silicon, using either charge or spin. The only difficulty is that we have to build something where the phosphorus atoms are well-defined distances apart, on a very small scale, tens of nanometres, and five years ago, when this was proposed, everyone thought, 'It's simply impossible to do that. The technology doesn't exist.' Well, the technology now exists.
Using a combination of ion implantation and high-resolution electron beam lithography, Andrew Dzurak and David Jamieson and their teams have developed a route where single phosphorus ions are implanted into silicon; that is detected so we can detect that one phosphorus arm went in then we implant another one next to it, and we can implant two phosphorus ions at controlled locations in the silicon. I won't really talk about that, but that technology has been developed.
On a slightly longer time scale, even more perfect construction can be achieved using a scanning tunnelling microscope. Michelle Simmons and her team at UNSW used a scanning tunnelling microscope tip to basically place individual phosphorus atoms on silicon with atomic precision, at better than 1 nm scale. And that [on screen] is the scanning tunnelling microscope.
So these two teams of researchers have developed two parallel strategies for building this thing. Now we have answered the question, 'Can you build it?' we know in theory it should work in practice is it going to work?
The only way to find out is to measure it and see. So what do we have to do to measure it? We just want to be able to read out the state of a quantum bit. With charge based architectures, you just have to tell whether the electron is on one of the phosphorus atoms or the other phosphorus atom. You just have to detect a single electron. That is difficult, but it has been done.
All the spin based architectures require the ability to detect a single spin, and that has not yet been achieved in the solid state. Bruce Kane, in his original paper in 1998 when he was working at UNSW, proposed a very ingenious way of detecting the state of a single spin. What he said was: imagine you have two phosphorus atoms, each with an electron, and we have transferred the nuclear spin information of the phosphorus atoms onto each of their electrons. Now we want to tell what is the state of, say, this electron here. What you do is to introduce a reference qubit. So let's say this one we know is up, and we want to know whether this [other] one is up or down.
We use the parallel exclusion principle. So if the two electron spins are pointing up, when we try and sit them both on the same phosphorus atom the parallel exclusion principle says you can't have two electrons with the same quantum state at the same point in space. So you can't get it to move over if both spins point up. But if one of the spins is pointing down, then you can have it move over. So we use parallel exclusion to map this difficult problem of detecting a single spin, a magnetic bit of information, into whether an electron can move, which is simply detecting the charge motion. And that can be done. All you need is a very sensitive electrometer.
So, for both charge and spin, all we need to do is to detect the motion of a single electron. And we just need a very, very sensitive, really fast and extremely reliable electrometer. What we use for that is the single electron transistor, which is this thing shown here.
Normally, if you plot the current through a transistor as a function of gate bias, it just increases smoothly like that. But in the single electron transistor it oscillates, with these really sharp little peaks. The interesting thing is that if I move from the top of this peak here to the top of that [next] peak there, I have changed the number of electrons in that transistor by one and only one. So going from here to here I have gone from n to n+1 electrons, to n+2, to n+3. So if I moved from here a little bit across and went up a bit, that is a fraction of one electron. And I can detect a fraction of one electron because it causes quite a big change in the amount of current flowing through my transistor. So, basically, I have got a very, very sensitive electrometer, able to detect a fraction of one electron. That is really good. Now I can use that to tell whether this electron moves over here or not.
The difficult part is that it does not just detect these electrons. In the solid state there are all sorts of other traps and impurities and things moving round, and there is a lot of charge noise. Telling the difference between spurious signals and our two single donors sitting in this big piece of silicon with metal gates on the top is non-trivial.
Click on image for a larger version of figure 4
What we have done is to develop a twin architecture, where we have two SETs. We put one single electron transistor detector over there, and one over here. This one detects the electron leaving, this one detects it arriving. We correlate the outputs, and only when we get a coincidence do we know that an electron went from here over to here.
How do we know that works? Well, the very first thing we did was that we went away and built a simulation structure entirely out of metal. We replace these two phosphorus atoms with two pieces of metal, and we push a single electron through a tunnel junction over to the other side and detect its motion. Then we replace those metal islands with clusters of phosphorus atoms and do the same thing. And finally we are going to head towards pushing single electrons from one phosphorus atom to the other the ultimate in single electronics.
Click on image for a larger version of figure 5
How do we do that? This is what we have been working on for the last three years. We have built up quite a big lab, with three dilution fridges. They go somewhat colder than Canberra at night, down to about 0.1 kelvin. We have rather fast single electron transistors which act as these electrometers, operating at between 300 and 400 MHz, cooled to about 0.1 kelvin. Here is the little chip with our qubit simulation on it; here are some surrounding electronics. It sits in the base of our dilution fridge with cryogenic amplifiers of 4 kelvin, an array of filters, room-temperature amplifiers, and that is the complete circuit.
I won't say very much more than that, other than to say that that is the quantum limit for charge sensitivity with a single electron transistor. It is about 2 x 10-6 electrons that you can detect in one second. We can detect 4 x 10-6 electrons in one second. So we are within a factor of 2 of the quantum limit, which is pretty good. There are only two groups worldwide that have this twin-detector capability, and we are one of them.
Click on image for a larger version of figure 6
So what do we see? Well, what we are going to try and do is use these red gates here to push an electron from this blue island onto this yellow one, and we are going to try and use these transistors here to 'see' that electron motion. We increase the electric field across here that is shown here as a function of time, that is the increasing electric field and every time an electron jumps from here to here, one of the single electron transistors sees a spike as it leaves and the other one sees a spike as it arrives. And then the next electron goes, and one sees a spike as it leaves and the other one sees a spike as it arrives, and then the next one and so on. So we are getting this characteristic sawtooth oscillation, in coincidence and in reverse. One sees it leave, one sees it arrive, and that is the correlation. You get a very clean signal.
Why do you want that correlation? Well, that is the average of four traces. If we don't average, every now and then you get hit by a piece of noise. So here are the spikes of individual charge transfers, and here is a piece of noise. It is very difficult to tell the difference: was that some charge transfers, or was that the charge transfer? But with two transistors you can say, 'No, it was here and here, and this stuff is rubbish. We'll just junk that.'
Click on image for a larger version of figure 7
So how are we doing with moving on to realistic buried 'clusters'? Heading toward single phosphorus atoms, we have implanted about 600 phosphorus atoms, in two clusters, and we are going to try and transfer a single electron from one to the other. That is the device that has been built. This is a scanning electron microscope image of the device. Here are the two donor sites, and here are two detectors. We increase the electric field to try and cause electrons to jump across, and we are looking for that periodic sawtooth oscillation.
Well, that was our first results. We got kind of excited about that. Maybe you don't share our excitement. We repeated that under lots of different conditions. We differentiate this data and look for a big spike when we get these jumps. And you can just see that there is a continuous set of spikes running along here, and we are absolutely certain that is charge transfer events periodic, or quasi-periodic, charge transfer events.
Click on image for a larger version of figure 8
The problem is that there is a lot of noise going on from other electrons moving round in the substrate, so we do the measurement a whole lot faster. This is data that literally came out of our dilution fridges three or four days ago, and now you can see this beautiful sawtooth oscillation as we increase the electric field. Hopefully, we are causing single electrons to transfer from one cluster to the other, so we are detecting individual motion between buried clusters.
Click on image for a larger version of figure 9
What about the correlation? If one of them sees it leave a cluster, the other one sees it arrive, so here is are similar sets of data. What we are looking for is lines, like this, that appear in both sets of data. You may think I've got rose-tinted glasses, so let me just give you a hand! Here are the lines [with red dots added]. I just fit them to this set of data on the left, and then I just copy exactly that and put it on the right. And there are signatures of stuff happening here that is definitely not happening here, so that is not to do with periodic charge transfer. But there are things happening here that are definitely happening here, things happening here that are definitely happening here. So our coincidence detector, although there is a lot of noise and we expected there to be a lot of noise is allowing us to tell the difference between electron motion, hopefully between these clusters, and other things that are happening in the substrate. We estimate that we are detecting about 0.03 electrons [0.03e] with our detectors when that single electron moves.
In summary: I have briefly mentioned that there are two parallel fabrication strategies for charge or spin qubits, using an atomic scale scanning tunnelling microscope or single ion implantation. We have developed this very sensitive read-out technique that can detect a fraction of an electron moving on microsecond time scales, and use that to see that our qubit is behaving the way we would hope. So we have a fabrication and a read-out capability. And most recently we have got evidence for this periodic charge transfer between buried clusters.
As to our future work, we want to make absolutely certain, beyond all shadow of a doubt, that that is really charge motion going from single electrons moving from here to here a little bit more work there and then what we would like to do is just to put individual phosphorus dopants and move a single electron from one phosphorus donor to the other, and then start doing coherent manipulation of the first solid state qubit in silicon. And then we will have demonstrated a silicon qubit. I think that really is a very exciting and a very near-term goal.
What about the future? Well, it is always dangerous to predict the future. This is a famous quote from the founder of IBM: 'I think there's a world market for maybe five computers.' 'Computers in the future may weigh no more than 1.5 tons' 1949, Popular Mechanics. 'There is no reason anyone would want a computer in their home' Ken Olson, the President and founder of Digital Equipment Corporation, which was bought out subsequently by Compaq, which was subsequently bought by HP. And the famous one from Bill Gates: '640k of memory ought to be more than enough for anybody.' So it is very dangerous to try and predict what will happen when. But I do think that Howard is right, in that we will have, within our lifetimes, useful quantum computer devices.
Perhaps this is an interesting quote [by Richard P. Feynman] to finish on: '...it seems that the laws of physics present no barrier to reducing the size of computers until bits of the size of atoms,' and that's precisely what we are doing 'and quantum behaviour hold sway.' That is exactly what we are trying to do, and we still haven't found a law of physics that says, 'No, you cannot do this.' All that is left is a lot of engineering and a lot of basic science to try and get the whole thing working on a large scale. Thank you.