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# Superconducting-qubit readout via low-backaction electro-optic transduction

## Abstract

Entangling microwave-frequency superconducting quantum processors through optical light at ambient temperature would enable means of secure communication and distributed quantum information processing1. However, transducing quantum signals between these disparate regimes of the electro-magnetic spectrum remains an outstanding goal2,3,4,5,6,7,8,9, and interfacing superconducting qubits, which are constrained to operate at millikelvin temperatures, with electro-optic transducers presents considerable challenges owing to the deleterious effects of optical photons on superconductors9,10. Moreover, many remote entanglement protocols11,12,13,14 require multiple qubit gates both preceding and following the upconversion of the quantum state, and thus an ideal transducer should impart minimal backaction15 on the qubit. Here we demonstrate readout of a superconducting transmon qubit through a low-backaction electro-optomechanical transducer. The modular nature of the transducer and circuit quantum electrodynamics system used in this work enable complete isolation of the qubit from optical photons, and the backaction on the qubit from the transducer is less than that imparted by thermal radiation from the environment. Moderate improvements in the transducer bandwidth and the added noise will enable us to leverage the full suite of tools available in circuit quantum electrodynamics to demonstrate transduction of non-classical signals from a superconducting qubit to the optical domain.

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## Data availability

The data and code supporting the figures are available on Zenodo at https://doi.org/10.5281/zenodo.6344913. Source data are provided with this paper.

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## Acknowledgements

We acknowledge funding from AFOSR MURI grant number FA9550-15-1-0015, from ARO CQTS grant number 67C1098620 and the NSF under grant number PHYS 1734006. We thank J. Beall and K. Cicak for help with our fabrication process. We thank J. Teufel, G. Smith, K. Quinlan, K. Adachi and L. Talamo for feedback on the manuscript.

## Author information

Authors

### Contributions

R.D.D., C.A.R. and K.W.L. conceived the experiment. B.M.B., M.D.U., J.M.K., S.M. and R.D.D. planned and carried out the measurements. M.D.U. constructed the optical cavity. R.D.D. designed and fabricated the cQED system. S.M. and P.S.B. developed the fabrication process for the chips hosting the electrical circuit and membrane, which were fabricated by S.M. All authors contributed to writing the manuscript.

### Corresponding author

Correspondence to R. D. Delaney.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

## Peer review

### Peer review information

Nature thanks Wolfgang Pfaff, Gary Steele and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Peer reviewer reports are available.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

## Extended data figures and tables

### Extended Data Fig. 1 Quantum efficiency measurement.

(a) Protocol for measurement-induced dephasing calibration. A weak measurement pulse is injected into a Ramsey sequence. The Ramsey sequence is then followed by a strong projective measurement of the qubit. (b) The coherence of the qubit ρge decays as a Gaussian function of the weak measurement amplitude $$\sqrt{{\bar{n}}_{{\rm{r}}}}$$. The points are data, while the line is a Gaussian fit. (c) Measurement of the SNR slope a of the electro-optic readout, in units of inverse drive voltage, as a function of Γe for four fixed optomechanical damping rates Γo. Each data point is obtained from a fit to a measurement of the sort shown in the inset, where it is seen that the SNR scales linearly as a function of drive voltage (bottom axis) or equivalently readout pulse amplitude (top axis).

### Extended Data Fig. 2 Characterisation of the quantum efficiency of the microwave readout apparatus.

The microwave readout efficiency $${\eta }_{{\rm{q}}}^{{\rm{mic}}}$$ is measured as a function of the electromechanical damping rate Γe. The points are data, while the line is a model including partial absorption of the readout pulse by the pump power-dependent reflection loss of the LC circuit, power-dependent added noise, fixed transmission losses and the independently measured added noise of the microwave heterodyne measurement chain. The shape of the curve is dominated by power-dependent LC circuit reflection loss, with the quantum efficiency of the microwave readout apparatus approaching zero at high power because the LC circuit is nearly critically coupled. From this model, we estimate 4.7 dB of loss (ηmic = 0.34) between transducer and the cQED system.

### Extended Data Fig. 3 Excess backaction from pump photon leakage.

(a) Circulators (total isolation of 63 dB) and interferometric cancellation are used to prevent the strong microwave pump from reaching the cQED system and dephasing the qubit. Cancellation is achieved by sending a microwave cancellation tone with amplitude equal to that of the reflected microwave pump but opposite phase into the second arm of the directional coupler. The phasor sum of this cancellation tone and the reflected microwave pump determines the pump power Pref propagating towards the cQED system. (b) The directional coupler acts as an interferometer, enabling interference between the reflected microwave pump and the cancellation tone. During normal operation of the transducer the cancellation tone is tuned to minimise Pref, but to estimate the effect of pump photons on the qubit the cancellation tone can be tuned to only partially interfere and tune Pref over several decades. The phasor sum shown here is for the case of constructive interference. (c) The number of pump photons in the cQED system $${\bar{n}}_{{\rm{p}}}$$ is measured as Pref is varied. During transducer operation the cancellation is typically tuned to achieve Pref < −95 dBm or equivalently $${\bar{n}}_{{\rm{p}}} < 1\times {10}^{-3}$$. The cancellation does not stay completely fixed over the course of the experiment due to small thermal drifts slightly changing the amplitude of Pref.

### Extended Data Fig. 4 Experimental schematic.

(a) Microwave layout demonstrating the exact configuration of the qubit readout/control pulses and the pumps for the electro-optic transducer. (b) Legend for various different microwave and optical components. (c) Cryogenic portion of the experiment. (d) Demodulation and detection scheme. The two digitisers allow for simultaneous measurement of the microwave and optical signals emitted from the transducer. (e) Simplified schematic of optical beam layout and balanced heterodyne detector.

### Extended Data Fig. 5 cQED system.

(a) The cQED system is a superconducting qubit coupled to a 3D quarter-wave post resonator which is in turn evanescently coupled to the waveguide above. A sapphire rod can be translated towards the end of the post resonator via a piezo-electric stepping module (Attocube ANPz101/LT/HV) in order to tune the resonator’s frequency. The sapphire rod is epoxied to a clamp with stycast 2850 and then bolted to the piezo-electric stepping module. A lid with a narrow hole for the sapphire rod to pass through is attached to the top of the waveguide to prevent coupling of modes in the Attocube mount to modes within the waveguide and the quarter-wave resonator. (b) Photo of the cQED system and Attocube mount. A copper braid is attached to the gold-plated copper qubit clamp to help thermalize the superconducting qubit.

### Extended Data Fig. 6 Qubit coherence time data.

Qubit coherence times under three different electro-optic transducer operating conditions: transducer off, transducer on with (Γe, Γo)/2π = (1.1, 5.0) kHz and just the laser on with (Γe, Γo)/2π = (0, 5.0) kHz. Turning just the laser on is indistinguishable from the transducer being turned off. Running the electro-optic transducer does reduce the dephasing time of the qubit (see the cyan hexagon). Circles represent T1 times, triangles represent T2 times and hexagons represent Tϕ.

## Supplementary information

### Supplementary Information

This Supplementary Information file contains the following three sections: Optical readout fidelity, Modelling transducer added noise, and State-space model.

## Rights and permissions

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Delaney, R.D., Urmey, M.D., Mittal, S. et al. Superconducting-qubit readout via low-backaction electro-optic transduction. Nature 606, 489–493 (2022). https://doi.org/10.1038/s41586-022-04720-2

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• DOI: https://doi.org/10.1038/s41586-022-04720-2