The large physical size of superconducting qubits and their associated on-chip control structures presents a practical challenge toward building a large-scale quantum computer. In particular, transmons require a high-quality-factor shunting capacitance that is typically achieved by using a large coplanar capacitor. Other components, such as superconducting microwave resonators used for qubit state readout, are typically constructed from coplanar waveguides, which are millimeters in length. Here, we use compact superconducting through-silicon vias to realize lumped-element capacitors in both qubits and readout resonators to significantly reduce the on-chip footprint of both of these circuit elements. We measure two types of devices to show that through-silicon vias are of sufficient quality to be used as capacitive circuit elements and provide a significant reduction in size over existing approaches.
We have fabricated and characterized systems consisting of superconducting quantum bits (qubits) of the transmon type, coupled to a tunable transmission line resonator. The resonator consists of a superconducting quarter wavelength coplanar waveguide (CPW) resonator that is made tunable by terminating the transmission line to ground through a superconducting quantum interference device (SQUID). Here we present measurements on two devices where we observe Rabi oscillations as we drive the qubit, and vacuum Rabi splitting both as we tune the qubits into resonance with the resonator and as we tune the resonator into resonance with the qubits. We also observe coherent interaction between two resonant qubits. In addition, we demonstrate that we can calculate the response very accurately using a multilevel Hamiltonian.
The leading approach to attempt quantum computing is based on superconductors. In particular, Circuit Quantum Electrodynamic systems (circuit QED) are used to couple photons stored in a microwave resonator to a quantum bit (qubit), allowing the qubit to be controlled and measured. A lumped element parallel RLC circuit will be used to model a superconducting coplanar microwave resonator, in order to gain an intuitive understanding of how various parameters affect its electromagnetic properties, and how they can be optimised to provide desired specifications. Resonator quality factors will also be realised, which describe the effects of coupling the microwave resonator to external input/output transmission lines. The qubit is generated by a superconducting capacitively shunted Josephson Junction; the transmon, and its operation and non-linear behaviour will be discussed in this report. The transmon is integrated with a microwave resonator to generate the circuit QED system, and the derivation of the systems Hamiltonian will allow us to determine the equations describing the behaviour of the system, and therefore how it may be controlled and measured. The Bloch sphere will be introduced, which provides a useful geometric representation of the state space of a two-level quantum system. Mapping the derived Hamiltonian to the time-dependent Schrodinger equation facilitates realisation of control mechanisms of the qubit based on rotations about the Bloch sphere.
We design and fabricate a compact superconducting qubit circuit made of nano-thick NbN film on a high-resistivity silicon substrate, carrying seven transmon qubits. By comparing with the conventional superconducting qubit circuits made of superconducting films with hundred-nanometer thickness, our superconducting qubit circuit has much smaller size in the readout circuit, whose resonator length is only about 1/20 of that in a conventional superconducting circuit. Transmons are measured and characterized in the frequency and time domains with different flux bias. The transition frequency f01 can be adjusted in the range of several GHz. The qubit circuits made of such nano-thick material with high kinetic inductance are promising in the integration of quantum circuits.
I discuss the design, fabrication and measurement at millikelvin-temperatures of Al/AlO
x/Al Josephson junction-based transmon qubits coupled to superconducting thin-film lumped element microwave resonators made of aluminum on sapphire. The resonators had a center frequency of around
6GHz, and a total quality factor ranging from 15,000 to 70,000 for the various devices. The area of the transmon junctions was about
150nm×150nm and with Josephson energy
EJ such that
10GHz≤EJ/h≤30GHz. The charging energy of the transmons arising mostly from the large interdigital shunt capacitance, was
Ec/h≈300MHz. I present microwave spectroscopy of the devices in the strongly dispersive regime of circuit quantum electrodynamics. In this limit the ac Stark shift due to a single photon in the resonator is greater than the linewidth of the qubit transition. When the resonator is driven coherently using a coupler tone, the transmon spectrum reveals individual ``photon number'' peaks, each corresponding to a single additional photon in the resonator. Using a weighted average of the peak heights in the qubit spectrum, I calculated the average number of photons
nˉ in the resonator. I also observed a nonlinear variation of
nˉ with the applied power of the coupler tone
Prf. I studied this nonlinearity using numerical simulations and found good qualitative agreement with data. In the absence of a coherent drive on the resonator, a thermal population of
5.474GHz photons in the resonator, at an effective temperature of
120mK resulted in a weak
n=1 thermal photon peak in the qubit spectrum. In the presence of independent coupler and probe tones, the
n=1 thermal photon peak revealed an Autler-Townes splitting. The observed effect was explained accurately using the four lowest levels of the dispersively dressed Jaynes-Cummings transmon-resonator system, and numerical simulations of the steady-state master equation for the coupled system. I also present time-domain measurements on transmons coupled to lumped-element resonators. From
T1 and Rabi oscillation measurements, I found that my early transmon devices (called design LEv5) had lifetimes (
T1∼1μs) limited by strong coupling to the
50Ω transmission line. This coupling was characterized by the the rate of change of the Rabi oscillation frequency with the change in the drive voltage (
dfRabi/dV) -- also termed the Rabi coupling to the drive. I studied the design of the transmon-resonator system using circuit analysis and microwave simulations with the aim being to reduce the Rabi coupling to the drive. By increasing the resonance frequency of the resonator
ωr/2π from 5.4
GHz to 7.2
GHz, lowering the coupling of the resonator to the transmission line and thereby increasing the external quality factor
Qe from 20,000 to 70,000, and reducing the transmon-resonator coupling
g/2π from 70
MHz to 40
MHz, I reduced the Rabi coupling to the drive by an order of magnitude (
∼ factor of 20). The
T1∼4μs of devices in the new design (LEv6) was longer than that of the early devices, but still much shorter than the lifetimes predicted from Rabi coupling, suggesting the presence of alternative sources of noise causing qubit relaxation. Microwave simulations and circuit analysis in the presence of a dielectric loss tangent
tanδ≃5×10−6 agree reasonably well with the measured
T1 values, suggesting that surface dielectric loss may be causing relaxation of transmons in the new designs.
We address the scaling-up problem for superconducting quantum circuits by using lumped-element resonators based on an alternative fabrication method of aluminum-aluminum oxide-aluminum (Al-
AlOx-Al) parallel-plate capacitors. The size of the resonators is only
0.04mm2, which is more than one order smaller than the typical size of coplanar resonators (
1mm2). The fabrication method we develop easily fits into the standard superconducting qubit fabrication process. We obtain capacitance per area $14\phantom{\rule{0.2em}{0ex}}\mathrm{fF}/\text{\ensuremath{\mu}}{\mathrm{m}}^{2}$ and the internal quality factor $1\ifmmode\times\else\texttimes\fi{}{10}^{3}$--$8\ifmmode\times\else\texttimes\fi{}{10}^{3}$ at the single-photon level. Our results show that such devices based on Al-
AlOx-Al capacitors could be further applied to the qubit readout scheme, including resonators, filters, amplifiers, as well as microwave metamaterials and innovative types of qubits, such as $0\ensuremath{-}\ensuremath{\pi}$ qubit.