Computing with Quantum Cats

by John Gribbin

  LEGGETT AND THE SQUID

  My own introduction to SQUIDs came in the 1970s, through my contacts at the University of Sussex, where Tony Leggett, a leading low-temperature physicist and later Nobel Prize winner, was then working. Leggett's unusual route to a Nobel Prize in physics is worth reporting. He was born into a Catholic family in Camberwell, South London, in 1938, the eldest of five children (he had two sisters and two brothers). The family soon moved to Upper Norwood, where he attended a Catholic elementary school before moving on to the College of the Sacred Heart in Wimbledon. Then, at the end of the 1940s, when his father got a job teaching physics and chemistry at a Jesuit school (Beaumont College) in Windsor, all three of the Leggett boys were allowed free tuition there, and the family moved to Staines, near the modern site of Heathrow Airport. In line with normal practice at the time, at the age of thirteen Tony had to choose which academic path to follow—classics, modern languages, or mathematics and science. As was also the practice at the time, the brightest pupils were steered towards classics, science being regarded as somewhat beyond the pale. So, in spite of his father's position, Tony became a classics scholar, studying Latin and Greek languages and literature. Even here, among the elite, he stood out academically, and was placed in classes with boys two years older than himself, eventually winning a scholarship to Balliol College, Oxford, at the end of 1954. The scholarship was, of course, to study classics (the course usually known as Greats); but in the interval between being awarded the scholarship and going up to Oxford in the autumn of 1955, Leggett was introduced to mathematics by a retired university teacher, a priest who was living at Beaumont—more or less as a hobby to pass the time. Although Leggett was fascinated by the subject and found he had an aptitude for it, math slid into the background during a happy undergraduate career reading Greats. But near the end of the third year of the four-year course “it gradually began to dawn on me,” says Leggett, “that I could not go on being a student forever and must start looking for gainful employment.”

  The most desirable possible career seemed to be the nearest thing to a continuation of the student life—a PhD and a university lectureship. The natural choice for someone with Leggett's background would have been philosophy; but he was put off by the fact that, as it seemed to him, there was no objective truth in philosophy, no criterion of whether a piece of work is “right” or “wrong.” He wanted, he said, to work in a field where there was “the possibility of being wrong without being stupid.” The subject which fits that criterion par excellence is physics. With no formal training in the subject, but with the confidence instilled by his experience of advanced mathematics, in the summer of 1958 Leggett applied to do a second Oxford degree, this time in physics, following the completion of his Greats course in 1959. Apart from convincing the powers that be at Oxford that he could cope, there was another not inconsiderable hurdle to surmount. The next year, 1959, was to be the last of compulsory military service in the UK, and as a student Leggett would be exempt; so he had to persuade the draft board that his second undergraduate degree was not merely a ruse to escape the call-up. He is convinced that a major factor in gaining the necessary exemption was the fact that in 1957 the Soviet Union had launched the first artificial Earth satellite, Sputnik 1, and the authorities had at last woken up to the importance of directing the best brains into science and engineering rather than classics (one wonders how many potential good scientists of Leggett's generation were lost by the streaming of the brightest students into the classics). With the draft board convinced, and a new scholarship from Merton College, Leggett commenced his physics course in 1959, emerging with a first class degree and going on to postgraduate work which led to a doctorate in 1964, awarded for investigations into the behavior of superfluid liquid helium.

  By then, he was supported by a fellowship at Magdalen College, which enabled him to spend a year at the University of Illinois at Urbana-Champaign, and a year at Kyoto University in Japan. In Kyoto, he immersed himself in the culture, living in Japanese accommodation, learning the language and avoiding “foreigners”; this was so unusual in the mid-1960s that, he later learned, his colleagues decided that he must be a trainee CIA agent. After Leggett took up a lectureship at Sussex University (where our paths crossed) in 1967, he continued to travel widely to work at research establishments around the world during the vacations, including another extended visit to Japan after he married a Japanese girl (whom he had actually met at Sussex) in 1972. In 1982, two years after being elected a Fellow of the Royal Society, he was offered and accepted a professorship at Urbana-Champaign, where he was based for the rest of his career. He was awarded the Nobel Prize in 2003 for his contributions to the theory of superconductors and superfluids, and knighted in 2004. “Above all,” he says, “I have worked on the theory of experiments to test whether the formalism of quantum mechanics will continue to describe the physical world as we push it up from the atomic level towards that of everyday life,” and he encapsulates this enterprise in his description of a SQUID-based device that acts like “Schrödinger's cat in the laboratory.”

  Common sense would tell us that in a SQUID ring, an electric current could flow one way or the other around the ring, but not both ways at once. Quantum physics says that the ring could exist in a superposition of states, like Schrödinger's cat, one corresponding to a clockwise current and one corresponding to a counterclockwise flow. This is not the same as saying that there are two separate currents, with one stream of electrons going one way and one stream going the other way; the whole ring, a visible, macroscopic object, is in a superposition. Theorists such as Leggett calculated that this situation should produce a measurable effect, described as a “splitting” of energy levels in the system. At the beginning of the twenty-first century, just such an effect was observed in delicate experiments at the State University of New York at Stony Brook, and at the Technical University of Delft. Subsequent experiments have confirmed the reality of these macroscopic superpositions. As Leggett puts it, this is “strong evidence for the existence of quantum superposition of macroscopically distinct states.”

  All this has profound implications for our understanding of the nature of quantum reality. It suggests that the measurement problem cannot simply be explained (or wished) away by saying that “collapse of the wave function” occurs just because objects are macroscopic. This might lead to a whole new understanding of quantum reality. But such deep waters are not my concern here. What matters FAPP is that quantum superposition and entanglement involving SQUID rings make them candidates for use in quantum computers.

  COMPUTING WITH SQUIDs

  The advantages of using SQUIDs are that both the current and the phase5 in the ring are quantum entities which can be in a quantum superposition, making them suitable for use as qubits, while different SQUIDs can be entangled with one another. So far, experiments have been done entangling both two and three superconducting qubits, involving simple processors that are in effect solid-state quantum processors resembling conventional computer chips. This makes it possible in principle to build CNOT and other gates. Even better, coupling three qubits is particularly important for some quantum error-correction processes which were demonstrated in a three-qubit system of this kind by Yale researchers in 2012. SQUIDs have the huge advantage over atomic-scale systems that they can be “engineered” in a more or less standard, classical way, and manufactured in large numbers on chips using existing technology (they don't have to be as big as wedding rings, of course). A team at the University of California, Santa Barbara, has already managed to put nine Josephson-junction-based quantum devices on a single 6 mm by 6 mm chip, although this does not in itself function as a quantum computer.

  The disadvantages are that neither the superpositions nor the entanglements last long (nothing unique about that), and the whole thing has to be operated at very low temperatures, close to absolute zero (–273 degrees Celsius) at 0.8 degrees on the Kelvin scale. But researchers have cracked one of the key DiV
incenzo requirements of a quantum computer, by using SQUIDs to develop the quantum bus that is needed to interact with each of the qubits in the computer.

  The technique involves placing two SQUIDs in a cavity between two layers of conducting material, where microwave photons (just like the photons in a microwave oven) can bounce between the conductors. The SQUIDs can emit and absorb photons, and the way they do this is tuned by adjusting the voltage across the gap. A SQUID that absorbs a photon becomes “excited,” and if it is already excited it can be triggered to emit a photon into the cavity. This process is a specific example of the phenomenon known as resonance, and is sometimes referred to as “hybridization” of the qubit and photon states. In resonance, the SQUID switches back and forth between excited and non-excited states. In order to transfer a quantum state from one SQUID to the other, the SQUIDs are first both tuned “off resonance” and one is put in some specified quantum state. This SQUID is then tuned in resonance to the cavity, and at the appropriate moment when the quantum rules tell us that the probability of its being excited is zero, it is tuned off resonance. This leaves the photon that “belongs” to the SQUID bouncing around in the cavity. The second SQUID is then tuned into resonance, and interacts with the photon left behind by the first SQUID. At the appropriate moment this SQUID is again tuned off resonance. At that point, the quantum state of the first SQUID has been transferred to the second SQUID. This is known as “quantum optics on a chip.” It's a small step—transferring a state between a single pair of SQUIDs. But it has been done, and it is a step in the right direction, suggesting, perhaps, a specific role for SQUIDs in computers that may also incorporate other kinds of qubits.

  Perhaps significantly, IBM is making a major effort to develop superconducting quantum computer technology. Asked how long it will be before we see a practicable quantum computer, Mark Ketchen, manager of the Physics of Information group at IBM's Watson Research Center, said in 2012: “I used to think it was 50 [years away]. Now I'm thinking it's 15 or a little more. It's within reach. It's within our lifetime.”6

  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.