Computing with Quantum Cats

by John Gribbin

  There is some merit in the many-universes interpretation, in tackling the problem of how something can apparently happen far away sooner than it could without faster-than light signaling. If, in a sense, everything happens, all choices are realized (somewhere among all the parallel universes), and no selection is made between the possible results of the experiment until later (which is what one version of the many-universes hypothesis implies), then we get over this difficulty.22

  Bizarre though it may seem, this is exactly the view espoused by the man who kick-started the modern study of quantum computation in the 1980s, David Deutsch. But that story belongs in Part Three of this book.

  When someone such as Richard Feynman says that the Universe is digital, it is the same as saying that it is “quantized,” as in quantum physics. Binary digits—bits—are quantized. They can either be 0 or 1, but they cannot be anything in between. In the quantum world, everything is digitized. For example, entities such as electrons have a property known as spin. This name is an unfortunate historical accident, and is essentially just a label; you should not think of the electron as spinning like a top. An electron can have spin ½ or spin –½ but it cannot have any other value. Electrons are part of a family of what we used to think of as particles, all of which have half-integer spin–½, and so on. These are known as fermions. The other family of particles that make up the everyday world, known as bosons, all have integer spin—1, 2 and so on. But there are no in-between values. A photon, a “particle of light,” is a boson with spin 1. This kind of quantization, or digitization, applies to everything that has ever been measured in the quantum world. So it is a natural step for quantum physicists to suppose that at some tiny scale, beyond anything that can yet be measured, space and time themselves are quantized.

  The scale on which the quantization, or graininess, of space would become noticeable is known as the Planck length, in honor of Max Planck, the German physicist who, at the end of the nineteenth century, made the breakthrough which led to the realization that the behavior of light could be explained in terms of photons. The size of the Planck length is worked out from the relative sizes of the constant of gravity, the speed of light, and a number known as Planck's constant, which appears at the heart of quantum mechanics—for example, the energy of a photon corresponding to a certain frequency (or color) of light is equal to that frequency multiplied by Planck's constant. The Planck length is 0.000000000000000000000000000000001 cm, or 10–33 cm in mathematical notation. A single proton is roughly 1020 Planck lengths across,1 and it is no surprise that the effects of this graininess do not show up even in our most subtle experiments.

  The smallest possible interval of time (the quantum of time) is simply the time it would take light to cross the Planck length, and is equal to 10–43 seconds. One intriguing consequence of this is that as there could not be any shorter time, or smaller time interval, then within the framework of the laws of physics as understood today we have to say that the Universe came into existence (was “born,” if you like) with an age of 10–43 seconds. This has profound implications for cosmology, but this is not the place to go into them.

  It also has profound implications for universal quantum simulators. The important point, which Feynman emphasized in his 1981 MIT lecture, is that if space itself is a kind of lattice and time jumps discontinuously, then everything that is going on in a certain volume of space for a certain amount of time can be described in terms of a finite number of quantities—a finite number of digits. That number might be enormous, but it is not infinite, and that is all that matters. Everything that happens in a finite volume of space and time could be exactly simulated with a finite number of logical operations in a quantum computer. The situation would be very similar to the way physicists analyze the behavior of crystal lattices, and Feynman was able to show that the behavior of bosons is amenable to this kind of analysis, although in 1981 he was not able to prove that all quantum interactions could be imitated by a simulator. His work was, however, extended at MIT in the 1990s by Seth Lloyd, who proved that quantum computers can in principle simulate the behavior of more general quantum systems.

  There's another way of thinking about the digitization of the world. Many accounts of the quantum world imply, or state specifically, that the “wave” and “particle” versions are of equal status. I've said so myself. But are they? It is a fundamental feature of a wave that it is continuous; it is a fundamental feature of a particle that it is not continuous. A wave, like the ripples spreading out from a pebble dropped in a still pond, can spread out farther and farther, getting weaker and weaker all the time until, far away from the place where the pebble was dropped, the ripples can no longer be detected at all. But either a particle is there or it isn't.

  Light is often regarded as a wave, the ripples in something called an electromagnetic field. But those ripples, if they exist, do not behave like ripples in a pond. The most distant objects we can detect in the Universe are more than 10 billion light years away, and light from them has been traveling for more than 10 billion years on its way to us. It is astonishing that we can detect it at all. But what is it that we actually detect? Not a very faint ripple of a wave. Astronomers actually detect individual photons arriving at their instruments, sometimes literally one at a time. As Feynman put it, “you put a counter out there and you find ‘clunk,’ and nothing happens for a while, ‘clunk,’ and nothing happens for a while.”2 Each “clunk” is a photon. Images of faint objects can be built up over many hours by combining these photons to make a picture—in one outstanding example, an image known as the Hubble Ultra-Deep Field was built up using photons gathered over nearly a million seconds (277 hours) of observation time on the Hubble Space Telescope. The fainter the object, the fewer photons come from it each second, or each million seconds; but each photon is the same as an equivalent photon from a bright object. Red photons always have a certain energy, blue photons a different energy, and so on. But you never see half, or any other fraction, of a photon; it's all or nothing. Which is why it is possible to simulate the Universe using a digital computer (provided it is a quantum computer). “You don't find a tiny field, you don't have to imitate such a tiny field, because the world that you're trying to imitate, the physical world, is not the classical world, and it behaves differently,” said Feynman. “All these things suggest that it's really true, somehow, that the physical world is representable in a discretized way.” This is the most important insight to carry forward into our discussion of quantum computers. Quantum computers actually provide a better representation of reality than is provided by our everyday experiences and “common sense.”

  Ion trap array incorporating a junction and linear ion trap sections, used by Winfried Hensinger and colleagues to demonstrate ion transport through a junction for the first time. Such a device is an important building block for a large-scale quantum computer.

  The great appeal of the Many Worlds Interpretation of quantum mechanics (MWI) is that it avoids the problem of the collapse of the wave function, for the simple reason that the wave function never collapses. The problem with other interpretations—often known as the measurement problem—is deciding at what point between the quantum world and the everyday world the collapse occurs. This is what the Schrödinger's cat puzzle is all about. Physicists have few qualms about accepting the possibility of a radioactive atom being in a superposition of states, but we all have qualms about the cat being in such a superposition. Does the collapse happen when the detector measures the radioactive material to see if it has decayed? Or is the cat's consciousness necessary to make the collapse happen? Could an ant be “aware” enough to cause the collapse? Or a bacterium? These are not facetious questions, because larger and larger molecules have been sent through the experiment with two holes and behaved in line with quantum mechanics; there is even talk of doing it with molecules of DNA, if not yet with bacteria or cats. John Bell highlighted the ludicrousness of trying to apply the Copenhagen Interpretation to the
Universe as a whole:

  Was the world wave function waiting to jump for thousands of millions of years until a single-celled living creature appeared? Or did it have to wait a little longer for some more highly qualified measurer—with a PhD? If the theory is to apply to anything but idealized laboratory operations, are we not obliged to admit that more or less “measurement-like” processes are going on more or less all the time more or less everywhere?1

  EVERETT SETS THE SCENE

  The Many Worlds Interpretation avoids these difficulties by saying, for example, that in the case of the cat in the box there are two universes, one with a dead cat and one with a live cat; and similarly in other situations, every quantum possibility is realized. In the mid-1950s the American researcher Hugh Everett III put the MWI on a proper mathematical footing, and showed that for all practical purposes it is exactly equivalent to the Copenhagen Interpretation. Since this meant it made no difference to their calculations, most practicing quantum mechanics ignored it. Unfortunately, there was a flaw in Everett's presentation of the idea which meant that even the few theorists who did think about the implications also found it hard to take seriously.

  Everett described the many worlds of his model in terms of splitting. In the case of Schrödinger's cat, this would mean that in the course of the “experiment” we start out with a single cat in a single universe (or world) and that the world then splits into two, one with a live cat and one with a dead cat. Everett used a different analogy, at least in the first draft of his idea, which he showed to his supervisor at Princeton, John Wheeler, in the autumn of 1955. He used the word “splitting,” and made an analogy with the splitting of an amoeba. You start with one amoeba, and then have two, each of which, if it had a memory, would remember the same experiences, or history, up to the point of the split. At that point, the two individuals go their separate ways, eventually to split again, and their offspring split in their turn, and so on. Wheeler “persuaded” Everett to leave the amoeba analogy out of his PhD thesis and the published version of his work, which appeared in the journal Reviews of Modern Physics in 1957. But Everett did say in print that “no observer will ever be aware of any ‘splitting’ process,” and clearly had the idea of one “history” branching repeatedly as time progressed.2 This was spelled out by Bryce DeWitt, an enthusiastic supporter of Everett's idea, who wrote: “Every quantum transition taking place in every star, in every galaxy, in every remote corner of the universe is splitting our local world on Earth into myriad copies of itself.” Or, as John Bell put it: “Quite generally, whenever there is doubt about what can happen, because of quantum uncertainty, the world multiplies so that all possibilities are actually realized. Persons of course multiply with the world, and those in any particular branch would experience only what happens in that branch.”3

  Again, the language is that of branching and multiplication of worlds by splitting. Bell is not enthusiastic, but, almost in spite of himself, does not dismiss the idea out of hand:

  The “many worlds interpretation” seems to me an extravagant, and above all an extravagantly vague, hypothesis. I could almost dismiss it as silly. And yet…It may have something distinctive to say in connection with the “Einstein Podolsky Rosen puzzle,” and it would be worthwhile, I think, to formulate some precise version of it to see if this is really so. And the existence of all possible worlds may make us more comfortable about the existence of our own world…which seems to be in some ways a highly improbable one.4

  Although Wheeler was initially enthusiastic about Everett's idea, as the years passed he developed qualms. Two decades later, he said: “I confess that I have reluctantly had to give up my support of that point of view in the end—much as I advocated it in the beginning—because I am afraid it carries too great a load of metaphysical baggage.”5 It seems to me to carry a lesser load of metaphysical baggage than the idea of the collapse of the wave function, even in this imperfect form. But there is a more serious objection to Everett's version of MWI than metaphysics.

  For the Everett MWI seems to contain the same flaw, the measurement problem, as the Copenhagen Interpretation itself. It's just that in one case the measurement puzzle refers to the moment of collapse, and in the other it refers to the moment of splitting. This might look like the death knell for the idea, at least as an alternative to the Copenhagen Interpretation; but Everett (and Wheeler, DeWitt and other supporters of the idea) missed a trick.

  I confess that I missed the same trick, long ago, although I had fewer qualms than Bell about espousing the MWI, which I enthusiastically endorsed in my book In Search of Schrödinger's Cat. But someone who did not miss this trick was Schrödinger himself, as I learned to my surprise when writing his biography.

  SOLVING THE MEASUREMENT PROBLEM

  In 1952, Schrödinger published a scientific paper entitled “Are There Quantum Jumps?” Arguing that there is no reason for a quantum superposition to collapse just because we look at it, or because it is measured, he said that “it is patently absurd to let the wave function be controlled in two entirely different ways, at times by the wave equation, but occasionally by direct interference of the observer, not controlled by the wave equation.” His solution was that the wave function does not collapse, and no choice is ever made between a superposition of states. Although Schrödinger himself—perhaps surprisingly—never pointed out the implications in terms of his famous cat puzzle, this neatly demonstrates the point he is making: in effect, he is saying that in the cat experiment, the wave functions leading to the “dead cat” and the “live cat” are equally real, and remain so both before and after the box is opened. In everyday language, there are two parallel worlds, one with a live cat and one with a dead cat; and—this is the crucial point—there always were two worlds, each starting out with a live cat but becoming different when one of the cats, but not the other, dies. There is no splitting, and no measurement problem. For once, the popular term “parallel worlds” is the most apt, and removes the image of branching realities from our minds. The two worlds (or universes) have identical histories up until the point where the experiment is carried out, but in one universe the cat lives and in the other the cat dies. They are like parallel lines, running alongside each other. And running on either side of those two parallel worlds are more parallel worlds, each slightly different from its immediate neighbors, with close neighbors having very similar histories and widely separated universes differing more significantly from one another. This is not, strictly speaking, an “interpretation” at all; it is, as Schrödinger pointed out, what the equations tell us. It is the simplest way to understand those equations. If we ever did an experiment like the one Schrödinger envisaged, we would not be forcing the universe to split into multiple copies of itself, but merely finding out which reality we inhabit.

  The response of the few people who noticed this idea at the time was summed up rhetorically by Schrödinger himself in a talk he gave in Dublin in 1952. I have quoted it before, but it is surely worth quoting again:

  Nearly every result [the quantum theorist] pronounces is about the probability of this or that or that…happening—with usually a great many alternatives. The idea that they may not be alternatives but all really happen simultaneously seems lunatic to him, just impossible. He thinks that if the laws of nature took this form for, let me say, a quarter of an hour, we should find our surroundings rapidly turning into a quagmire, or sort of a featureless jelly or plasma, all contours becoming blurred, we ourselves probably becoming jelly fish. It is strange that he should believe this. For I understand he grants that unobserved nature does behave this way—namely according to the wave equation. The aforesaid alternatives come into play only when we make an observation—which need, of course, not be a scientific observation. Still it would seem that, according to the quantum theorist, nature is prevented from rapid jellification only by our perceiving or observing it…it is a strange decision.

  All of this has led me to change my view on the nature of quant
um reality. As Bell's theorem and the experiments described in Chapter 4 make clear, the world is either real but non-local, or local, but not real. In In Search of Schrödinger's Cat, I came down in favor of locality, and concluded (echoing John Lennon) that “nothing is real,” at least until it is measured. Now, I am inclined to accept non-locality, with the corollary that the world is real—or rather, that the many worlds are all real. Not “nothing is real,” but “everything is real,” since wave functions never collapse.6

  If Everett had been aware of Schrödinger's views when he came up with his own version of MWI a few years later, he could have produced an even more satisfactory package of ideas than he did. But it is still unlikely that many people would have taken it very seriously until the experimental proof of Bell's theorem had arrived. Schrödinger's insight languished in obscurity for more than thirty years, and when David Deutsch elaborated the modern version of the Many Worlds Interpretation in the 1980s he did so without drawing directly on this aspect of Schrödinger's work—indeed, without being aware of Schrödinger's contribution to MWI.

  THE WORLDS OF DEUTSCH

  David Deutsch is an unusual physicist with unconventional habits. Although he doesn't like too much attention being given to his eccentricities, since he feels this may divert attention from the underlying importance of his work, and might be taken as implying (incorrectly) that you have to be weird to be creative, the stories are as irresistible (if as irrelevant) as those about Einstein not wearing socks or Turing's bicycle chain. Deutsch lives in an ordinary, rather unkempt-looking house in a suburb of Oxford, and as I discovered the visitor has to be prepared to negotiate their way from the front door past piles of boxes and papers to the darkened room, dominated by computer screens, in which he works. The curtains are almost invariably drawn shut, and Deutsch tends to work at night and sleep (a little) in the day—lunchtime is typically around 8 pm, followed by a solid twelve hours’ work. Although he is affiliated with the Center for Quantum Computation at Oxford's Clarendon Laboratory, and is a non-stipendiary visiting professor of physics, Deutsch has no paid academic post, living off lecturing and writing (plus the proceeds of various prizes he has been awarded7); colleagues are more likely to encounter him at an international meeting in some far-off land than among the dreaming spires of Oxford.