Designing a Josephson ring circuit for a passive on-chip microwave circulator
Yutaka Takeda 1 and Yasunobu Nakamura 1,2
1 Research Center for Advanced Science and Technology (RCAST), The University of Tokyo, 2 RIKEN Center for Quantum Computing (RQC)

takeday@g.ecc.u-tokyo.ac.jp

Abstract
Microwave circulators are one of the essential components to build a quantum computing system using superconducting qubits. As conventional circulators are bulky andpotentially set a limit of a scale of the system, on-chip circulators not relying on ferrites are intensively studied these days. We investigate a passive Josephson ring circulator
proposed by J. Koch et al. in 2010 towards its experimental implementation. Here we discuss two issues on experimental difficulties of Josephson ring circulators: uniformity ofcircuit parameters and impedance matching. The original scheme does not have enough tuning knobs for impedance matching under a finite deviation of circuit parameters. We
propose a modified circuit configuration to solve this difficulty towards experimental realization of on-chip circulators.
Introduction

Proposal

Circulators in superconducting quantum computersSuperconducting qubits are expected to be aplatform for large-scale quantum computers
running on quantum error correcting codes. To
realize fault-tolerant quantum computers, it isnecessary to scale up the number of qubits to~106 while maintaining high fidelities of qubit
control and readout. In a typical readout circuitof a superconducting qubit, circulators are used
to route the readout signal and to isolate the qubit
from the noise from a amplifier chain.
Input line

Two-mode operation of Josephson ring circulator

UTokyo/RikenIsolation

κκ+/-Imaginary component: Split diff. modes+0-gκ ω0g
ω0 κiβκ ω0κIntroduce large
direct couplings

ω0ω0g

ω0

iβα+iβα+iβω0 κκ ω0

ω0 κiβα+iβJosephson Ring

Separate common-modefor two-mode operation

Issues in terms of scalability

a00a++• Large size

ω0

• Fabrication compatibility

a-0+-• High magnetic field

Qubit chip0

Effect of complex coupling between resonators

Freq.
Routing

Freq.

Number of qubits 102 → 106

Since the ferrite circulators commonly used arebulky and have a large stray magnetic field, they
could be a limitation for scaling up
superconducting quantum computers. The goalof this research is to develop an on-chip
circulator as an alternative to ferrite circulators.

Output line

We propose a new operating regime ofJosephson ring circulators by adding
sufficiently large real-valued couplings
between resonators intentionally. This
modification relaxes the required conditions,and the impedance mismatch caused by aJosephson enery randomness in real devices
can be compensated by a single tuning knob.

Real component: Lift common mode

-Device Design
Previous Studies

Josephson ring

On-chip circulators using superconducting circuits• Common fabrication process with qubits• Lower magnetic field operation
Active circuit

Passive circuit

Break time-reversal symmetry (TRS)
by external AC drive

Break TRS by inherit properties of a superconducting circuit(No external AC drive)

Demonstrations• Frequency conversion + delay

Theoretical proposals (not realized yet)
• Aharonov-Bohm effect

B. Chapman et al. PRX 7, 041043 (2017)

Resonators

Josephson ring

1mmCoupling• Aharonov-Casher effect

F. Lecocq et al. PRApplied 7, 024028 (2017)

NbAl(False-colored SEM image)

ParametersJ. Koch et al. PRA 82, 043811 (2010)• Parametric coupling

Si200um

Frequency

8.9 GHz

External linewidth38, 50, 63 MHz

Charging energy Ec/h

1.24 GHz

Josephson energy EJ/h

7-9 GHzEJ/Ec

5.6-7.3

Resonator-Josephson ring

70 MHzResonator-Resonator

430 MHz

C. Müller et al. PRL 120, 213602 (2018)

Issues in terms of scalability

Experimental difficulties• Many coaxial lines• Sensitive to charge noise• Complex parameter tuning• Lack of tuning knobs ← solve this problem

Principle
Implementation of 3-port circulator

Flux bias vs eigenfrequency of Josephson ring

The circulator is a non-reciprocal element which transmits incoming signal tonext port, such as 1→2, 2→3 and 3→1. By diagonalizing the S-matrix for acirculator, this behavior turns out to be equivalent to reflecting all 3-phasesignals perfectly with 0-, ±2π/3-phase shifts respectively for the input 3-phase
mode.
0 1 0
𝑆= 0 0 1
1 0 01𝑆′ =Diagonalize

00

#!"$%
e0 00

Flux bias vs external coupling for impedance matching

Frequency separation of common mode

We measured the reflection and transmission spectra at 10 mK with asufficiently high probe power where the Josephson ring was saturated andimaginary couplings vanished. We confirmed frequency separation of thecommon mode was achieved while maintaining sufficient three-fold symmetry.
>1 GHz0#&" %e $a0a+κω0a-αα

κ ω0

ω0 κα

Reflection phase of the resonators which havedifferent eigenfrequencies for different 3-phase
excitations, respectively

Josephson ring circulator

J. Koch et al. PRA 82, 043811 (2010)

J. Koch et al. have shown that effective
couplings between three resonators mediatedby a Josephson ring circuit can take complex
values and are tunable with external flux. Asa special case, the coupled resonators withexternal ports behave as a circulator when
two conditions are satisfied.
Circulator conditions for effective couplings

PortResonator

Future works• Improve uniformity of Josephson junctions• Suppress charge noise

Gate voltage
Josephson ringConclusionΦJosephson Ring Circulator

1. Real component is zero
2. Imaginary component is matched to the external linewidth: impedance matching

Objective
Realization of a passive on-chip circulator to replace ferrite circulators insuperconducting qubit readout circuits
Proposal
New operating regime of Josephson ring circulators overcoming one of theexperimental difficulties: lack of tuning knobs problem

Problem: lack of tuning knobs
This work was supported by JSPS KAKENHI (20J13515), JST ERATO (JPMJER1601) and MEXT Q-LEAP (JPMXS0118068682).