Simulations Capture A Quantum Butterfly

Using Google’s quantum chip, an international team of researchers has successfully simulated a fractal pattern known as the Hofstadter butterfly.

AsianScientist (Dec. 8, 2017) – In a collaboration between Google and researchers at universities in California, Singapore and Greece, researchers have used photons in Google’s quantum chip to simulate the surprising and beautiful pattern of the Hofstadter butterfly, a fractal structure characteristic of the behavior of electrons in strong magnetic fields. The study is published in Science.

Hofstadter’s butterfly first appeared in 1976, in calculations of electrons in a two-dimensional material within a strong magnetic field. The butterfly maps the splits and shifts of the electron’s energy levels with changes in the field strength.

In this study, the researchers used quantum simulators, which are special-purpose quantum computers, to reproduce Hofstadter’s butterfly. The feat was performed on Google’s chain of nine superconducting quantum bits (qubits) and relied on the team’s invention of a novel spectroscopy technique which they dubbed ‘hit and listen’. The technique maps the energy levels of light particles—microwave photons—stored in the nine qubits.

“Our method is like hitting a bell. The sound it makes is a superposition of all the basic harmonics. By hitting it in different positions a few times and listening to the tune long enough, one can resolve the hidden harmonics. We do the same with the quantum chip, hitting it with photons and then following its evolution in time,” explained Professor Dimitris Angelakis at the Centre for Quantum Technologies, National University of Singapore.

The researchers saw the butterfly by hitting the qubits with one photon at a time. They also hit the qubits with two photons simultaneously, and made the qubits disorderly—programming some randomness into their properties—to study the complex phenomenon known as many-body localization. This is a quantum phase transition, akin to the phase change that happens when water freezes into ice, that determines whether materials are conductors or insulators.

The team found precursors of many-body localization by applying their ‘hit and listen’ technique to different regimes of disorder and interaction. Their results highlight how a quantum simulator can reproduce all kinds of exotic complex quantum behavior. This will enable researchers to simulate and engineer materials with exotic electronic conduction properties, potentially opening up a range of new applications.

“With chips similar to the one used in this experiment, we are interested to study problems at the core of condensed matter, statistical mechanics and non-equilibrium dynamics,” said Google’s Dr. Pedram Roushan, a quantum electronics engineer.

The article can be found at: Roushan et al. (2017) Spectral Signatures of Many-body Localization with Interacting Photons.


Source: National University of Singapore.
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