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a The symmetric DC-SQUID contains two orthogonal modes57,58, the common mode (coupler) and the differential mode (actuator). We selectively couple the former to two bosonic modes and the latter to the drives to take advantage of the natural symmetries of the Hamiltonian in Eq. (1). b Implementing the purely differential drive through a 3D buffer post-cavity (figure is exaggerated for illustrative purposes). The natural separation in electric and magnetic fields in the λ/4 mode is used to purely drive the actuator, without exciting the coupler. The sensitive quantum information is stored in two high-Q λ/4 post-cavities (Alice and Bob) that participate in the coupler, enabling parametric beamsplitting between them. The inset shows an optical micrograph of the SQUID device, displaying the purposely offset antenna pad that counters residual drive-asymmetry. c Frequency stack for relevant modes in the system. The difference of the two drive frequencies (Δd) is fixed to be equal to the cavity detuning (Δab) for resonant beamsplitting. The drives are placed symmetrically around the buffer mode resonance, which is engineered to be far-red detuned from the coupler frequency.
We now present the full experimental realization (Fig. 1b) of a high-fidelity beamsplitter that strongly suppresses undesirable coupler heating. Our construction consists of a high-purity aluminum package hosting three coaxial λ/4 stub cavity modes: the buffer mode and the two high-Q storage modes6. The storage modes are capacitively coupled to the Y-shaped antenna of the SQUID42 and have a negligible mutual inductance to the SQUID loop, ensuring that they exclusively participate43,44 in the coupler mode:
While this device was optimized for performance in the single-photon manifold, any drive-induced increase in the self-Kerr of the cavities would lead to coherent errors in higher-photon manifolds. The sideband interaction resulting from our choice of mode frequencies exacerbates this effect, with up to 128 KHz of inherited Kerr at the operating point. Numerous avenues exist to minimize this driven nonlinearity if desired (see Supplementary Note 6), including choosing a slightly higher coupler frequency, arraying multiple SQUIDs, or dynamical Kerr cancellation47. If minimizing inherited self-Kerr is vital, such as in schemes utilizing large coherent states, then implementing these improvements or using an alternative scheme like Kerr-free three-wave mixing22,48 may be required.
We precisely characterize the fidelity and noise bias of our beamsplitter by using it to implement universal control of the dual-rail qubit subspace, allowing techniques akin to standard randomized benchmarking (RB) protocols49,50,51. First, we identify the amplitude and frequency required for a fixed-length pulse (Fig. 3d) to achieve the beamsplitter unitary
that generate the Clifford group for the dual-rail qubit (Fig. 3d, Supplementary Note 9). This allows a form of direct randomized benchmarking52, which under uniform sampling should convert both dephasing and coherent control errors into an effective depolarization channel. The dominant but detectable error of cavity photon loss appears as a leakage to the orthogonal state \(\left0_a0_b\right\rangle\), which is not converted to depolarization under this protocol, but can be separately quantified and selected out in post-processing.
Beyond the context of parametric interactions, we have also demonstrated the delivery of AC flux in a high-Q 3D environment. This can be used to control other devices in similar architectures that require fast-flux modulation. The electromagnetic simulation techniques we have developed are also readily applicable to other work involving driven circuit-QED systems, for both 3D and planar devices.
Finally, the demonstration of high-fidelity control in the dual-rail subspace motivates the hypothesis that this subspace could itself be used as a computational qubit12,24,36. The error-hierarchy of detectable decay over dephasing makes the dual-rail qubit amenable to erasure conversion53, an approach potentially yielding high thresholds in the surface-code architecture. The single-qubit control demonstrated here can be extended to realize a high-fidelity gate-set17 for multi-qubit control, charting a path towards a general dual-rail qubit-based architecture in circuit-QED. The performance in higher-photon manifolds is the subject of further research, with promising avenues including arraying the SQUID element, and creating parity-protected couplers with suppressed Kerr nonlinearity.
Any additional effects due to a spatial non-uniformity of the magnetic field threading the loop can be addressed through a purposely-engineered asymmetric capacitance in the on-chip SQUID device (Fig. 5a). This asymmetry in the capacitance serves as a control knob for tuning the coupling between the electromotive force and the coupler mode in the presence of an alternating magnetic field, allowing to compensate for residual drive asymmetry56. To illustrate this effect, we analyze the circuit model in Fig. 5b that captures this effect to represent the actual experimental device. We take into account a non-uniform AC magnetic field that is distributed across the device, not only inducing a flux in the SQUID loop, but also inducing an electromotive force on the shunting capacitors. Assuming the geometric inductance of the loop is much smaller than the Josephson inductance (Supplementary Note 1), we arrive at the effective Hamiltonian of
Decoherence rates are extracted from short sections of the long-time evolution under both drive tones, as a function of drive amplitude. The sideband collision of coupler and Bob (see Supplementary Note 5) clearly limits the fidelity at high amplitudes, and we operate on the boundary of this collision (gray dashed line), where κBS is limited by κ1.
We thank J. Venkatraman and X. Xiao for helpful conversations on parasitic nonlinear resonances. We are grateful to J. Curtis, A. Koottandavida, and I. Tsioutsios for technical assistance and providing useful code. We thank B. Chapman for providing parametric amplifiers used in this experiment, and A. Read for help with DC-flux line wiring. We are grateful to C. Wehr and H. M. Moseley for help with designing substrate clamps and K. Chou for advice on beamsplitter control. We thank A. Miano for help simulating the dc-flux spectroscopy of the SQUID. We also thank P. Winkel, M. Devoret, B. Chapman, S. de Graaf, S. Xue, J. D. Teoh, T. Tsunoda, S. Chakram, and J. Huang for useful discussions. This research was sponsored by the Army Research Office (ARO) under grant nos. W911NF-16-1-0349, W911NF-18-1-0212 and W911NF-23-1-0051. The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of the Army Research Office (ARO) or the US Government. Fabrication facilities use was supported by the Yale Institute for Nanoscience and Quantum Engineering (YINQE) and the Yale SEAS Cleanroom.
Y.L. and A.M. designed and conducted the experiment, under the supervision of R.J.S. Y.L., A.M., and S.G. designed the experimental device and developed the differential drive scheme. Y.L. fabricated the DC-SQUID and ancilla transmon chip devices with help from S.G. and L.F. A.M., Y.L., and J.G. conducted measurements and analyzed the data. J.G., A.M., and Y.L. implemented the dual-rail qubit randomized benchmarking. Y.Z. and J.C. provided theoretical support for analyzing parametric processes and randomized benchmarking, respectively. S.M.G. provided important theoretical insights during the writing of the manuscript. A.M., Y.L., J.G., and R.J.S. wrote the manuscript with feedback from all co-authors.
I'm a bit stuck with the selection of the right step down converter and a fuse circuitry. The step down converter has an input voltage of 12V and an output voltage of 3.3V. Of course, it is a good idea to fuse the input side of the converter in case it is damaged. But is it necessary to adjust the fuse size such that it blows when the output side of the converter is shortened?
For example, the TPS62132 has a short circuit protection where it limits the current to 1.6A whereas the maximum output current is 3A. Is it necessary to fit the fuse size on the input side of the converter to the output 1.6A? Or can I just leave the converter enabled even in case of a short on the output side?
That 1.6 A current limit is only during start up or fault conditions when Vout is below about 0.5 V. Normal current limit is 3.6 A min 4.2A typ 4.9 A max. You don't typically have to use a fuse for output short circuit protection. Under some fault conditions, the internal FETs may be damaged. You may want to provide some fuse protection for that case. It depends on the source current capability of your input supply.
If for some reason the internal FETs were to short out (due to EOS damage for instance), the the IC would present a low impedance path from VIN to GND. If your input supply can source 25 A, you may see the IC catch fire and you may also possibly burn copper traces on your PCB. I would probably use a fuse on your input.
Ah yes of course! So I can use e.g. a 5A fuse on the input side of the converter and I don't have to worry about short circuits on the outside of the converter? I mean, if a component on the 3.3V side is damaged it doesn't matter if the converter blows 1.6A through it, right? The component is already broken and the converter doesn't care.
The 0.5 V is just an internal threshold for the TPS62132 for the higher or lower current limit. The output voltage will ramp thru that part during start up and may fall to that level during overcurrent. TPS62132 cannot actually regulate to that voltage, so there is no "application" for 0.5 V operation. Hopefully this answers your question.
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