Rapid on-demand generation of thermal states in superconducting quantum circuits

Abstract

We experimentally demonstrate the fast generation of thermal states of a transmon using a single-junction quantum-circuit refrigerator (QCR) as an in-situ-tunable environment. Through single-shot readout, we monitor the transmon up to its third-excited state, assessing population distributions controlled by QCR drive pulses. Whereas cooling can be achieved in the weak-drive regime, high-amplitude pulses can generate Boltzmann-distributed populations from a temperature of 110 mK up to 500 mK within 100 ns. As we propose in our work, this fast and efficient temperature control provides an appealing opportunity to demonstrate a quantum heat engine. Our results also pave the way for efficient dissipative state preparation and for reducing the circuit depth in thermally assisted quantum algorithms and quantum annealing.

Figures (4)

• Figure 1: Measurement setup and device. (a) False-color optical micrograph of the sample. The transmon qubit (purple) is coupled to the reset resonator (light green) which is connected to the input line through the QCR (inset). The QCR is oriented such that the normal-conductor side of the NIS junction connects to the input line, whereas the superconducting Al part is in galvanic contact with the Nb resonator. The qubit is coupled to a separate resonator for readout (dark green). (b) Simplified circuit diagram of the chip and the experimental setup with colors matching to those in (a). The transmon qubit is represented by two parallel Josephson junctions and a capacitor, and it is controlled through a dc flux line of the junction loop and an rf drive line for qubit state preparation. The QCR is shown as an NIS junction biased with a dc source for bias offset and an arbitrary waveform generator (AWG) for pulsing. (c) Tunneling process in the NIS junction depending on bias voltage $V$. If $|eV|<\Delta$ (left), tunneling is only possible with the absorption of a photon (cooling), whereas higher voltages (right) also allow elastic tunneling and photon emission, leading to heating. (d) Pulse sequence: Three different arbitrary waveform generators (AWGs) are used to create subsequent state preparation, QCR, and readout pulses. Preparation pulses are only required for the calibration measurement in Fig. \ref{['fig:result']}(a), and are not applied in heating experiments. The QCR pulse is a net-zero square pulse with a fundamental frequency of 100 MHz.
• Figure 2: Resonator, qubit, and QCR characterization. (a) Current through the QCR as a function of voltage across it, providing the superconductor gap and Dynes parameters. (b) Normalized trajectory average amplitude of the tone channeled through the qubit readout resonator as a function of voltage that induces flux through junction loop of the qubit and the frequency of the tone. (c) Trajectory average amplitude of the a tone channeled through the qubit readout resonator as a function of the QCR dc voltage $V_{QCR}$ applied at the junction and the frequency $f_{RO}$ of the tone. The frequency shift of 1.5 MHz occurs at the gap voltage obtained form (a). (d) Average qubit readout signal as a function of the flux-inducing voltage $V_{flux}$ and the frequency of a qubit excitation tone $f_q$ around the flux sweet spot at 130 mV with the QCR turned off. All following measurements are conducted at the sweet spot.
• Figure 3: Single-shot measurements with 10000 shots per prepared qubit state. (a) Calibration measurement of all prepared states g--h superimposed and the corresponding fit to a Gaussian-mixture model with four components. The shaded ellipses for states g (blue), e (red), f (green), and h (gray) represent the $1\sigma$ covariances of each qubit state. The h-state fit possibly includes even higher-energy states due to its large width. (b) As (a) but for the thermal equilibrium state at $V_\textrm{QCR}=0$ without any state preparation pulses. (c) As (b), but after a 100-ns QCR pulse with amplitude $V_\textrm{QCR}=1.2$ mV. The population shift toward high-energy states arises from heating caused by the high pulse amplitude $V_\textrm{QCR}>\Delta$. (d) Qubit state populations extracted from single-shot measurements as functions of the QCR pulse amplitude for a fixed pulse length of $100\,\mathrm{ns}$, compared to a fitted Boltzmann distribution truncated at the sixth transmon state. Owing to the wide distribution of the h-state, we assume that the states i and j are mostly contained within the $1\sigma$ boundary of the h-state.
• Figure 4: Temperature $T$ of the closest Gibbs state extracted from single shot measurements of the transmon. (a) Transmon temperature as function of QCR pulse amplitude for a fixed pulse time of 100 ns (markers) agrees well with the theory model for energies above the superconducting gap (solid line) as expected from Ref. Hsu2020, see supplemental material (SM) for details. For large pulse amplitudes, the heating rate of 0.36 K/mV agrees well with the measured data well above the gap voltage $\Delta/e$. The errorbars represent the deviation of the measured states from an ideal Gibbs state, for example due to truncation errors. (b) Measured qubit temperature (markers) as a function of the QCR pulse length for three different amplitudes above the gap voltage as indicated. We also show fitted exponential functions of the form $T(t)=T_0+A(1-e^{-\frac{t}{\tau}})$ (solid lines) yielding a time constant $\tau=185\,\mathrm{ns}$ for $V_{\mathrm{QCR}}=0.3\,\mathrm{mV}$, $\tau=80\,\mathrm{ns}$ for $V_{\mathrm{QCR}}=0.6\,\mathrm{mV}$, and $\tau=109\,\mathrm{ns}$ for $V_{\mathrm{QCR}}=1.2\,\mathrm{mV}$.