IBM Research paper - Superconducting qubit 0.1ms

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					  Superconducting qubit in waveguide cavity with coherence time approaching 0.1ms

          Chad Rigetti,1 Stefano Poletto,1 Jay M. Gambetta,1 Britton Plourde,2 Jerry M. Chow,1 A. D.
        C´rcoles,1 J. R. Rozen,1 George A. Keefe,1 Mary B. Rothwell,1 Mark B. Ketchen,1 and M. Steffen1
                            IBM T.J. Watson Research Center, Yorktown Heights, NY 10598, USA
                      Department of Physics, Syracuse University, Syracuse, New York 13244-1130, USA
               We report a superconducting artificial atom with an observed quantum coherence time of T2 =
            95µs and energy relaxation time T1 = 70µs. The system consists of a single Josephson junction
            transmon qubit embedded in an otherwise empty copper waveguide cavity whose lowest eigenmode
            is dispersively coupled to the qubit transition. We attribute the factor of four increase in the
            coherence quality factor relative to previous reports to device modifications aimed at reducing qubit
            dephasing from residual cavity photons. This simple device holds great promise as a robust and
            easily produced artificial quantum system whose intrinsic coherence properties are sufficient to allow
            tests of quantum error correction.

            PACS numbers: 03.67.Ac, 42.50.Pq, 85.25.-j

   Superconducting quantum circuits are one of the lead-        fabrication processes, facilities, and measurement setups?
ing candidate technologies for large scale quantum com-         Second, what is the origin of the dephasing process sup-
puting. They have been used to observe a violation of           pressing T∗ well below the no-pure-dephasing limit of
a Bell inequality [1]; implement a simple two-qubit gate        2T1 ? Is it intrinsic to the junctions or to this qubit ar-
favorable for scaling [2]; generate three-qubit entangle-       chitecture? The weight and urgency of these questions
ment [5]; perform a routine relevant for correction [3];        are increased by implications on scaling potential: if the
and very recently to demonstrate a universal set of quan-       results are reproducible and decoherence times can be
tum gates with fidelities greater than 95% [4]. Most of          extended close to the 2T1 limit for observed T1 times,
these devices employ small angle-evaporated Josephson           this technology becomes an immediate candidate for the
junctions as the critical non-linear components that pro-       construction of prototype processors for testing QEC,
duce an anharmonic spectrum and allow coherent state            without significant need of longer coherence. It would
control within a computational subspace. While existing         also suggest that other systems based on small angle-
superconduting qubit architectures appear to be consis-         evaporated junctions, such as traditional planar inte-
tent with basic requirements for quantum error correction       grated circuit architectures, may also be able to attain
(QEC) and fault tolerance [7], the construction and op-         similar performance if present performance limits can be
eration of much larger systems capable of meaningfully          identified and overcome.
testing such procedures will require individual qubits and         In this Letter we report a device in the 3D design
junctions with a very high degree of coherence. Current         that demonstrates the basic reproducibility of Paik, et
estimates for threshold error rates, along with the cu-         al. and, further, shows that the decoherence times can be
mulative nature of errors originating from control, mea-        further extended by taking precautions to protect against
surement, and decoherence, makes it likely that coherent        qubit dephasing induced by the fluctuations of the cav-
lifetimes at least 10−3 times longer than typical gate and      ity photon number during qubit operation. With these
measurement times are needed [6], corresponding for typ-        precautions our system has significantly enhanced coher-
ical systems to quantum lifetimes of 20 to 200µs.               ence, with with T2 =95µs (Q2 ≈2.5×106 ) and T1 = 70µs
   Progress towards longer qubit coherence has contin-          (Q1 ≈1.8×10 ). This level of performance places this
ued for the past decade, spurred largely by clever meth-        device well within the regime where microwave control
ods of decoupling noise and loss mechanisms from the            techniques can be used to perform quantum gates with
qubit transition and thereby realizing actual Hamiltoni-        fidelities exceeding those required for error correction.
ans more closely resembling their idealized versions. Re-          In the 3D cQED framework, qubits are manufactured
cently, Paik, et al. made a breakthrough advance [9] by         with a standard lithographic process while the cavities,
embedding a transmon-style qubit [11, 12] in a waveg-           simple macroscopic resonant enclosures, are produced in-
uide cavity. This system, dubbed three-dimensional cir-         dependently and with very different techniques, such as
cuit QED (3D cQED), led to the observation of signif-           precision machining or laser etching. Individual qubits
icantly enhanced qubit lifetimes T1 of 25–60µs and T∗    2      and cavities can be treated as discrete components; their
of 10–20µs corresponding to quality factors for dissipa-        properties, materials, and designs may be varied indepen-
tion and decoherence of Q1 ≈1.8×106 and Q2 ≈7×105 ,             dently without special effort. The large mode volumes,
respectively.                                                   structural simplicity, and absence of very large aspect
   These results lead to two important questions. First,        ratio thin films make full-device electromagnetic simula-
are similar coherence properties observable using other         tion highly accessible. These properties in turn facilitate

a high degree of practical control and engineerability of      a                                                                     e
qubit system and its electromagnetic environment.                                                                              50K


   In this work we exploit these and other properties of 3D
cQED systems to engineer a device more robust against                                                                     HEMT

a leading candidate for the dominant dephasing process                                                                    LNA 2.8K
observed in earlier work: qubit dephasing due to the pres-
ence and fluctuations of residual photon population in the


cavity. We do this by three parallel methods. First, we
select qubit and cavity parameters to reduce the expected                                                            NbTi
qubit dephasing rate per residual photon in the funda-                                       18.6mm                  coax

mental cavity mode. Second, we engineer the device to            15.5mm
limit the spectral proximity of and couplings to higher                                                                   isolator
modes of the cavity. We employ a symmetric cavity              b                                                          ( x 2)
                                                               TE101         TE102        TE201
shape such that the next nearest mode after the funda-
mental that couples to the qubit is at ≈ 24GHz, or more                                                                   12GHz
than 20GHz detuned from the qubit transition. This de-
                                                               11.84 GHz     18.80 GHz    20.77 GHz
sign minimizes the role of higher modes and makes the          TE301         TE202                        DUT      cryoperm
standard single-mode cavity approximation more robust.                                                             shield
Third, we aim to suppress residual cavity population by                                                                              d
following a simple rule: the thermal photon temperature        24.03 GHz     25.19 GHz    28.00 GHz
of a resonant mode, be it linear or nonlinear, is upper-
                                                               c qubit       resonator   environment
bounded by the temperature of the dissipation source
limiting its quality factor (Q). Typically, the quality fac-                                       IN
tors of cQED resonators are limited by the ohmic envi-
ronment external to the resonator to which the device is
coupled. But it is notoriously difficult to ensure that the
modes of a feedline are thermalized to very low temper-
                                                               FIG. 1. (color online) Transmon qubit in three-dimensional
atures [8]. Rather than solving this problem directly, we      copper waveguide cavity with long coherence. (a) Device
instead make use of an ideal cold resistor – the interior      model (HFSS) showing interior volume of the waveguide en-
walls of a bulk oxygen-free high-conductivity (OFHC)           closure housing a sapphire chip and transmon qubit, with
copper cavity – as the limiting source of dissipation. In      two symmetric coaxial connectors for coupling signals in/out.
conjunction with the under-coupling of the cavity to the       (b) Eigenmodes of the enclosure with sapphire chip (obtained
external environment, this internal cavity dissipation is      with HFSS eignemode solver) illustrating robustness of single-
                                                               mode-cavity approximation. The qubit is positioned at a cav-
expected to thermalize the cavity photon population to
                                                               ity symmetry point where the fundamental mode (TE101) is
the temperature of the bulk copper, which in turn is eas-      maximal. Device dimensions and symmetries imply that next
ily anchored to the lowest available temperature.              mode interacting with qubit (TE301) is > 20 GHz detuned
   The three-dimensional circuit QED sytem we report           from qubit. (c) Equivalent circuit diagram of device. The in-
is described in the two-level, dispersive, and single-mode     terior walls of the OFHC copper waveguide cavity provide a
cavity approximations by the Hamiltonian [10]                  readily thermalized cold resistor (light blue) that is expected
                                                               to sink the residual cavity photon population to the lowest
                              ω01                              available temperature. (d) Optical imgage of transmon, con-
            H/¯ = ωc a† a −
              h                   σz − χa† aσz .        (1)
                               2                               sisting of two capacitor pads 350x700µm2 each, separated by
                                                               a 50µm wire interrupted by a shadow evaporated Al/AlOx/Al
The term proportional to a† aσz can be interpreted as a        Josephson junction. Pads are formed of mesh with 5µm wires
cavity photon number dependent shift of the qubit transi-      and 25µm2 holes to suppress vortex trapping and motion. (c)
tion frequency (ac-Stark shift), or as a qubit state depen-    Cryogenic microwave measurement setup. Epxeriments per-
dent shift of the cavity frequency (cavity pull). For trans-   formed at base temperature of 8mK in a BlueFors cryogen-free
                                                               dilution refrigerator.
mons the cavity pull χ = −g 2 EC /(∆2 − ∆EC ) where g is
the bare coupling strength, ∆ = ω01 − ωc is the cavity–
qubit detuning and EC = e2 /2CΣ is the transmon charg-         surement of the qubit state [10]. It can result from both
ing energy and CΣ is the total qubit capacitance [11]. In      thermal and coherent cavity photon populations.
the strong dispersive coupling regime the cavity pull can        We represent thermal driving of the resonator by the
be larger than the intrinsic linewidth of the qubit transi-    master equation [13]
tion. In such systems, fluctuations of the cavity photon
number scramble the qubit frequency and place a limit                   i
on coherence. This occurs through the same mechanism               ρ = − [H, ρ] + κj (nthj + 1)D[a]ρ + κj (nthj )D[a† ]ρ,
that allows the cavity photons to induce a projective mea-                                                              (2)

          ˆ          ˆ ˆ      ˆ ˆ    ˆ ˆ
where D[L]ρ = 2LρL† − L† Lρ − ρL† L /2 is the stan-
dard Linblad super-operator for dissipation, κj is the
cavity relaxation rate through source j, and nthj =

                                                                   signal [a.u.]
1/(ehω01 /kTj −1) is the thermal photon number for source
j at temperature Tj . Following a similar procedure to
Refs. [14, 16] the thermal-induced dephasing rate at
times long compared to 1/κtot is
                                                      
       κtot               2iχ       8iχ j κj nthj                                  0   10   20    30       40       50    60         70   80
Γth =       Re      1+           +                 − 1 .                                              time [µs]
        2                 κtot           κ2

For large κtot /χ [17],

                                                                   signal [a.u.]
                                                       
                 4χ2      j κj nthj
         Γth =                               κj nthj + 1   (4)
                        tot               j

while it saturates to Γth = j κj nthj for large χ/κtot .                                                                        T1=70µs

   These suggest different possible strategies to mitigate
                                                                                   0   50   100   150     200       250   300       350   400
cavity photon induced dephasing: suppress fluctuations                                                   time [us]
of the photon number by using very high Q cavities, ef-
fectively pushing photon shot noise to lower and lower             FIG. 2. (color online) Quantum state lifetimes. (a) Quantum
frequencies; or, suppress the photon number with a cold            coherence time. (b) Energy relaxation time.
dissipation source internal to the cavity. In the first strat-
egy, one must ensure that the modes of the feedlines cou-
pled to the cavity are cold at all relevant frequencies,           Measurement is performed with standard circuit QED
as the cavity modes will thermalize to the same tem-               dispersive measurement techniques [15] using the low-
perature. In the second, the internal cold dissipation is          est resonant mode of the enclosure (TE101) which is
expected to thermalize all cavity modes. In both cases,            found experimentally at 12.1GHz. The cavity is closed
one pays a price in effective signal to noise of the mea-           with brass screws, wrapped with Eccosorb foam and alu-
surement, but for different reasons. The cold dissipation           minized mylar to protect against stray radiation [18],
leads to a loss of information-carrying photons within the         placed inside a cryoperm magnetic shield, and thermal-
cavity before they can be measured; the high Q approach            ized to the mixing chamber stage of a dilution refrigera-
requires longer and longer measurement integration and             tor.
repetition times.                                                     Control and measurement signals are supplied from
   In this Letter we follow the second strategy by em-             room temperature electronics to the cavity through stan-
ploying the interior surfaces of an enclosure machined             dard attenuated wideband coaxial lines. Measurement
from bulk OFHC copper as an ideal cold resistor that               signals exiting the cavity pass through (respectively) a
appears as parallel damping of the effective cavity res-            12GHz low pass filter (K&L LP12000) thermalized to
onant circuit and limits its Q. The cavity, accordingly,           10mK with a copper wire wrap; two double-junction and
is under-coupled to the input and output transmission              magnetically shielded isolators (Pamtech) thermalized to
lines.                                                             10mK via large copper plates with multiple high-pressure
   Our device is shown in figure 1. The transmon qubit              contact points; a NbTi/NbTi superconducting cable from
junction has characteristic energy EJ /h=10.3946 GHz.              10mK to the 2.8K stage and thermalized at each end
The qubit capacitance is determined from measurement               and at its midpoint (80mK) with wire wrap. At 2.8K
to be CΣ =91f F, implying EJ /EC =49, placing the qubit            the signal is amplified by a low-noise wideband HEMT
in the transmon regime [10–12]. Qubits are produced in             amplifier (Caltech) operating from 6-18GHz with a noise
a 3” wafer process on c-plane 330µm thick sapphire prior           temperature of 10-15K. The signal is amplified again at
to dicing into 3.2mm×6.7mm chips. The chip is enclosed             room temperature before being mixed down to 10MHz
in a cavity machined from bulk OFHC copper. The cav-               and digitized. In-phase and quadrature components of
ity is formed by two halves and has in the assembled               the signal are summed to produce a measurement of the
state an interior volume 18.6×15.5×4.2mm3 plus sym-                qubit energy eigenstate.
metric cylindrical perturbations (d=7.7mm; h=4mm) of                  We performed standard measurements to characterize
the ceiling to accommodate commercial bulkhead SMA                 qubit device properties and performance. We find the
connectors through which signals are coupled in and out.           following parameters: ω01 /2π ≈4.2 GHz; ωc /2π ≈12.1

GHz; g/2π =153 MHz; χ=780 kHz; and a cavity with               performance, along with the simplicity and discrete na-
an internally limited Qc =10,400 [19] implying a Purcell       ture of the qubits and cavities, makes this technology
limit on qubit energy relaxation time of about 400µS, well     an intriguing candidate for the construction of prototype
above the measured T1 . Excited state lifetime and Ram-        quantum processors with 10-1000 qubits, though more
sey fringes experiments yield T1 = 70µs and T2 =95µs           work is called for to determine whether multi-qubit sys-
(Figure 2). Our data are consistent with our hypoth-           tems can be demonstrated with similar performance.
esis that a 3D circuit QED system whose cavity has a             We acknowledge support from IARPA under Contract
lower internal quality factor can facilitate significantly      No. W911NF-10-1-0324. We acknowledge discussions
improved qubit coherence.                                      and contributions from John Smolin, Seth Merkel, Jack
   What are the trade-offs with this approach? The ex-          Rohrs and Joel Strand.
perimenter pays a price in convenience: the increased
internal dissipation implies that for every photon exiting
the cavity to be amplified and measured three are dis-
sipated in the normal metal walls. This places greater
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demands on the performance of the amplification chain
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modes are already thermalized to the lowest available               B. R. Johnson, J. A. Smolin, J.R. Rozen, G. A. Keefe,
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challenging to realize in practice due to basic materials           Rev. Lett. 107, 080502 (2011).
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properties at mK temperatures and the sensitivity of the
                                                                    M. Girvin, R. J. Schoelkopf, Nature 482 382–385 (2012)
system to even small fractions of a photon. In one ex-          [4] J. M. Chow,et al.,in preparation.
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reduce this temperature as much as possible and a bound             Chow, J. M. Gambetta, L. Frunzio, S. M. Girvin, M. H.
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liability of the thermal link between the qubit substrate           Schoelkopf, Nature Physics 5, 105 - 109 (2009)
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be done, for example, with bulk copper cavities whose               Stochastic Methods with Applications to Quantum Optics
interior walls are partially coated with a thin layer of            (Springer, New York, 2004).
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breakthrough results of Paik, et al. by constructing a
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3D qubit system based on a single-junction transmon                 062320 (2004)
in a copper waveguide cavity with lifetimes T2 =95µs           [16] A. A. Clerk and D. Wahyu Utami, Phys. Rev. A, 75,
and T1 =70µs. Our results provide evidence that the                 042302 (2007).
highly coherent properties of qubits based on small            [17] P. Bertet, et al., Phys. Rev. Lett. 95, 257002 (2005).
shadow evaporated Josephson junctions may be robust            [18] A. D. Corcoles, J. M. Chow, J. M. Gambetta, C. Rigetti,
to changes fabrication processes, facilities, and measure-          J. R. Rozen, G. A. Keefe, M. Beth Rothwell, M. B.
                                                                    Ketchen, and M. Steffen, Applied Physics Letters 99,
ment setups. By pursuing three parallel approaches to
                                                                    181906 (2011)
improving coherence limits due to cavity photon induced        [19] An otherwise identical cavity made of bulk (supercon-
dephasing we have attained a factor of four improvement             ducting) aluminum was measured to have Q=40,000.
in the coherence quality factor Q2 =2.5×106 of a super-
conducting qubit relative to previous reports. Our de-
vice falls well within the range of coherent performance
required for large scale tests of error correction and fault
tolerant quantum computing procedures. We believe this

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