Peer review of: Breaking the trade-off between fast control and long lifetime of a superconducting qubit (2020)

REVIEWER COMMENTS 

Reviewer #1 (Remarks to the Author): 

In their manuscript, "Breaking the trade-off between fast control and long lifetime of a 
superconducting qubit," the authors demonstrate the operation of a Josephson quantum filter (JQF) 
and use it to enhance the relaxation time of a superconducting qubit. In contrast to usual Purcell 
filters that consist of microwave structures that suppress emission at the qubit frequency (while 
transmitting at the readout frequency), the JQF is an transmon itself that reflects at low powers (a 
single photon emitted as the result of a qubit relaxation event), yet saturates at higher powers, which 
include those that are used for qubit control. This allows lifetime enhancement of the qubit without a 
concomitant increase in drive power for control, which can be detrimental. 

The authors present compelling evidence and a rigorous analysis included in a detailed 17 pages of 
supplemental notes. They use input-output theory to describe waveguide QED, an architecture not as 
common as the usual circuit QED that is the dominant architecture for building quantum computers 
with superconducting circuits (indeed that takes place in this work on the readout side with the "usual" 
Purcell filter), and is also quite different since it treats propagating fields in a waveguide instead of 
photon modes in a resonator. This is an opportunity to overview waveguide QED, but the essential 
physics should be a bit more intuitive in the text, and it gets somewhat bogged down by the 
framework in the supplement. This phenomenon is generic and can be seen (as in Ref. S4, for 
example) as a diagonalization of the dissipator in Eq. 1 into bright and dark states with different 
correlated decay rates. Going into the parameter regime where the filter external decay rate is much 
greater than that of the qubit, the qubit state is approximately the dark state, and is non-radiative. 
This is all stated in the supplement, but a more thorough explanation should be brought into the main 
text. 

Along the same lines, the physics of JQF saturation should be elaborated on, and how it relates to the 
work in Ref. 26 and resonance fluorescence. Could the off-resonant split peaks of a Mollow triplet 
observed in Ref. 26 cause undesired Stark shifts on the qubit? 

Overall, the manuscript presents a novel device and thoroughly analyzes its properties, and with the 
minor clarifications mentioned above, I recommend for publication in Nature Communications. 

Reviewer #2 (Remarks to the Author): 

The authors have presented a careful, extensive experimental and theoretical study of a device they 
term the "Josephson Quantum Filter" (JQF). This device acts as an amplitude-sensitive filter for 
quantum signals, suppressing qubit decay to a control line but allowing strong control signals to pass 
through to the qubit. In a clever trick, the authors make their JQF frequency-tunable to allow it to be 
detuned from the qubit, thus isolating the behavior of each device and allowing them to be separately 
characterized. The authors characterize the JQF itself with direct microwave reflectometry and 
characterize the qubit with both standard pulsed dispersive readout and with direct reflectometry. 
They then tune the devices into resonance and then show that the qubit decay is suppressed while 
Rabi frequencies are constant, i.e. control tones are unaffected by the filter. They present exhaustive 
analytical and numerical theory in the supplement to support their results. I find no fault with either 
the experiment or theory, and I regard this as very strong work. I recommend this paper be published 
after minor revisions. 

I have a minor concern about the usefulness of the result which I believe the authors can address 
without further experimental work. The device does add a moderate amount of complexity--adding the 
JQF takes the device from a single transmon and resonator to two of each, with the second transmon 
flux-tunable. This added complexity must be justified, which the authors do by referencing the 
reduced power dissipation the JQF allows. This would be a much more compelling statement if the 
authors can quantitatively cite how much power dissipation is avoided with some reasonable numbers. 
For example, if one takes 100 qubits, each with a control-line-limited T1 = 1 ms without JQFs, each 
driven simultaneously with a 10 ns pi-pulse which is 20dB attenuated at the base stage, how much 
power is dissipated compared with a similar setup with reasonable JQF coupling parameters? How 
sensitive would this be to fabrication parameters--i.e. will the JQF work with all fixed qubits and 
resonators assuming state-of-the-art ~1% variation in junction size? 

Minor specific comments/suggestions follow: 

1) The theory relies on the rotating wave approximation. Will this ever break down under reasonable 
operating conditions? Please add a short discussion to the supplement. 
2) Would a lumped-element resonator between the qubit and JQF work? Does intrinsic loss in the 
resonator play a role? Please note this in the main text. 
3) Does the resonator give any response when the JQF is tuned off resonance? If so please discuss. 
4) Please discuss the physical significance of the negative correlated decay rate. 
5) When calculating the single-photon power, is that factor of 4 supposed to be in the denominator or 
the numerator? Perhaps cite the source for this calculation or re-derive it? 
6) The qubit temperature with the JQF on resonance is above 90 mK. Is this typical for other qubits 
without strong control line coupling? Could there be a mechanism by which the JQF causes extra 
excitations? Please discuss in the main text. 
7) Typically thermal excitation mechanisms are discussed as part of the overall decay channel. Please 
justify discussing them as separate channels. 
8) Please explicitly cite the numbers for T1 and T2 enhancement in the main text. 
9) Please explicitly lable the insets in Fig 4, or otherwise indicate that they are zoom-ins. 
10) Please include a prediction (numerical or analytical) for the maximum coherence enhancement if 
the resonator length d is exactly half a wavelength. 
11) Please explain why an incomplete saturation of the JQF causes faster Rabi decay compared to no 
JQF. 
12) In the supplement, the JQF dephasing and thermal population are not 0, they are just small 
enough to be difficult to measure. Please modify the table to indicate this. 

Overall, great work, it was very interesting! 
-Eli Levenson-Falk 
University of Southern California