High-Coherence Fluxonium Qubit

We report superconducting fluxonium qubits with coherence times largely limited by energy relaxation and reproducibly satisfying $T_2>100\mu \mathrm{s}$ ($T_2>400\mu \mathrm{s}$ in one device). Moreover, given the state-of-the-art values of the surface loss tangent and the $1/f$ flux-noise amplitude, the coherence time can be further improved beyond 1 ms. Our results violate a common viewpoint that the number of Josephson junctions in a superconducting circuit—over $10^2$ here—must be minimized for best qubit coherence. We outline how the unique to fluxonium combination of long coherence time and large anharmonicity can benefit both gate-based and adiabatic quantum computing.

Popular Summary

The key characteristic of a superconducting quantum bit (or qubit) is coherence time, which measures how long a qubit can hold information. We report record long coherence—reaching 0.5 ms—in fluxonium, a relatively unexplored superconducting artificial atom with properties desirable for engineering fast, controllable interactions between qubits. Our work significantly expands the toolbox of quantum superconducting circuits, especially in the context of scaling up quantum processors.

A notable feature of fluxonium is that it consists of a superconducting loop interrupted by over 100 Josephson junctions, strips of insulating material a few nanometers thick sandwiched between superconducting layers. This leads to an exceptionally large value of the total inductance of the loop, which makes fluxonium distinct and useful. Having so many junctions per qubit has been generally viewed as a liability for establishing long coherence times. Yet, we conclude that even longer coherence time is likely with our design in the near future by simply upgrading our fabrication procedures to the state of the art. Our experiment thus delivers an important lesson: Complex multijunction circuits can have superior coherence when properly designed.

The reported combination of high coherence and strong anharmonicity of fluxoniums can be readily utilized for improving the fidelity of digital logical operations and constructing analog simulators of strongly interacting quantum spin models.

Figure 1

(a) Images of a single-junction fluxonium device indicating the antenna, the loop, the small junction, and the chip mounted in a copper resonator. (b) The three-element circuit model of fluxonium. (c) Implementation of a large-value inductance $L$ using a linear chain of Josephson junctions. (d),(e) The particle-in-a-box potential energy, the spectrum, and the eigenstates for the circuit model in (b) in the cases ${\varphi }_{\mathrm{ext}}=0$ (d) and ${\varphi }_{\mathrm{ext}}=\pi$ (e), which is the focus of the present work.

Figure 2

Two-tone spectroscopy transmission signal (arbitrary units) as a function of the spectroscopy frequency and flux through the loop for device $A$. The contrast is optimized piecewise to maximize the visibility of the resonances. Lines indicate a fit to the spectrum of the Hamiltonian (1). The extra resonance line crossing (not anticrossing) the qubit transition 0–1 is the red sideband of the 0–4 transition and the readout at 7.5 GHz.

Figure 3

(Top) Normalized energy relaxation time (a quantity inversely proportional to the spectral density of noise coupled to the $\varphi$ variable) as a function of the qubit transition frequency measured by tuning flux in devices $A$, $B$, $G$, $H$. (Bottom) Same quantity, including repeated in time measurements, for all devices $A–I$ biased at their half-integer flux sweet spots. Dashed lines represent a dielectric loss theory (see text).

Figure 4

(a) Coherence time $T_2$ (markers) and the qubit frequency (dashed line) as a function of the flux. Solid line indicates a prediction for the first-order coupling to a $1/f$ flux noise. (b) Gaussian echo signal away from the sweet spot (top) and an exponential echo signal at the sweet spot (bottom). (c) Interleaved measurement of temporal fluctuations of $T_1$ (blue markers) and $T_2$ (green markers) at ${\varphi }_{\mathrm{ext}}=\pi$ over a time interval of approximately 12 h.

Figure 5

Cryogenic experimental setup.