Suppressing relaxation in superconducting qubits by quasiparticle pumping

Authors: Simon Gustavsson, Fei Yan, Gianluigi Catelani, Jonas Bylander, Archana Kamal, Jeffrey Birenbaum, David Hover, Danna Rosenberg, Gabriel Samach, Adam P. Spears, Steven J. Weber, Jonilyn L. Yoder, John Clarke, Andrew J. Kerman, Fumiki Yoshihara, Yasunobu Nakamura, Terry P. Orlando, William D. Oliver

First Author’s Primary Affiliation: Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA

Manuscript: Published in Science

Introduction:

Superconducting qubits offer a promising platform for the realization of a functioning quantum computer. There are typically two coherence times relevant to qubit systems, the depolarization time $T_1$ , and the dephasing time, often called $T_2$ . When a qubit undergoes a depolarization event, the qubit emits energy and its state changes, which is also referred to as a “bit flip”. Similarly, when a qubit undergoes a dephasing event, the phase of its quantum state changes, often called a “phase flip”. Unfortunately, quantum systems are always subject to several avenues of decoherence, where the quantum system loses information to its environment. Many schemes to minimize decoherence events exist, dating back to the famous Hahn echo experiment, where refocusing pulses are used to refocus dephasing errors in spin systems (a really nice visual example of this can be seen here). Many of these protocols act as dynamic enhancement of the dephasing time of the quantum system. This paper in Science introduces the first dynamic enhancement of the depolarization time of a superconducting qubit by pumping excitations into a bath of quasiparticles and minimizing their interactions with a superconducting flux qubit.

Experimental Setup and Operating Principle:

This experiment uses two different types of devices, labeled device A and device B. Device A is a flux qubit consisting of four Josephson junctions contained in a superconducting loop (indicated by the smaller red crosses in Fig. 1). A Josephson junction consists of two superconducting islands interrupted by a thin layer of non-superconducting material. In a superconductor, electrons pair together to form ”Cooper pairs” and these Cooper pairs flow through the superconductor without resistance. The physical quantity which describes the state of the effective quantum two level system in this experiment is the direction of the current flowing in the lower superconducting loop. In order to determine the direction of the circulating current, a superconducting quantum interference device (SQUID) acts as a sensitive detector of local magnetic fields and measures the magnetic flux produced by these circulating currents. The SQUID also contains Josephson junctions, which are indicated by the largest red crosses in Fig. 1. This measurement technique involves applying a current to the SQUID, which can be responsible for the generation of quasiparticles, making this device geometry a prime candidate for studying their effects on quantum devices.

Figure 1
Schematic of the first device used in the experiment. The larger red X’s indicate the Josephson junctions which are part the SQUID used for readout, and the smaller X’s indicate the Josephson junctions within the qubit. The qubit states correspond to circulating currents through the lower loop of the figure. The blue circle represents a quasiparticle tunneling across a Josephson junction, which leads to energy decay from the qubit.

In most cases, the quantum system can lose energy to many different decay channels. One primary source of this depolarization is the release of energy from the qubit into quasiparticles, which are unpaired electrons (electrons that are not part of a Cooper pair). It is possible to measure the average number of these quasiparticles by directly measuring the depolarization rate of the system. In order to do this measurement, the authors must give the system some energy to put the qubit into its excited state. By measuring the probability of the qubit remaining in its excited state as a function of time after this excitation pulse, the authors fit the resulting data to the following equation:

$p(t) = e^{\langle n_{qp}\rangle\left(\textrm{exp}\left(-t/ \tilde{T}_{1qp}\right) -1 \right)}e^{-t/T_{1R}}.$

(Equation 1)

The probability of the qubit remaining in the excited state is given as $p(t)$ , the average number of quasiparticles is represented by $\langle n_{qp} \rangle$ , $\tilde{T}_{1qp}$ is the relaxation time provided by a single quasiparticle, and $T_{1R}$ is the decay of the qubit excitation into all channels. By fitting experimental data to Eq. 1, the authors are able to extract the quasiparticle number as a fit parameter, as well as distinguish the difference between qubit decays into quasiparticles versus decays into other channels. A measurement of the qubit lifetime and fit to Eqn. 1 is shown in Fig. 2. The authors find that the average quasiparticle number in this measurement is $\langle n_{qp} \rangle = 2.5$ , the decay induced by a single quasiparticle is $T_{1qp} = 23 \mu s$ , and decay to all other channels is given by $T_{1R} = 55 \mu~s$ .

Figure 2
A measurement of qubit energy relaxation. The dots represent the measured data and the black line is a fit to Eqn. 1. The fit parameters are given in the box in the upper right hand corner. From the fit, we see that there is an average population of 2.5 quasiparticles.

Although the presence of quasiparticles can reduce the lifetime of the qubit, this idea can be used advantageously to extend the lifetime of the qubit by using special control schemes. When the qubit emits energy into the bath of quasiparticles, the qubit loses energy $\hbar \omega_q$ , where $\omega_q$ is the resonant frequency of the qubit. In turn, the bath of quasiparticles must gain the same amount of energy, $\hbar \omega_q$ . This increase of quasiparticle energy leads to an increase of the velocity of the quasiparticle and ”pushes” it away from the qubit so that it can no longer cause depolarization of the qubit! The authors take advantage of this mechanism by exciting the qubit a number of times with a pulse of microwaves (often times these excitations are called $\pi$ pulses since they rotate the qubit state by $\pi$ radians on a unit sphere, see this page for a nice visual example!). By waiting for an amount of time $30 \mu~s$ between $\pi$ pulses, any decay of the qubit during this time is most likely into quasiparticles, since the authors measure $\tilde{T}_{1qp} < T_{1R}$ (see. Fig. 2). By applying many of these pulses and continuously monitoring the qubit population, the authors see that the decay of the qubit excited state slows down with each consecutive $\pi$ pulse! The results for up to four pulses can be seen in Fig. 3.

Figure 3
Measurement of qubit population with consecutive $\pi$ pulses. It is clear that the qubit decay ”slows down” with each consecutive pulse, indicating that there are fewer quasiparticles causing decay with each measurement.

Figure 3
Measurement of qubit population with consecutive $\pi$ pulses. It is clear that the qubit decay ”slows down” with each consecutive pulse, indicating that there are fewer quasiparticles causing decay with each measurement.

In order to fully investigate the impact of these quasiparticle pumping pulses, the authors extend this process to include up to 40 $\pi$ pulses under the same conditions. The authors measure the qubit decay time (defined to be the amount of time it takes for the signal to decay by a factor of 1/e) as a function of the number of refocusing pulses with a time interval of $10~\mu s$ between pumping pulses. After the last pulse, the authors measure the probability of the qubit being in its excited state as a function of time after the last pulse (a similar measurement to that in Fig. 3, only this time with the sequence of pumping pulses added to the beginning of the measurement protocol). The authors find that the qubit decay time increases with the number of pumping pulses, implying that each pulse is actually pushing these quasiparticles away from the qubit. The results are shown in in Fig. 4.

Figure 4
(a) Pulse sequence which describes the quasiparticle pumping mechanism. Consecutive $\pi$ pulses are applied to the qubit with some variable time $\Delta$ T $= 30\mu$ s, finally the qubit is excited into its excited state and its decay is measured. (b) Results of the measured qubit decay as a function of the number of pump pulses. The observed qubit decay time increases with increasing pulse number. (c) The measured quasiparticle population, which is shown to initially decrease with pulses number before saturating near $\langle n_{qp} \rangle = 0.5$ . (d) Measured induced decay per quasiparticle.

Figure 4
(a) Pulse sequence which describes the quasiparticle pumping mechanism. Consecutive $\pi$ pulses are applied to the qubit with some variable time $\Delta$ T $= 30\mu$ s, finally the qubit is excited into its excited state and its decay is measured. (b) Results of the measured qubit decay as a function of the number of pump pulses. The observed qubit decay time increases with increasing pulse number. (c) The measured quasiparticle population, which is shown to initially decrease with pulses number before saturating near $\langle n_{qp} \rangle = 0.5$ . (d) Measured induced decay per quasiparticle.

In addition, the authors extract the mean quasiparticle number as a function of pulse number, and find that the quasiparticle number decreases with each pulse until the quasiparticle number saturates near $\langle n_{qp} \rangle \sim 0.5$ . The authors also find that the lifetime of the qubit due to a single quasiparticle decreases with pulse number, which is somewhat surprising, since we would expect that each individual quasiparticle would impact the qubit lifetime in the same way. This feature is understood because as the number of pulses is increased, the quasiparticles near the qubit generally have larger energy and will actually give some energy back to the qubit as well as taking energy away from it. These competing factors may actually lead to a reduction of $\tilde{T}_{1qp}$ .

To verify that this pumping scheme works for different types of systems, the authors utilize the same experimental protocol on another type of qubit, called a C-shunt flux qubit (see Fig. 5a for an image of the device), which is less sensitive to quasiparticles. The authors use the same method of applying $\pi$ pulses to the qubit to transfer energy to the quasiparticle bath, and their results are shown in Fig. 5.

Figure 5
(a) New device geometry which is less sensitive to quasiparticle tunneling. Because the readout mechanism doesn’t involve sourcing a current near the Josephson junctions which constitute the qubit, one might expect quasiparticles to be less important for qubit relaxation. (b) Measured qubit decay with and without quasiparticle pumping pulses. As seen from the fit, the qubit decay time increases by approximately a factor of two.

As seen in Fig. 5, even though the device is less sensitive to quasiparticles, when the authors use 5 pumping pulses, the average number of quasiparticles decreases by a factor of two and the qubit lifetime is increased by a factor of two!

Finally, in order to investigate the consistency of this pumping scheme, the authors continuously monitor the qubit decay with and without pumping pulses over 9 hours. In this data set, the experimental setup is in a configuration where the qubit decay is well described only by a single exponentially decaying function. Even so, the authors still find that the qubit decay time is increased when the pumping scheme is applied (see Fig. 6a). In the absence of quasiparticle pumping, the authors find large fluctuations in the decay time of the qubit, which leads to low signal-to-noise ratio in the data (see Fig. 6b, left panel, and Fig. 6c). When the pumping sequence is applied to the system, the measurements become much more stable, with fluctuations in the signal dominated by the noise added by the amplifiers in the system (see Fig. 6c).

Figure 6
(a) Measured qubit decay approximately one week after the data in the previous figure. In this data set, the decay is well described by only a single exponential function, yet the presence of pumping pulses is still found to increase the decay constant of the qubit lifetime. (b) Measurements of the qubit decay time as a function of time without (left) and with (right) quasiparticle pumping pulses. The pumping sequence significantly reduces the fluctuations in time of the measured data. (c) Standard deviation as a function of time of the data in (b). It is clear that the pumping pulses keep the fluctuations at a constant value in time, while in the absence of pumping pulses, the fluctuations are much larger at short delay times.

Conclusions:

In conclusion, the authors have introduced a new type of control scheme over superconducting qubits which gives energy to a local bath of quasiparticles near the qubit, and therefore ”pushes” them away from the qubit. As the quasiparticles diffuse away from the qubit, the qubit loses energy into the quasiparticle bath less frequently and therefore the qubit decay time is increased. Additionally, the authors verify that this scheme improves the qubit decay time across two different types of device geometries and find that it decreases fluctuations in the measured signal from the system. These experiments allow the authors not only to learn about the quasiparticle population in their devices, but also simultaneously improve the device performance. Outside of the field of quantum error correction, this work is the first demonstration of a dynamic enhancement of the qubit depolarization time $T_1$ .

Introduction:

Experimental Setup and Operating Principle:

Conclusions:

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