Building a modular architecture with superconducting quantum computing chips is one of the means to achieve qubit scalability, allowing the screening, selection, replacement, and integration of individual qubit modules into large quantum systems. However, the nondestructive replacement of modules within a compact architecture remains a challenge. Liquid metals, specifically gallium alloys, can be alternatives to solid-state galvanic interconnects. This is motivated by their self-healing, self-aligning, and other desirable fluidic properties, potentially enabling the nondestructive replacement of modules at room temperatures, even after operating the entire system at millikelvin regimes. In this study, we present coplanar waveguide resonators (CPWRs) interconnected by gallium alloy droplets, achieving high internal quality factors up to nearly one million and demonstrating performance on par with the continuous solid-state CPWRs. Leveraging the desirable fluidic properties of gallium alloys at room temperature and their compact design, we envision a modular quantum system enabled by liquid metals.
REFERENCES
1.
S.
Bravyi
,
A. W.
Cross
,
J. M.
Gambetta
,
D.
Maslov
,
P.
Rall
, and
T. J.
Yoder
, “
High-threshold and low-overhead fault-tolerant quantum memory
,” Nature
627
, 778
–782
(2024
).2.
D.
Rosenberg
,
D.
Kim
,
R.
Das
,
D.
Yost
,
S.
Gustavsson
,
D.
Hover
,
P.
Krantz
,
A.
Melville
,
L.
Racz
,
G.
Samach
et al, “
3D integrated superconducting qubits
,” npj Quantum Inf.
3
, 42
(2017
).3.
D.-R. W.
Yost
,
M. E.
Schwartz
,
J.
Mallek
,
D.
Rosenberg
,
C.
Stull
,
J. L.
Yoder
,
G.
Calusine
,
M.
Cook
,
R.
Das
,
A. L.
Day
et al, “
Solid-state qubits integrated with superconducting through-silicon vias
,” npj Quantum Inf.
6
, 59
(2020
).4.
A.
Gold
,
J.
Paquette
,
A.
Stockklauser
,
M. J.
Reagor
,
M. S.
Alam
,
A.
Bestwick
,
N.
Didier
,
A.
Nersisyan
,
F.
Oruc
,
A.
Razavi
et al, “
Entanglement across separate silicon dies in a modular superconducting qubit device
,” npj Quantum Inf.
7
, 142
(2021
).5.
C.
Conner
,
A.
Bienfait
,
H.-S.
Chang
,
M.-H.
Chou
,
É.
Dumur
,
J.
Grebel
,
G.
Peairs
,
R.
Povey
,
H.
Yan
,
Y.
Zhong
et al, “
Superconducting qubits in a flip-chip architecture
,” Appl. Phys. Lett.
118
(23
), 232602
(2021
).6.
S.
Kosen
,
H.-X.
Li
,
M.
Rommel
,
D.
Shiri
,
C.
Warren
,
L.
Grönberg
,
J.
Salonen
,
T.
Abad
,
J.
Biznárová
,
M.
Caputo
et al, “
Building blocks of a flip-chip integrated superconducting quantum processor
,” Quantum Sci. Technol.
7
, 035018
(2022
).7.
P.
Zhao
,
Y.
Zhang
,
G.
Xue
,
Y.
Jin
, and
H.
Yu
, “
Tunable coupling of widely separated superconducting qubits: A possible application toward a modular quantum device
,” Appl. Phys. Lett.
121
(3
), 032601
(2022
).8.
J.
Niu
,
L.
Zhang
,
Y.
Liu
,
J.
Qiu
,
W.
Huang
,
J.
Huang
,
H.
Jia
,
J.
Liu
,
Z.
Tao
,
W.
Wei
et al, “
Low-loss interconnects for modular superconducting quantum processors
,” Nat. Electron.
6
, 235
–241
(2023
).9.
R. N.
Das
,
J.
Yoder
,
D.
Rosenberg
,
D.
Kim
,
D.
Yost
,
J.
Mallek
,
D.
Hover
,
V.
Bolkhovsky
,
A.
Kerman
, and
W.
Oliver
, “
Cryogenic qubit integration for quantum computing
,” in IEEE 68th Electronic Components and Technology Conference (ECTC)
(
IEEE
, 2018
), pp. 504
–514
.10.
P.
Koppinen
,
L.
Väistö
, and
I.
Maasilta
, “
Complete stabilization and improvement of the characteristics of tunnel junctions by thermal annealing
,” Appl. Phys. Lett.
90
(5
), 053503
(2007
).11.
I. M.
Pop
,
T.
Fournier
,
T.
Crozes
,
F.
Lecocq
,
I.
Matei
,
B.
Pannetier
,
O.
Buisson
, and
W.
Guichard
, “
Fabrication of stable and reproducible submicron tunnel junctions
,” J. Vac. Sci. Technol. B
30
(1
), 010607
(2012
).12.
J. B.
Hertzberg
,
E. J.
Zhang
,
S.
Rosenblatt
,
E.
Magesan
,
J. A.
Smolin
,
J.-B.
Yau
,
V. P.
Adiga
,
M.
Sandberg
,
M.
Brink
,
J. M.
Chow
et al, “
Laser-annealing Josephson junctions for yielding scaled-up superconducting quantum processors
,” npj Quantum Inf.
7
, 129
(2021
).13.
M. D.
Dickey
, “
Stretchable and soft electronics using liquid metals
,” Adv. Mater.
29
, 1606425
(2017
).14.
L.
Ren
,
J.
Zhuang
,
G.
Casillas
,
H.
Feng
,
Y.
Liu
,
X.
Xu
,
Y.
Liu
,
J.
Chen
,
Y.
Du
,
L.
Jiang
et al, “
Nanodroplets for stretchable superconducting circuits
,” Adv. Funct. Mater.
26
, 8111
–8118
(2016
).15.
W.
Zhao
,
J. L.
Bischof
,
J.
Hutasoit
,
X.
Liu
,
T. C.
Fitzgibbons
,
J. R.
Hayes
,
P. J.
Sazio
,
C.
Liu
,
J. K.
Jain
,
J. V.
Badding
et al, “
Single-fluxon controlled resistance switching in centimeter-long superconducting gallium–indium eutectic nanowires
,” Nano Lett.
15
, 153
–158
(2015
).16.
G.
Li
,
X.
Wu
, and
D.-W.
Lee
, “
A galinstan-based inkjet printing system for highly stretchable electronics with self-healing capability
,” Lab Chip
16
, 1366
–1373
(2016
).17.
K. B.
Ozutemiz
,
J.
Wissman
,
O. B.
Ozdoganlar
, and
C.
Majidi
, “
Egain–metal interfacing for liquid metal circuitry and microelectronics integration
,” Adv. Mater. Interfaces
5
, 1701596
(2018
).18.
J.
Ma
,
F.
Krisnadi
,
M. H.
Vong
,
M.
Kong
,
O. M.
Awartani
, and
M. D.
Dickey
, “
Shaping a soft future: Patterning liquid metals
,” Adv. Mater.
35
, 2205196
(2023
).19.
N.
Lazarus
,
S. S.
Bedair
, and
I. M.
Kierzewski
, “
Ultrafine pitch stencil printing of liquid metal alloys
,” ACS Appl. Mater. Interfaces
9
, 1178
–1182
(2017
).20.
Y.-G.
Park
,
H. S.
An
,
J.-Y.
Kim
, and
J.-U.
Park
, “
High-resolution, reconfigurable printing of liquid metals with three-dimensional structures
,” Sci. Adv.
5
, eaaw2844
(2019
).21.
G.
Li
,
X.
Wu
, and
D.-W.
Lee
, “
Selectively plated stretchable liquid metal wires for transparent electronics
,” Sens. Actuators, B
221
, 1114
–1119
(2015
).22.
A.
Tabatabai
,
A.
Fassler
,
C.
Usiak
, and
C.
Majidi
, “
Liquid-phase gallium–indium alloy electronics with microcontact printing
,” Langmuir
29
, 6194
–6200
(2013
).23.
M-g
Kim
,
D. K.
Brown
, and
O.
Brand
, “
Nanofabrication for all-soft and high-density electronic devices based on liquid metal
,” Nat. Commun.
11
, 1002
(2020
).24.
Y.-W.
Wu
,
S.
Alkaraki
,
S.-Y.
Tang
,
Y.
Wang
, and
J. R.
Kelly
, “
Circuits and antennas incorporating gallium-based liquid metal
,” Proc. IEEE
111
, 955
(2023
).25.
B.
Foxen
,
J.
Mutus
,
E.
Lucero
,
R.
Graff
,
A.
Megrant
,
Y.
Chen
,
C.
Quintana
,
B.
Burkett
,
J.
Kelly
,
E.
Jeffrey
et al, “
Qubit compatible superconducting interconnects
,” Quantum Sci. Technol.
3
, 014005
(2017
).26.
I.
Besedin
and
A. P.
Menushenkov
, “
Quality factor of a transmission line coupled coplanar waveguide resonator
,” EPJ Quantum Technol.
5
(1
), 16
(2018
).27.
See https://github.com/Boulder-Cryogenic-Quantum-Testbed/scresonators for “
Boulder-cryogenic-quantum-testbed/scresonators
” (2023
).28.
M. S.
Khalil
,
M.
Stoutimore
,
F.
Wellstood
, and
K.
Osborn
, “
An analysis method for asymmetric resonator transmission applied to superconducting devices
,” J. Appl. Phys.
111
(5
), 054510
(2012
).29.
J.
Gao
, The Physics of Superconducting Microwave Resonators
(
California Institute of Technology
, 2008
).30.
A.
Bruno
,
G.
De Lange
,
S.
Asaad
,
K.
Van Der Enden
,
N.
Langford
, and
L.
DiCarlo
, “
Reducing intrinsic loss in superconducting resonators by surface treatment and deep etching of silicon substrates
,” Appl. Phys. Lett.
106
(18
), 182601
(2015
).31.
J.
Burnett
,
A.
Bengtsson
,
D.
Niepce
, and
J.
Bylander
, “
Noise and loss of superconducting aluminium resonators at single photon energies
,” J. Phys.: Conf. Ser.
969
, 012131
(2018
).32.
C. R. H.
McRae
,
H.
Wang
,
J.
Gao
,
M. R.
Vissers
,
T.
Brecht
,
A.
Dunsworth
,
D. P.
Pappas
, and
J.
Mutus
, “
Materials loss measurements using superconducting microwave resonators
,” Rev. Sci. Instrum.
91
(9
), 091101
(2020
).33.
B.
Chiaro
,
A.
Megrant
,
A.
Dunsworth
,
Z.
Chen
,
R.
Barends
,
B.
Campbell
,
Y.
Chen
,
A.
Fowler
,
I.
Hoi
,
E.
Jeffrey
et al, “
Dielectric surface loss in superconducting resonators with flux-trapping holes
,” Supercond. Sci. Technol.
29
, 104006
(2016
).34.
L.
Faoro
and
L. B.
Ioffe
, “
Internal loss of superconducting resonators induced by interacting two-level systems
,” Phys. Rev. Lett.
109
, 157005
(2012
).35.
L.
Faoro
and
L. B.
Ioffe
, “
Interacting tunneling model for two-level systems in amorphous materials and its predictions for their dephasing and noise in superconducting microresonators
,” Phys. Rev. B
91
, 014201
(2015
).36.
J. L.
Mallek
,
D.-R. W.
Yost
,
D.
Rosenberg
,
J. L.
Yoder
,
G.
Calusine
,
M.
Cook
,
R.
Das
,
A.
Day
,
E.
Golden
,
D. K.
Kim
et al, “
Fabrication of superconducting through-silicon vias
,” arXiv:2103.08536 (2021
).37.
K. D.
Crowley
,
R. A.
McLellan
,
A.
Dutta
,
N.
Shumiya
,
A. P.
Place
,
X. H.
Le
,
Y.
Gang
,
T.
Madhavan
,
M. P.
Bland
,
R.
Chang
et al, “
Disentangling losses in tantalum superconducting circuits
,” Phys. Rev. X
13
, 041005
(2023
).38.
J.
Gao
,
M.
Daal
,
A.
Vayonakis
,
S.
Kumar
,
J.
Zmuidzinas
,
B.
Sadoulet
,
B. A.
Mazin
,
P. K.
Day
, and
H. G.
Leduc
, “
Experimental evidence for a surface distribution of two-level systems in superconducting lithographed microwave resonators
,” Appl. Phys. Lett.
92
(15
), 152505
(2008
).39.
G.
Stan
,
S. B.
Field
, and
J. M.
Martinis
, “
Critical field for complete vortex expulsion from narrow superconducting strips
,” Phys. Rev. Lett.
92
, 097003
(2004
).40.
J. M.
Sage
,
V.
Bolkhovsky
,
W. D.
Oliver
,
B.
Turek
, and
P. B.
Welander
, “
Study of loss in superconducting coplanar waveguide resonators
,” J. Appl. Phys.
109
(6
), 063915
(2011
).© 2024 Author(s). Published under an exclusive license by AIP Publishing.
2024
Author(s)
You do not currently have access to this content.
