Feb 28 2019
When erecting a quantum computer, errors have to be dealt with—in both senses of the term. Quantum bits ("qubits"), which can assume the logical values 0 and 1 simultaneously and so perform calculations faster, are very vulnerable to perturbations. A probable solution for this is quantum error correction, which means that each qubit is characterized "redundantly" in more than a few copies, such that faults can be detected and finally rectified without disturbing the delicate quantum state of the qubit itself.
In principle, this is very challenging. Nevertheless, several years ago, an alternative proposal was put forth in which information is not stored in numerous redundant qubits, but instead in the many oscillatory states of a single quantum harmonic oscillator. The study team of Jonathan Home, professor at the Institute for Quantum Electronics at ETH Zurich, has currently achieved such a qubit encoded in an oscillator. Their outcome has been reported in the scientific journal Nature.
Periodic oscillatory states
In Home's laboratory, PhD student Christa Flühmann and her colleagues deal with electrically charged calcium atoms that are captured by electric fields. Using suitably selected laser beams, these ions are cooled down to extremely low temperatures at which their oscillations in the electric fields (within which the ions slosh to and fro like marbles in a bowl) are described by quantum mechanics as so-called wave functions. "At that point things get exciting", says Flühmann, who is the first author of the Nature paper. "We can now manipulate the oscillatory states of the ions in such a way that their position and momentum uncertainties are distributed among many periodically arranged states."
In this case, "uncertainty" refers to Werner Heisenberg's famed formula, which stipulates that in quantum physics, the product of the measurement uncertainties of the particle’s position and velocity (more exactly: the momentum) can never go below a definite minimum. For example, if one wants to exploit the particle so as to know its position very well—physicists refer to this as "squeezing"—one automatically renders its momentum less certain.
Reduced uncertainty
Squeezing a quantum state in this manner is, on its own, only of limited value if the goal is to make exact measurements. However, there is an ingenious way out: if, on top of the squeezing, one readies an oscillatory state in which the particle’s wave function is spread over many periodically spaced positions, the measurement vagueness of each position and of the respective momentum can be smaller than Heisenberg would permit. Such a spatial distribution of the wave function—the particle can be in numerous places at once, and only a measurement decides where one really finds it—is suggestive of Erwin Schrödinger's famous cat, which is, at the same time, dead and alive.
This intensely reduced measurement uncertainty also means that the least variation in the wave function, for example, by some outside disturbance, can be established very specifically and—at least in theory—rectified.
Our realisation of those periodic or comb-like oscillatory states of the ion are an important step towards such an error detection. Moreover, we can prepare arbitrary states of the ion and perform all possible logical operations on it. All this is necessary for building a quantum computer. In a next step we want to combine that with error detection and error correction.
Christa Flühmann, PhD Student, Institute for Quantum Electronics, ETH Zurich.
Applications in quantum sensors
A few experimental hurdles have to be dealt with on the way, Flühmann confesses. The calcium ion primarily needs to be joined to another ion by electric forces, so that the oscillatory state can be read out without terminating it. Still, even in its current form the technique of the ETH scientists is of significant interest for applications, Flühmann explains: "Owing to their extreme sensitivity to disturbances, those oscillatory states are a great tool for measuring tiny electric fields or other physical quantities very precisely."