Physicists Reveal New Understanding of Quantum Mechanics in Circuits

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Theoretical physicist Jens Koch tilts the tiny object on his fingertip to reveal a meandering line — a resonator for microwave photons — and pinhead-sized superconducting qubit.

“It’s quantum mechanics on a chip,” says Koch, physics and astronomy and a member of the Center for Applied Physics and Superconducting Technologies (CAPST).

Quantum mechanics is typically associated with microscopic particles, such as atoms, electrons, or photons. However, within the past 20 years the field’s undergone a revolution in how people think about it. As first proposed by Nobel-Prize winning physicist Anthony Leggett, quantum mechanics also applies to macroscopic objects, such as circuits composed of aluminum wires and microwave resonators. As a postdoctoral fellow at Yale, Koch was involved in the discovery of two quantum circuits that are widely used in laboratories around the world, including by researchers at Google, IBM, and many other groups racing to build superconducting-based quantum computers.

Still, there was still an ambiguity in the development of quantum mechanics for electrical circuits. The problem was that when physicists introduced time-dependent magnetic flux into the circuit — a means to tune or change energy levels within the superconductor — application of the existing theory could lead to contradictory results. Although experiments were successful, the theoretical description — known as circuit quantization — was not particularly clear and there were discrepancies in the published literature, which the Northwestern research team discovered and sought to rectify.

“Our new paper goes through a careful analysis of how to resolve these inconsistencies and properly quantize the circuit in the presence of time-dependent flux,” says James Sauls, physics and astronomy, CAPST codirector, and coauthor of the paper with Koch and Northwestern graduate student Xinyuan You. “This discovery is not only a significant advance in the formulation of the quantum theory of electrical circuits, but it marks another step in the evolution of theoretical quantum mechanics.”

Published May 21 in Physical Review, the manuscript reports the first  research from the new quantum initiative of CAPST, a collaborative venture between Northwestern University and the Department of Energy’s Fermi National Accelerator Laboratory.

Quantum Mechanics You Can ‘See’

The chip Koch displayed is a simple example of quantum mechanics, but one that an experimentalist might place in a specialized apparatus known as a dilution refrigerator, where it is cooled to temperatures as low as 10 millikelvin, or -459.7°F.

“At that temperature, these circuits behave more like atoms than classical circuits,” says Koch, a renowned physicist in the area of circuit quantization development. “They have discrete energy levels and physicists have only fairly recently learned that circuits composed of macroscopic components — inductors, capacitors, Josephson junctions — can be fully governed by the laws of quantum mechanics.”

The discovery that macroscopic entities adhered to the principals of quantum mechanics proved to be revolutionary for the field. The new circuit quantization theory developed at CAPST enhances it in a critical way.

Superconducting Circuits

Superconducting circuits are electrical circuits fabricated from superconducting materials. Due to the flexibility in circuit design, such circuits hold substantial promise as qubits, Sauls says.

In quantum computing, a qubit is the basic unit of information — the quantum version of the classical binary bit. In a classical system, a bit would have to be in either one state or the other, but quantum mechanics allows the qubit to be in all states simultaneously, a property fundamental to quantum mechanics and quantum computing.

Many of the superconducting circuits used as qubits to date are sensitive to magnetic fields. For instance, the energy levels of the qubit may change when an experimentalist tunes the value of a magnetic field. “The appropriate way to quantify how a magnetic field will influence the circuit is magnetic flux, which measures the strength of the magnetic field integrated over the circuit area,” says Koch.

The new theory provides a significant advance in the ability to handle real circuits, which invariably have flux noise present, says Sauls. The project — which took about a year to complete — was borne out of Koch’s collaborations with David Schuster at the University of Chicago. Those efforts were recently bolstered by Northwestern’s inclusion in the multi-institutional Chicago Quantum Exchange as well as the University’s launch of the Initiative at Northwestern for Quantum Information Research and Engineering (INQUIRE), which was created as an effort to bridge multiple academic domains, bringing together faculty research groups and labs pursuing quantum science and engineering from the University’s Physics, Chemistry, Materials Science & Engineering, Electrical & Computer Engineering, and Computer Science Departments. Page 1 of 2

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