Electron charge qubit with 0.1 millisecond coherence time Xianjing Zhou1 2Xinhao Li1Qianfan Chen1Gerwin Koolstra3Ge Yang4 5Brennan Dizdar6Yizhong Huang2Christopher S. Wang6Xu Han1 2Xufeng Zhang7David I. Schuster2 6 8 and Dafei Jin1 2 9

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Electron charge qubit with 0.1 millisecond coherence time

Xianjing Zhou,1, 2, ∗Xinhao Li,1, ∗Qianfan Chen,1Gerwin Koolstra,3Ge Yang,4, 5 Brennan Dizdar,6Yizhong

Huang,2Christopher S. Wang,6Xu Han,1, 2 Xufeng Zhang,7David I. Schuster,2, 6, 8, †and Dafei Jin1, 2, 9, ‡

1Center for Nanoscale Materials, Argonne National Laboratory, Lemont, Illinois 60439, USA

2Pritzker School of Molecular Engineering, University of Chicago, Chicago, Illinois 60637, USA

3Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA

4The NSF AI Institute for Artiﬁcial Intelligence and Fundamental Interactions, USA

5Computer Science and Artiﬁcial Intelligence Laboratory, Massachusetts Institute of Technology, Cambridge,

Massachusetts 02139, USA

6James Franck Institute and Department of Physics, University of Chicago, Chicago, Illinois 60637, USA

7Department of Electrical and Computer Engineering, Northeastern University, Boston, Massachusetts 02115, USA

8Department of Applied Physics, Stanford University, Stanford, California 94305, USA

9Department of Physics and Astronomy, University of Notre Dame, Notre Dame, Indiana 46556, USA

(Dated: 21 February 2023)

Electron charge qubits are compelling candidates for solid-state quantum computing because of their inherent

simplicity in qubit design, fabrication, control, and readout. However, all existing electron charge qubits,

built upon conventional semiconductors and superconductors, suﬀer from severe charge noise that limits the

coherence time to the order of 1 microsecond. Here, we report our experimental realization of ultralong-

coherence electron charge qubits, based upon isolated single electrons trapped on an ultraclean solid neon

surface in vacuum. Quantum information is encoded in the motional states of an electron that is strongly

coupled with microwave photons in an on-chip superconducting resonator. The measured relaxation time T1

and coherence time T2are both on the order of 0.1 milliseconds. The single-shot readout ﬁdelity without using

a quantum-limited ampliﬁer is 98.1%. The average single-qubit gate ﬁdelity using Cliﬀord-based randomized

benchmarking is 99.97%. Simultaneous strong coupling of two qubits with the same resonator is demonstrated,

as a ﬁrst step toward two-qubit entangling gates for universal quantum computing. These results manifest

that the electron-on-solid-neon (eNe) charge qubits outperform all existing charge qubits to date and rival

state-of-the-art superconducting transmon qubits, oﬀering an appealing platform for quantum computing.

Quantum bits (qubits) are the fundamental building

blocks in quantum information processing. A key

measure of a qubit’s performance is its coherence time,

which describes how long a superposition between two

quantum states |0iand |1ican persist 1. Among

a handful of on-chip solid-state qubits today 2,3, a

coherence time on the order of 0.1 ms or longer

has only been achieved in semiconductor quantum-

dot and donor qubits based on electron spins 4–7,

and superconducting transmon and ﬂuxonium qubits

based on capacitively and inductively shunted Josephson

junctions 8–11. By contrast, the coherence time in

the traditional semiconductor quantum-dot qubits and

superconducting Cooper-pair-box (CPB) qubits based on

electron charges (motional states) is at most on the order

of 1 µs4,12. Given that a typical gate time is around

10 ns in such systems, in order to make electron charge

qubits serious contenders for quantum computing, it is

imperative to increase their coherence time to at least

the order of 0.1 ms, that is, a &104ratio between the

coherence and gate times 13.

The short coherence time for conventional electron

charge qubits is commonly recognized as a result

of their high sensitivity to environmental noise, e.g.,

charge ﬂuctuations in ordinary host materials 7,14.

Nonetheless, if their coherence time can be substantially

prolonged, electron charge qubits will possess unique

advantages: (i) They can be conveniently designed and

fabricated with no need of spin-puriﬁed substrates 6or

patterned micromagnets 15, signiﬁcantly reducing the

manufacturing cost 16. (ii) They can be fully electrically

controlled with no involvement of magnetic ﬁelds 17,

intrinsically eliminating the compatibility issues between

magnetic ﬁelds and superconducting circuits 18,19. (iii)

They can be individually addressed and readout by

microwave photons owing to the much stronger coupling

between an electric dipole and electric ﬁeld than a

magnetic dipole and magnetic ﬁeld 4,20, fundamentally

avoiding the complexities of high microwave power 21 or

spin-charge conversion 15,22.

In this paper, we report our experimental realization

of unconventional electron charge qubits with 0.1 ms

long coherence time, based upon single electrons trapped

on a solid neon surface 23. Neon (Ne), as a noble-gas

element, is inert against forming chemical bonds with

any other elements. In a low-temperature and near-

vacuum environment, it spontaneously condenses into an

ultrapure semi-quantum solid 24 devoid of any two-level-

system (TLS) ﬂuctuators, quasiparticles, or dangling

bonds that are present in most ordinary materials 17,25.

Its small atomic polarizability and negligible spinful

isotopes make it akin to vacuum with minimal charge

and spin noise for electron qubits 24,26. By integrating

an electron trap in a superconducting quantum circuit,

the charge (motional) states of an electron can be

controlled and readout by microwave photons in an

on-chip resonator. Our previous demonstration of the

electron-on-solid-neon (eNe) qubit platform has shown

arXiv:2210.12337v2 [quant-ph] 19 Feb 2023

an appreciable relaxation time T1of 15 µs and coherence

time T2of 220 ns 23.

Here we successfully extend both T1and T2into 0.1 ms

time scale by making three critical advancements: (i)

annealing solid Ne to pursue the best surface quality, (ii)

stabilizing the electron trapping potential to ensure the

lowest (<10 Hz) background noise, and (iii) operating

the qubit at charge-noise-insensitive (sweet) spots. With

0.1 ms long coherence time, we manage to perform

single-shot readout of the qubit states 27 and obtain

a 98.1 % readout ﬁdelity without using a quantum-

limited ampliﬁer. This is on par with the readout

ﬁdelity of the state-of-the-art transmon qubits with a

similar ampliﬁcation chain 27,28. We further manage

to perform Cliﬀord-based randomized benchmarking 29

and obtain an average single-qubit gate ﬁdelity of

99.97 %, which is well above the fault-tolerance threshold

for quantum error correction with surface codes 30.

Moreover, we manage to simultaneously couple two

electron qubits with the same resonator, as a ﬁrst step

toward two-qubit entangling gates for universal quantum

computing 31. These results manifest that the eNe

charge qubits outperform all traditional semiconductor

and superconducting charge qubits and rival the best

superconducting transmon qubits today.

Qubit design

The eNe qubit is situated in an electron trap in

a niobium (Nb) superconducting quantum circuit that

is fabricated on an intrinsic silicon (Si) substrate, as

shown in Fig. 1a. A channel of 3.5 µm in width and

1µm in depth is etched into the substrate. A quarter-

wavelength double-stripline microwave resonator runs on

the bottom through the channel. A dc electrode, called

the trap, also runs on the bottom, but from the other

end of the channel into the open end of the resonator.

The channel, resonator, and trap are all deformed into

oval shapes in the trapping region to accommodate the

desired functionalities as described below. On the ground

plane outside the channel, four additional dc electrodes,

made into two pairs and called the resonator-guards and

trap-guards respectively, surround the trapping region.

The dc bias voltages applied to these dc electrodes, as

well as the resonator with a tuning-fork structure 32,

tune the trapping potential. We ensures the lowest

charge noise from our apparatus by using an ultra-

stable high-precision digital-to-analog converter (DAC)

at room temperature and lowpass ﬁlters with 10 Hz cutoﬀ

frequency at mK temperature.

The qubit states |0iand |1iare deﬁned by the

electron’s motional (charge) states, i.e., the ground

state |giand the ﬁrst excited state |eirespectively, in

the y-direction across the channel. The electric dipole

transition between |giand |eistrongly couples with the

electric ﬁeld, which points from one stripline to the

other, of the microwave photons in the antisymmetric

(diﬀerential) mode of the resonator 23,32. The bare

resonator frequency, deﬁned after neon ﬁlling but before

electron-photon coupling, is ωr/2π=fr= 6.4262 GHz.

The resonator linewidth is κ/2π= 0.46 MHz, which is

dominated by the input and output photon coupling. All

the microwave measurements are done in a transmission

conﬁguration through the resonator.

We ﬁll a controlled amount of liquid Ne into the sample

cell, using a homemade gas-handling puﬀ system, to wet

the channel and quantum circuit at around 26 K. We cool

the system down along the liquid-vapor coexistence line

and turn the liquid into solid by passing the solid-liquid-

gas triple point at the temperature Tt= 24.6 K and

pressure Pt= 0.43 bar 33. We hold the temperature at

10 K for 1 – 2 hours to anneal the solid and smooth out

the surface 34, and then continuously cool down to the

base temperature around 10 mK for experiments. The

thickness of solid Ne that covers the trapping region

is estimated to be tens of nanometers. Electrons are

emitted from a heated tungsten ﬁlament above the

quantum circuit and are trapped on the solid Ne surface

under the combined actions of natural surface potential

and applied electric potential 23,24,35,36.

Qubit spectroscopy

We ﬁrst verify the strong coupling between a trapped

single electron and microwave photons in the circuit

quantum electrodynamics (cQED) architecture (see

Methods). By varying the resonator-guard voltage Vrg

and keeping all other voltages ﬁxed, we tune the qubit

frequency fqacross fr. The normalized transmission

amplitude (A/A0)2through the resonator is plotted in

Fig. 1b. Two avoided crossings, known as the vacuum

Rabi splitting, can be clearly seen. A line cut in Fig. 1b at

the on-resonance condition fq=fr, marked by the pink

arrows, is plotted in Fig. 1c. By ﬁtting the curve with

the input-output theory, we obtain the electron-photon

(qubit-resonator) coupling strength g/2π= 2.3 MHz,

and the on-resonance qubit linewidth γ/2π= 0.36 MHz.

The fact that g > κ > γ indicates that the qubit

and resonator are strongly coupled. In this vacuum

Rabi splitting measurement, the average intra-resonator

photon number ¯nis kept below 1, as can be veriﬁed by

the ac Stark eﬀect 37 (see Methods).

We use two-tone qubit spectroscopy to reveal the qubit

spectrum tuned by Vrg , as plotted in Fig. 1d. The

dependence of fqon Vrg can be identiﬁed as the white

curve, where the drive frequency fdhits fqand induces

a sudden phase shift. The spectrum suggests that fq

is nearly a quadratic function of Vrg and contains a

minimum at the so-called charge sweet spot, as indicated

by the yellow arrow. On this spot, where fq=fss =

6.3915 GHz and Vrg =Vss =−270 mV, the charge

qubit is ﬁrst-order insensitive to the low-frequency charge

noise and holds the longest coherence time along the

spectrum 38.

State control and readout

We perform real-time state control and readout on the

eNe qubit in the dispersive regime. Rabi oscillations 39

are observed by driving the qubit on the sweet spot, using

Gaussian-shaped microwave pulses with ﬁxed frequency

fqand amplitude Apulse, and variable pulse duration

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Electronchargequbitwith0.1millisecondcoherencetimeXianjingZhou,1,2,*XinhaoLi,1,*QianfanChen,1GerwinKoolstra,3GeYang,4,5BrennanDizdar,6YizhongHuang,2ChristopherS.Wang,6XuHan,1,2XufengZhang,7DavidI.Schuster,2,6,8,andDafeiJin1,2,9,1CenterforNanoscaleMaterials,ArgonneNationalLaboratory,Lemont,Illinois...

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Electron charge qubit with 0.1 millisecond coherence time Xianjing Zhou1 2Xinhao Li1Qianfan Chen1Gerwin Koolstra3Ge Yang4 5Brennan Dizdar6Yizhong Huang2Christopher S. Wang6Xu Han1 2Xufeng Zhang7David I. Schuster2 6 8 and Dafei Jin1 2 9.pdf

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Electron charge qubit with 0.1 millisecond coherence time Xianjing Zhou1 2Xinhao Li1Qianfan Chen1Gerwin Koolstra3Ge Yang4 5Brennan Dizdar6Yizhong Huang2Christopher S. Wang6Xu Han1 2Xufeng Zhang7David I. Schuster2 6 8 and Dafei Jin1 2 9

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