Pulsed Reset Protocol for Fixed-Frequency Superconducting Qubits

D.J. Egger, M. Werninghaus, M. Ganzhorn, G. Salis, A. Fuhrer, P. Müller, and S. Filipp

Phys. Rev. Applied 10, 044030 – Published 10 October 2018

Abstract

Increasing coherence times of quantum bits is a fundamental challenge in the field of quantum computing. With long-lived qubits it is, however, inefficient to wait until the qubits have relaxed to their ground state after completion of an experiment. Moreover, for error-correction schemes it is important to rapidly reinitialize syndrome qubits. We present a simple pulsed qubit reset protocol based on a two-pulse sequence. A first pulse transfers the excited-state population to a higher excited qubit state and a second pulse transfer it into a lossy environment provided by a low- $Q$ transmission-line resonator, which is also used for qubit read-out. We show that the remaining excited-state population can be suppressed to $(1.7 \pm 0.1) %$ and that this figure may be reduced by further improving the pulse calibration.

Received 2 March 2018
Revised 7 August 2018

DOI:https://doi.org/10.1103/PhysRevApplied.10.044030

Physics Subject Headings (PhySH)

Quantum computation Quantum control Quantum information with solid state qubits

Superconducting qubits

Microwave techniques

Quantum Information, Science & Technology

Authors & Affiliations

D.J. Egger, M. Werninghaus, M. Ganzhorn, G. Salis, A. Fuhrer, P. Müller, and S. Filipp^*

IBM Research GmbH, Zurich Research Laboratory, Säumerstrasse 4, 8803 Rüschlikon, Switzerland

^*sfi@zurich.ibm.com

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Vol. 10, Iss. 4 — October 2018

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Figure 1
(a) Level diagram of the transmon-resonator system along with the relevant pulses to reset the qubit. (b) Pulsed reset protocol. Before a quantum algorithm commences, the reset pulse sequence is performed: first, the remaining qubit population in state $| e ⟩$ is transferred to state $| f ⟩$ with the pulse $X_{π}^{e \to f}$ ; second, the population in $| f ⟩$ is transferred to the read-out resonator with the $| f 0 ⟩ \leftrightarrow | g 1 ⟩$ drive, where it rapidly decays to the environment. (c) Room-temperature electronics. A 30-dB amplifier enhances the rate at which the $|f 0⟩ \leftrightarrow |g 1⟩$ transition is driven.
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Figure 2
(a) Spectroscopy measurement as a function of the amplitude and frequency of the $| f 0 ⟩ \leftrightarrow | g 1 ⟩$ drive with the transmon prepared in the $| f ⟩$ state (light color). The drive amplitude is stated as a function of the peak-to-peak output voltage of the AWG. At resonance (dark color), the qubit population is transferred to the low- $Q$ read-out resonator. The white dots indicate drive frequency and amplitude pairs for which we performed a time-resolved measurement of the population transfer between the qubit and the resonator; see Fig. 3. The numbers associated to the white dots indicate the time it takes to transfer the population from the qubit $| f ⟩$ state to the resonator $| 1 ⟩$ state.
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Figure 3
(a) Time-resolved Rabi oscillations between $| f 0 ⟩$ and $| g 1 ⟩$ for different AWG output voltages indicated by the white dots in Fig. 2. The transmon is initially prepared in state $| f ⟩$ with use of an $X_{π}^{g \to e}$ pulse followed by a $X_{π}^{e \to f}$ pulse. (b) Population remaining in the qubit at the first minimum shown in (a). In (a),(b) each point is the median of five measurements and the error bars are the 25th and 75th percentiles.
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Figure 4
(a) Single-shot calibration data obtained with the $| g ⟩$ and $| f ⟩$ states to train a linear support-vector-machine classifier. The resulting decision boundary is indicated by the background color. The blue and orange dots correspond to the training data knowing that no $π$ pulse and a $π$ pulse, respectively, have been applied to the qubit before measurement. (b) Single-shot data after a 155-ns $| f 0 ⟩ \leftrightarrow | g 1 ⟩$ pulse. The population in the qubit is 1.8% as determined from 2000 single-shot measurements. The decision frontier obtained from (a) is used to distinguish whether each data point corresponds to the qubit being in an excited state or the ground state. (c) Time-resolved trace of the transmon population comparing the pulsed reset to the natural $T_{1}$ decay (thick red line) of the qubit. The qubit is initialized in the $| e ⟩$ state with a $| g ⟩ \to | e ⟩ π$ pulse. The pulsed reset time trace is measured starting after the $| e ⟩ \to | f ⟩ π$ pulse, which lasts $75 ns$ , whereas the $T_{1}$ trace starts immediately. The simulated time trace (thin black line) is obtained from a master equation. (d) The difference between the measured qubit population in (c) and the solution of the master equation describing our system.
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Figure 5
Population in the qubit for different trigger rates. (a) Pulse sequence. After an initial $X_{π}^{g \to e}$ pulse used to identify $| e ⟩$ in the $I$ - $Q$ read-out plane, the qubit is repeatedly measured at each successive trigger pulse. (b) Population in the qubit with (triangles) and without (circles) the pulsed reset sequence. Each data point is the median of ten measurement featuring 2000 rounds. The error bars show the 25th (lower) and 75th (upper) percentiles of the measured qubit population. The dashed gray line shows that thermal population.
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Figure 6
Single-shot data (blue points) in the $I$ - $Q$ plane in the case with $T_{1}$ reset (a) and with the pulsed reset (b). This data set is one of the ten measurements shown in Fig. 5 at $R = 1 kHz$ . The measured population is $({1.73}_{- 0.10}^{+ 0.15}) %$ with $T_{1}$ reset and $({0.43}_{- 0.20}^{+ 0.16}) %$ with pulsed reset. The background shows the decision boundary obtained from calibration data (not shown). The dots in the clear and dark regions correspond to the qubit being in the excited states and the ground state, respectively.
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