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Immunization of quantum computers against errors

In the ETH experiment, the calcium ions oscillate so that their wave functions resemble those of a comb. The measurement uncertainty can thus be distributed over many teeth of this type, which in principle allows precise detection of error. Credit: Visualizations: Christa Flühmann / Shutterstock

Building a quantum computer requires counting with errors – in more than one sense. Quantum bits, or "qubits", which can simultaneously take logical values ​​zero and one and thus perform calculations more quickly, are extremely sensitive to disturbances. One possible solution is quantum error correction, which means that each qubit is redundantly represented in multiple copies, so that errors can be detected and possibly corrected without disturbing the quantum's fragile state. -even. Technically, it is very demanding. However, several years ago, another proposal proposed to store information not in several redundant qubits, but rather in the many oscillatory states of a single quantum harmonic oscillator. The research group of Jonathan Home, professor at ETH Zurich's quantum electronics institute, has now achieved such an oscillator-encoded qubit. Their results were published in the scientific journal Nature.

Periodic oscillatory states

In Home's laboratory, Ph.D. Christa Flühmann, a student, and her colleagues work with electrically charged calcium atoms trapped by electric fields. By using appropriately selected laser beams, these ions are cooled to very low temperatures and their oscillations in the electric fields, within which the ions move like balls in a bowl, are described by mechanical quantum like functions called waves. "At this point, things become exciting," says Flühmann, the first author of the Nature paper. "We can now manipulate the oscillatory states of ions in such a way that their uncertainties about position and momentum are distributed among many states arranged periodically."

Here, "uncertainty" refers to the famous formula of Werner Heisenberg, according to which, in quantum physics, the product of the uncertainties of measuring the position and velocity (more precisely: the moment) of a particle can never go below a well-defined minimum. For example, manipulating the particle to know its position well – what physicists call it "squeezing" – requires making its momentum less certain.

Reduced uncertainty

This compression of a quantum state alone has only limited value if the objective is to carry out precise measurements. However, there is a clever solution: if, in addition to tightening, an oscillatory state is prepared in which the wave function of the particle is distributed over many periodically spaced positions, the measurement uncertainty of each position and the respective momentum can be reduced. that Heisenberg would allow. Such a spatial distribution of the wave function (the particle can be in several places at once and only one measure determines where it actually lies) recalls the famous cat Erwin Schrödinger , both dead and alive.

This greatly reduced measurement uncertainty also means that the smallest change in the wave function, for example by an external disturbance, can be determined very precisely and, at least in principle, corrected. "Achieving these periodic oscillatory or comb-shaped ion states is an important step towards such error detection," says Flühmann. "In addition, we can prepare arbitrary states of ion and perform all possible logical operations on it.All this is necessary for the construction of a quantum computer.We wish, in a next step , associate that with error detection and correction. "

Applications in quantum sensors

Flühmann admits that some experimental obstacles must be overcome along the way. The calcium ion must first be coupled to another ion by electric forces, so that the state of oscillation can be read without destroying it. Yet, even in its current form, the ETH researchers' method is of great interest for applications, says Flühmann: "Because of their extreme sensitivity to disturbances, these oscillatory states are an excellent tool for accurately measuring minute electric fields or other physical quantities. "

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More information:
Flühmann C, TL Nyuyen, Marinelli M, Negnevitsky V, Mehta K, Home J: Encoding of a qubit in a mechanical oscillator with trapped ions. Nature, February 27, 2019, DOI: 10.1038 / s41586-019-0960-6

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ETH Zurich

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