a switching event occurs, quasiparticles are
created in close vicinity to the SQUID junctions, leading to an increase in the overall quasiparticle density.
We next investigate quasiparticle pumping in
a dispersively read-out C-shunt flux qubit (device
B), consisting of a flux qubit loop shunted by a
large capacitance (Fig. 3A). Although the capacitor improves the qubit coherence by reducing its
sensitivity to charge noise, the C-shunt flux qubit
is still affected by quasiparticle fluctuations.
As reported in (24), the qubit was observed to
switch between a stable configuration, with a
purely exponential decay with T1 > 50 ms, and an
unstable configuration, with nonexponential decay and temporal fluctuations. The switching between the various configurations was found to
occur on a slow time scale, ranging from hours to
several days. Similar switching events between
stable and unstable configurations have also been
observed in a fluxonium qubit and were attributed
to fluctuations in the quasiparticle density (22).
We next investigated how the quasiparticle
pumping sequence affects the coherence of de-
vice B, both in stable and unstable configura-
tions. Because the switching between different
configurations is random but slow, we were care-
ful to average only over intervals when no
switching event occurred. Figure 3B shows the
decay of device B, measured with and without
N = 5 quasiparticle pumping pulses. The data
were taken when the device was in a config-
uration where the qubit decay was clearly non-
exponential, which is well captured by fits to
Eq. 1 (solid lines in Fig. 3B). We observed a drop
in the quasiparticle population from 0.87 to 0.35,
leading to a twofold enhancement in the qubit
decay time. Note that the long-time decay rate
is identical for both traces, as expected because
the pumping scheme does not affect nonquasi-
particle relaxation channels. The results demon-
strate that the pumping scheme works even though
device B does not have a ground electrode for
trapping quasiparticles, but it has been shown
that vortices in the capacitor pads can also act
as quasiparticle traps (26). The pumping scheme
should also be applicable to other qubit modal-
ities in which quasiparticle tunneling contributes
to qubit relaxation.
The data in Fig. 3B were acquired by continuously measuring qubit decay traces over a 1-hour
period and averaging them together. Figure 4
shows similar repeated measurements of the
qubit decay with and without pumping pulses,
but these traces were acquired about a week
after the data in Fig. 3. In the more recent data
set, the qubit is in a configuration where the
averaged decay function is relatively well described by a single exponential, both with and
without pumping pulses (Fig. 4A), and the five
pumping pulses improve the decay time by only
~6%. However, when investigating the individual decay traces (Fig. 4B), we found substantial
amounts of noise and temporal fluctuations in
the readout signal for the data without pumping
pulses. These random variations vanish when implementing the pumping sequence (right panel
of Fig. 4B).
To quantify the improvements in variability,
we calculated the standard deviation of the read-
out signal over 9 hours of data (Fig. 4C). With
pumping pulses, the standard deviation is inde-
pendent of the readout delay t and can be as-
cribed to the noise of the high–electron-mobility
(HEMT) amplifier used for amplification. With-
out pumping pulses, the standard deviation is
substantially larger for t < 50 ms but approaches
the same level as for N = 5 for long delay times.
The increased noise is caused by variations in the
qubit T1 time, which lead to strong fluctuations
in the qubit population directly after the initial p
pulse. The fluctuations are reduced as the qubit
decays to the ground states for long t, leaving
only the contributions from the HEMT noise.
Our implementation of a stochastic scheme
to dynamically shape the environment by pumping quasiparticles in a superconducting flux qubit
lead to substantial improvements in both qubit
coherence times and coherence variability. In addition to applications in superconducting qubits,
we anticipate our results to be of practical importance for implementing Majorana fermions
in hybrid semiconductor–superconductor systems,
where the presence of a single quasiparticle is
detrimental to the device performance (25).
REFERENCES AND NOTES
1. E. Hahn, Phys. Rev. 80, 580–594 (1950).
2. K. W. Murch, S. J. Weber, K. M. Beck, E. Ginossar, I. Siddiqi,
Nature 499, 62–65 (2013).
3. D. J. Reilly et al., Science 321, 817–821 (2008).
4. W. Happer, Rev. Mod. Phys. 44, 169–249 (1972).
5. S. O. Valenzuela et al., Science 314, 1589–1592 (2006).
6. D. Wineland, R. Drullinger, F. Walls, Phys. Rev. Lett. 40,
7. J. Aumentado, M. W. Keller, J. M. Martinis, M. H. Devoret, Phys.
Rev. Lett. 92, 066802 (2004).
8. P. J. D. Visser et al., Phys. Rev. Lett. 106, 167004 (2011).
9. V. F. Maisi et al., Phys. Rev. Lett. 111, 147001 (2013).
10. E. M. Levenson-Falk, F. Kos, R. Vijay, L. Glazman, I. Siddiqi,
Phys. Rev. Lett. 112, 047002 (2014).
11. R. Lutchyn, L. Glazman, A. Larkin, Phys. Rev. B 72, 014517
12. J. M. Martinis, M. Ansmann, J. Aumentado, Phys. Rev. Lett.
103, 097002 (2009).
13. G. Catelani et al., Phys. Rev. Lett. 106, 077002 (2011).
14. J. Leppäkangas, M. Marthaler, Phys. Rev. B 85, 144503
15. L. Sun et al., Phys. Rev. Lett. 108, 230509 (2012).
16. D. Ristè et al., Nat. Commun. 4, 1913 (2013).
17. J. Schreier et al., Phys. Rev. B 77, 180502 (2008).
18. G. Catelani, S. E. Nigg, S. M. Girvin, R. J. Schoelkopf,
L. I. Glazman, Phys. Rev. B 86, 184514 (2012).
19. S. E. de Graaf et al., Phys. Rev. Lett. 111, 137002
20. J. Wenner et al., Phys. Rev. Lett. 110, 150502 (2013).
21. I. M. Pop et al., Nature 508, 369–372 (2014).
22. U. Vool et al., Phys. Rev. Lett. 113, 247001 (2014).
23. M. Bal, M. H. Ansari, J.-L. Orgiazzi, R. M. Lutchyn, A. Lupascu,
Phys. Rev. B 91, 195434 (2015).
24. F. Yan et al., Nat. Commun. 7, 12964 (2016).
25. D. Rainis, D. Loss, Phys. Rev. B 85, 174533 (2012).
26. C. Wang et al., Nat. Commun. 5, 5836 (2014).
27. I. Nsanzineza, B. L. Plourde, Phys. Rev. Lett. 113, 117002
28. M. Taupin, I. M. Khaymovich, M. Meschke, A. S. Mel’nikov,
J. P. Pekola, Nat. Commun. 7, 10977 (2016).
29. Supplementary materials are available on Science Online.
30. K. Geerlings et al., Phys. Rev. Lett. 110, 120501 (2013).
31. M. Stern et al., Phys. Rev. Lett. 113, 123601 (2014).
We thank M. Blencowe, D. Campbell, M. Devoret, J. Grover,
P. Krantz, and I. Pop for useful discussions and P. Baldo,
V. Bolkhovsky, G. Fitch, J. Miloshi, P. Murphy, B. Osadchy, K. Parrillo,
R. Slattery, and T. Weir at MIT Lincoln Laboratory for technical
assistance. This research was funded in part by the Office of the
Director of National Intelligence (ODNI), Intelligence Advanced
Research Projects Activity (IARPA), and the Assistant Secretary
of Defense for Research and Engineering via MIT Lincoln Laboratory
1576 23 DECEMBER 2016 • VOL 354 ISSUE 6319 sciencemag.org SCIENCE
Fig. 4. Reduction of
qubit coherence variations with quasiparticle pumping. (A)
Averaged qubit decay,
measured with and
pulses. The decay
function is close to
exponential in both
cases. The decay time
increases by ~6% with
the pumping pulses.
The traces have not
been normalized to
account for the decay
during the pulse
reduced contrast for
the data with N = 5. The
data were measured
with DT = 30 ms.
(B) Individual traces of
the averaged decay
data shown in (A), measured without (left) and with five pumping pulses (right). The pumping sequence substantially reduces the temporal fluctuations observed in the decay without pumping
pulses. (C) Standard deviation of the data in (B), demonstrating the strong reduction in temporal
shot-to-shot fluctuations in the presence of the pumping pulses.