Superconducting circuits
for quantum technologies
Yasunobu Nakamura
RIKEN Center for Quantum Computing
Department of Applied Physics, Graduate School of Engineering,
The University of Tokyo

RIKEN Center for Quantum Computing (RQC)
since April 2021

2

RQC PIs

Bartosz Regula

Hayato Goto

Tomotaka Kuwahara

3

RQC research topics
Superconducting
quantum computers

Opticalquantum computers

Other quantum platforms

Siliconquantum computers

Quantum computing theory4

20th century: Century of quantum mechanics
1900 Blackbody radiation (Planck)1905 Photoelectric effect (Einstein)1913 Bohr model of atoms
1925 Matrix mechanics (Heisenberg)
1925 Wave mechanics (Schrödinger)
1928 Band theory in solids (Bloch)

Moore’s law 1965～

https://ja.m.wikipedia.org/wiki/%E3%83%95%E3%82%A1%E3%8
2%A4%E3%83%AB:AMD_EPYC_Rome_12nm_IO_die_shot_3.jpg

Fugaku@RIKEN

20th century: Century of Quantum Mechanics
21st century: Century of Quantum Information Science
Quantum Mechanics
as a fundamental principle ofphysics, chemistry, engineering, etc.
Conceptof Quantum
1900

Formulationof QM

Applicationsof QM

1950

Quantum Information Scienceat the frontier ofinformation science and technology
Birth & Growthof QIS

Applicationsof QIS

2000

2050

Here we are

Our challenge:
How far can we control quantum systems in terms ofthe number of degrees of freedom, time, speed, precision, etc.?

Schrödinger’s paradox
Macro-realism vs. Quantum mechanics
Schrödinger 1935

Dead and AliveMacroscopic quantum coherence

Leggett 1980

φ0
Superconducting loopwith a Josephson junction

Josephson effect

B. D. Josephson 1962

Number 𝒏𝒏 ⇔ Phase 𝜽𝜽
Cooper-pair tunneling-2enEEel
2EJ
n=-2 -1 0123-10

θ/π1D tight-binding model ⇒ Bloch band1Macroscopic quantum tunneling

Saturation of escape rate

Energy level quantization

J. M. Martinis, M. H. Devoret, et al. PRB 35, 4682 (1987).
R.F. Voss and R.A. Webb (IBM), PRL 47, 265 (1981); D.B. Schwarz et al. (SUNY), PRL 55, 1547 (1985).

Single-electron devices
1990s

drain
gate
island200nm

source-V/2---++++gate+Vg

0.15

drain
+V/2

current (nA)sourceT=4.2 K V=2 mV

0.10

0.05

0.00-4-202gate voltage (V)4Superposition of charge-number states in Cooper-pair box

PRL 1997

reservoirbox----insulator

++++

gate

E

Cooper-pairtunnelingn=0 1nV. Bouchiat et al. Phys. Scr. T76, 165 (1998) Saclay

Superconducting quantum bits
Charge qubit

Flux qubitφChiorescu, YN, Harmans, Mooij, Science (2003)

Artificial two-level system in circuits
 Coherent control of macroscopic system
YN, Pashkin, Tsai, Nature (1999)

Superconducting qubit – nonlinear resonator
LC resonator

Josephson junction resonator
Josephson junction = nonlinear inductorenergyanharmonicity ⇒ effective two-level system

inductive energy = confinement potentialcharging energy = kinetic energy ⇒ quantized states

Superconducting qubit – nonlinear resonator
LC resonator

Superconductingqubit= Artificial atom~mmIAtom~ÅI• Superconductivity ⇒ low-loss• Josephson effect ⇒ Strong nonlinearity• Macroscopic size ⇒ Strong couplingPossible decoherence sourcesmagnetic-field noise?
trapped vortices?
paramagnetic/nuclear spins?
charge fluctuations?

environment
circuit modes?

phonons?

quasiparticle
tunneling?

photons?
charge/Josephson-energy fluctuations?

Coherence time of superconducting qubits
Echo and dynamical
decoupling
Environmentengineering with cavity

Low-energy
qubitNon-equilibrium
quasiparticle engineering
High-frequency
noise shielding
Dilutedsurface/interface effectImproved
surface/interface/dielectric
Energy-levelengineering
Decoupling fromcharge noise

W. D. Oliver and P. Welander, MRS BULLETIN 38, 816 (2013) MIT-LLScaling-up superconducting quantum computers

54 qubits
Google AI Quantum

Nature 574, 505 (2019)

127 qubits
IBM

https://www.ibm.com/blogs/think/jp-ja/wpcontent/uploads/sites/21/2021/11/IBM_ChipO
pen_BLK_1000x1000.jpg

66 qubits
USTC

Phys. Rev. Lett. 127, 180501 (2021)

Scaling-up superconducting quantum computers

72 qubits
Google AI Quantum
arXiv:2207.06431

433 qubits
IBM

https://www.ibm.com/quantum/roadmap
https://www.youtube.com/watch?v=Szw0KwbKowI

121 qubits
Zhejiang Univ.

arXiv:2211.09802

Quantum error correcntion
andfault-tolerant quantum computing

2D
surface code for fault-tolerant
QC
Fault-tolerant
quantum computing:Surface code

Data qubits

Syndrome qubits

Error threshold 𝒑𝒑𝐭𝐭𝐭𝐭～0.6%

Error detection protocol

A. Fowler et al. PRA 86, 032324 (2012) UCSB

Towards quantum error correction

Not yet break-even

Surface code d=3

ETH Zurich

Nature 605, 669 (2022)

Surface code d=5

Google AI Quantum
arXiv:2207.06431

USTCPhys. Rev. Lett. 129, 030501 (2022)

IBM

arXiv:2203.07205

Braiding operationZhejiang Univ.

arXiv:2211.09802

2D integration with 3D wiring

Superconducting
bump contact

Flip-chip coverIntegrated qubit chip

Superconducting
through silicon vias
Al package

Contact probes

Coaxial cables

16-qubit chip

5 mm
26

64-qubit chip

5 mm

Unit cell structureQubit

Readout resonator (λ/4)

Josephson
junction

Purcell filter(λ/2 resonator)

Yellow: TiNWhite: Al
Gray: SiBlack: TSV

2 μm

Capacitive
coupler

0.5 mm

0.2 μmUnit cell structureユニットセル構造
Qubit
Readout resonator (λ/4)
0.5 mmJosephson
junction

Purcell filter(λ/2 resonator)

Yellow: TiNWhite: Al
Gray: Si
Black: TSV

Capacitivecoupler

Backside

Qubit

GND

Resonator

Single-qubit gate

Rabi oscillation
X gateTwo-qubit gate

Cross-resonance

ZX gateQubit readout
Qubit

Cavity mode

Interaction

Dispersive limit

Qubit

Qubit

|1⟩

|0⟩

𝜔𝜔q

Interaction

|e⟩

~~

|2⟩Cavity mode𝜔𝜔c|g⟩

CavityFrequency

Packaging with vertical access33

Cryostat for 64Q system Input
OutputTotalHEMT
amplifiers

96 lines*16 lines
112 lines 16 low-temperature HEMT
amplifierControllines

 16 Impedance-matched
Josephson parametricamplifier (JPA)

Readoutlines Magnetic shield Radiation shield at 10 mK* Qubit control
Readout signal input
JPA pump

641616

Magnetic shield for
64Q package
Magnetic shields for JPAsCustom-made control system for 64Q system

Control and readout fidelities
Coherence time
: T1 ~ 40 μs, T2E ~ 60 μs
Single-shot readout : 0.990 (~350 ns)
Initialization: 0.997
Single-qubit gate
: 0.9996 (~17 ns)
Two-qubit gate
: 0.991 (~170 ns)
Single-shot readout

Single-qubit gate

Best values

Two-qubit gate(cross resonance)

Fidelity : 0.991(3)Fidelity (Q0) : 0.99907(4)Fidelity (Q1) : 0.99964(7)36Tentatively operable qubits
Estimation from measured qubit parameters

Broken qubit
Frequency-collision
qubit pair

Coherence times:
T1 ~ 10-20 μs
T2E ~20-40 μs

Grounded transmon
with floated coupling buses

HEMT wiring
issues (?)

37

Microwave quantum optics: Cavity QED and waveguide QED
Cavity QEDAtom + 0D mode (discrete)
Strong coupling

Waveguide QEDAtom + 1D mode (continuum)
Mode matching, interference“Strong coupling”
O. Astafiev et al. Science 327, 840 (2010)

Quantum nondemolition detection of microwave photons
Y/2

𝝎𝝎𝐪𝐪
𝝎𝝎𝐜𝐜

𝝎𝝎𝐩𝐩

Readout- Y/2

Pulse mode

Pump

Pumptt• Dark count probability
Pdc = 0.0147• Quantum efficiency𝜼𝜼 = 0.84
S. Kono et al. Nature Phys. 14, 546 (2018)

Readoutt• Internal loss of the cavity• Dephasing• Mismatch of 𝜿𝜿 and 𝟐𝟐𝝌𝝌Conditional Wigner tomography
F= 0.9844

F= 0.84

Correctedfor 𝜼𝜼𝐝𝐝𝐝𝐝𝐝𝐝 = 𝟎𝟎. 𝟒𝟒𝟒𝟒

S. Kono et al. Nature Phys. 14, 546 (2018)

Qubit readout with intrinsic Purcell filter
2D implementation•Readout time

36 ns

•Readout fidelity 99.62%•QND fidelity

Y. Sunada

99.63%

ωq /2π=8.09 GHz
ωr /2π=9.25 GHz
T1= 40 μs

κ/2π=66 MHz
χ/2π=-5.5 MHz

Hybrid quantum systems using collective modes
Superconducting quantum electronics
Superconducting
Circuits

Quantummagnonics

Surface
plasmonpolariton

Nonlinearity
Quantum
nanomechanics+acoustics

MicrowaveFerromagnet
MagnonNanomechanics
PhononLight

0.1 mmQuantum magnonics
Kittel mode

YIG single crystal

Bac
Bstatic~300 mT

Microwave resonator
1mm sphereCoupling with a superconducting qubit

Vacuum Rabi splitting

qubit

Y. Tabuchi et al. Science 349, 405 (2015)

Magnon-number-resolving spectroscopy
Strong dispersive regime

𝜔𝜔𝐹𝐹𝐹𝐹𝐹𝐹

Ground state…

Qubit Excitation

𝑔𝑔𝑚𝑚

𝑔𝑔𝑞𝑞
𝜔𝜔𝑞𝑞

MagnonEnergyTE102

D. Lachance-Quirion et al. Sci. Adv. 3, e1603150 (2017).

|3〉𝑚𝑚|2〉𝑚𝑚|1〉𝑚𝑚|0〉𝑚𝑚

Magnon-number-resolving spectroscopy
D. Lachance-Quirion et al.
Sci. Adv. 3, e1603150 (2017).

Model: J. Gambetta et al. Phys. Rev. A 74, 042318 (2006) Yale

Magnon number resolving via Ramsey interferometry

D. Lachance-Quirion et al. Applied Physics Express 12, 070101 (2019);
See also D. Lachance-Quirion et al. Sci. Adv. 3, e1603150 (2017)

Single-shot detection of a magnon
Single-shot

D. Lachance-Quirion et al. Science 367, 425 (2020)

Quantum electromechanics

SiNx

AlSi

A. Noguchi et al. New J. Phys. 18, 103036 (2016)

300 nm

50 nm
100 nmGround-state cooling

displacement ~ fm
A. Noguchi et al. New J. Phys. 18, 103036 (2016)

Summary
Superconducting qubits= Nonlinear resonator circuits using Josephson effect= Artificial atoms realized in electric circuits• Superconducting quantum computing• High-fidelity control of a quantum system with a large Hilbert space• Challenges against decoherence, for scaling-up, and toward fault tolerance• Microwave quantum optics• Circuit (cavity) QED & waveguide QED• Control and measurement of confined/itinerant microwave photons• Hybrid quantum systems• Extending quantum technology to other degrees of freedom