Computing with Quantum Cats (28 page)

But this is not the only game in town. In a parallel development, so-called quantum dots have also been inserted into microwave cavities and probed in the same way, by a team at Princeton. This, again, is an eminently scalable technology, but starting from a very different scale.

CORRALLING WITH QUANTUM DOTS

At the other end of the physical scale from macroscopic superconducting qubits, we find the possibility of using single electrons as the bits in a quantum computer. This is the ultimate development of conventional computer chip technology using semiconductors, where a well-developed industry already exists based on the ability to “build” structures on the scale of nanometers (one nm is a billionth of a meter). The construction process involves depositing layers of semiconducting material, one on top of the other, in so-called semiconductor lithography, and interesting things happen where layers of different material meet.

The basic idea is to create a three-dimensional structure, like a submicroscopic bubble, in which a single electron can be “corralled”—confined in a small volume with a known energy level—and can be moved up and down energy levels as required. These corrals are known as “quantum dots.” The sizes (diameters) of quantum dots are in the range from 5 nm to 50 nm; they can form spontaneously when one semiconductor material is deposited on another layer of a different semiconductor, because the different electrical properties of the two layers can cause atoms to migrate in a thin layer parallel to the boundary between the two materials, forming patterns in which the overall effect of the electric field of the atomic nuclei creates dips in the local electric field. These
dips can be thought of as the electrical equivalent of potholes in a worn road. Electrons can be trapped in these (three-dimensional) potholes in a similar way to pebbles being trapped at the bottom of a pothole.

Another approach, pioneered at the University of New South Wales, manipulates individual atoms to form the quantum dot. A team led by Professor Michelle Simmons made a quantum dot by replacing seven atoms in a silicon crystal with phosphorus atoms. The dot is just 4 nm across, and acts as a classical transistor. Even without quantum effects, this offers the prospect of smaller, faster computers; but “we are basically controlling nature at the atomic scale,” says Simmons, and “this is one of the key milestones in building a quantum computer.”
⁷

But what can you do with such a trapped electron? There are two particularly promising possibilities as far as quantum computing is concerned. The first is known as the charge qubit. It involves two neighboring quantum dots, and an electron which can be moved from one quantum dot to the other.
⁸
Or, of course, it can be in a superposition, where no decision about which dot it is in can be made until it is measured. If the dots are labeled left (L) and right (R), then we have a qubit with L corresponding to 0 (say) and R corresponding to 1. Two-qubit systems built along these lines have already been constructed; one of the most promising possibilities, potentially scalable, involves two layers of gallium arsenide (a material already widely used in semiconductor technology) separated by a layer of aluminum-gallium-arsenide. This ticks one of the DiVincenzo boxes; another plus is that initialization can easily be achieved by injecting electrons into the system. On the negative side, decoherence
times are short, and although two-qubit systems have been constructed, it has not yet been possible to make a two-qubit gate out of quantum dots.

So how about using spin? The fairly obvious idea of representing the state of a qubit by the spin of a single electron, reminiscent of the way the NMR technique uses the spin of an atomic nucleus, has been given the fancy name spintronics. Spin has the great advantage for computer work that it is a very clear-cut property.
⁹
There are two, and only two, spin states, which can be thought of as “up” and “down,” and which can be in a superposition. Techniques which define the state of a qubit in terms of energy, for example, may specify the two lowest energy levels of a system as “0” and “1,” but there are other energy levels as well, and electrons (or whatever is being used to store the information) can leak away into those levels. Decoherence times for electron spins can be as long as a few millionths of a second, but because electrons have such a small mass it is easy to alter their spin state using magnetic fields. This is particularly important in manufacturing fast gates. So spintronics is a promising way of satisfying the DiVincenzo criterion of having gates that operate faster than decoherence occurs. Even better, it ought to be possible to store information using the spins of nuclei, which have still longer decoherence times, up to a thousandth of a second, and then to convert the information into electron spins for processing.

As with the charge qubit, the technique ought to be scalable—it is probably the easiest of all the techniques I am describing to scale—and simple to initialize; measurement is not too difficult. But, as ever, there is a downside. Until recently, nobody was able to address the spin of a single
electron. This would make it impossible to construct a set of quantum gates. And in order to minimize the decoherence problem, such systems, like the superconducting systems, have to be run at very low temperatures, close to absolute zero. But the Princeton experiments involving quantum dots trapped in microwave cavities offer the potential for addressing individual electrons, with, in effect, the properties of an electrical system a centimeter or two long being determined by the spin of a single electron.

It's a sign of how fast work in this field is progressing that in the very week I was writing this section another team at the University of New South Wales announced that, in collaboration with researchers from the University of Melbourne and from University College, London, they had succeeded in manipulating an individual electron spin qubit bound to a phosphorus donor atom in a sample of natural silicon.
¹⁰
They achieved a spin coherence time exceeding 200 microseconds, and hope to do even better in isotopically enriched samples. “The electron spin of a single phosphorus atom in silicon,” they say, “should be an excellent platform on which to build a scalable quantum computer.” Their planned next step—probably achieved by the time you read this—is to manipulate the spins of electrons associated with two phosphorus atoms about 15 nm apart; the electrons have overlapping “orbits,” and the spin imparted to the electron on one atom will depend on the spin of the electron associated with the other atom. This is the basis of a two-bit gate.

In such a fast-moving field, it would be foolish to try to keep up with the pace of change in a book that will not be published for several months after I finish writing; so, as ever, I will largely restrict myself to the basic principles of the
different techniques. The one that bears most resemblance to the electron spin approach uses nuclear spin; not in the way we encountered it before, but as one of the most promising prospects for quantum computer memory.

THE NUCLEAR OPTION

In 2012, news came of two major developments in nuclear-spin quantum memory, reported in the same issue of the journal
Science
.
¹¹
Both are based on the kind of solid-state technology familiar to manufacturers of classical semiconducting computer chips. The first involves ultra-pure samples of silicon-28, an isotope which has an even number of nucleons (protons and neutrons) in each atomic nucleus, so that overall there is no nuclear spin. The samples are 99.995 percent pure. This provides a background which the researchers, a team from Canada, Britain and Germany, describe as a “semiconductor vacuum.” It has no spins to interact with the nuclei of interest, which greatly reduces the likelihood of decoherence. With this material as a background, the silicon can be doped with donor atoms such as phosphorus
¹²
(just as in conventional chips), each of which does have spin.

The term “donor” means that the phosphorus atom has an electron which it can give up. Each silicon atom can be thought of as having four electronic bonds, one to each of its four nearest neighbors in a crystal lattice; an occasional phosphorus atom can fit into the lattice, also forming four bonds with its neighbors, but with one electron left over. Such a doped silicon lattice forms an n-type semiconductor. Using a coupling which is known as the hyperfine interaction, the spin state of the donor electron (which can itself, in
principle, act as a qubit) can be transferred to the nucleus of the phosphorus atom, stored there for a while, then transferred back to the electron. All of this involves manipulating the nuclei with magnetic fields, running the experiment at temperatures only a few degrees above absolute zero, and monitoring what is going on using optical spectroscopy. But crucially, although they appear daunting to the layman, the techniques used to monitor hyperfine transitions optically are already well established as standard for monitoring ion qubits in a vacuum.

In the experiments reported so far, ensembles of nuclei, rather than individual phosphorus nuclei, were monitored. But the decoherence time was 192 seconds, or as the team prefer to point out, “more than three minutes.” We have already arrived in the era of decoherence times measured in minutes, rather than seconds or fractions of a second, which is a huge and valuable step towards a practical working quantum computer. And the technique should be extensible to the readout of the state of single phosphorus atoms, as well as being suitable to other donor atoms.

Compared with this, the achievement of the other team reported in the same issue of
Science
may seem at first sight less impressive. Using a sample of pure carbon (essentially, diamond) rather than silicon, a joint US-German-British team achieved a decoherence time of just over one second. But they did so at room temperature, reading out from a single quantum system, and they make a reliable estimate, based on cautious extrapolation from the existing technology, that “quantum storage times” exceeding a day should be possible. That really would be a game changer.

In these experiments, crystals of diamond made from
99.99 percent pure carbon-12 (which, like silicon-28, has no net nuclear spin) were grown by depositing them from a vapor. Like a silicon atom, each carbon atom can bond with four neighbors. But such crystals contain a few defects known as nitrogen-vacancy (N-V) centers. In such a defect, one carbon atom is replaced by a nitrogen atom, which comes from the air; but since each nitrogen atom can only bond with three carbon atoms there is a gap (the vacancy) where the bond to the fourth next-door carbon atom ought to be. In effect, this vacancy contains two electrons from the nitrogen atom and one from a nearby carbon atom, which exist in an electron spin resonance (ESR) state. N-V centers absorb and emit red light, so they interact with the outside world and can be used as readouts of the quantum state of anything they interact with at the quantum level—the fifth of the DiVincenzo criteria—or as a means of making inputs to the system. The bright red light associated with N-V centers also makes it easy to locate them in the crystal.

The “anything” the N-V center interacts with in these experiments is a single atom of carbon-13, which has overall nuclear spin, located one or two nanometers away. At this distance, the coupling between the carbon-13 nucleus and the ESR associated with the N-V center (another example of the hyperfine interaction at work) is strong enough to make it possible to prepare the nucleus in a specified quantum spin state and to read the state back, but not strong enough to cause rapid decoherence. For the concentration of carbon-13 used in the experiments, about 10 percent of all the naturally occurring N-V centers had a carbon-13 nucleus the right distance away to be useful; but each measurement involved just a single N-V center interacting with a single carbon-13
nucleus. Other experiments have shown that it is possible to entangle photons with the electronic spin state of N-V centers, providing another way of linking the nuclear memory to the outside world, potentially over long distances.

The storage time achieved in these experiments was 1.4 seconds. But even using simple refinements, such as reducing the concentration of carbon-13 to decrease the interference caused by unwanted interactions, it should be possible to extend this by more than 2,500 times, to an hour or so; from there it will be a relatively smaller step, using techniques pioneered in other fields, to go up by another factor of 25 to get nuclear spin memories that last for more than a day, at room temperature. But proponents of quantum computing are still far from putting all their eggs in one basket, attractive as this one might be. Even the NMR approach, which is now almost ancient history by the standards of the field, is still providing potentially useful insights.

THE NUTS AND BOLTS OF NMR

In the
previous chapter
, I got a little ahead of myself by describing the exciting first results of quantum computation using nuclear magnetic resonance, the first successful quantum computation technique, without really explaining the fundamental basis of NMR. It is time to redress the balance.

Atomic nuclei are made up of protons and neutrons.
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The simplest nucleus, that of hydrogen, consists of a single proton; the next element, helium, always has two protons in the nucleus, but may have either one or two neutrons; these varieties are known as helium-3 and helium-4, respectively, from the total number of particles (nucleons) in the nucleus.
Going on up through heavier chemical elements, the very pure form of silicon used by Michelle Simmons and her colleagues is a variety (isotope) known as silicon-28, because it has 28 nucleons (14 protons and 14 neutrons) in the nucleus of each atom. Another isotope, silicon-29, has 14 protons and 15 neutrons in each nucleus. The crucial distinction, for the purposes of quantum computation, is the difference in spin between nuclei with an even number of nucleons and nuclei with an odd number of nucleons.