Session Q30: Focus Session: Superconducting Qubits: Architecture, Tunable, and Static Coupling

Coupling superconducting qubits and resonators

The performance of superconducting qubits has evolved rapidly in recent years, with coherence times now often measured in tens of microseconds. This makes superconducting qubits a promising candidate for a scalable quantum computing architecture and for modeling quantum systems. To realize this potential, consideration must be given to coupling multiple qubits to a system of microwave resonators in a way that balances coherence times, control and readout times, crosstalk, and space constraints. We compare three methods of coupling qubits to resonators: inductive coupling through a shared kinetic inductance with the resonator, capacitive coupling to a voltage antinode, and coupling to a three-dimensional superconducting cavity. We will also present designs and measurements of samples incorporating both inductively and capacitively coupled qubits on the same coplanar resonator. Lastly, we discuss a three-qubit/two-resonator system with one qubit bridging the two resonators that could serve as the building block of a large-scale architecture.   

Inductive coupling to the fluxonium qubit

Fluxonium is a highly anharmonic artificial atom, which utilizes an inductance formed by an array of large Josephson junctions to shunt the junction of a Cooper-pair box. The first excited state transition frequency is widely tunable with flux, and due to interactions of transitions to the second excited state with the readout cavity, a dispersive readout is possible over the entire five octave range. Previous fluxonium samples relied on a capacitive coupling to the readout cavity, but there is evidence that dielectric losses in these capacitors contributes significantly to relaxation [1]. We present a new method of coupling to the cavity through a mutual inductance, reducing relaxation through dielectric loss. \\[4pt] [1] V. E. Manucharyan et al., arXiv:1012.1928v1 (2010).   

A dc SQUID Phase Qubit with Controlled Coupling to the Microwave Line

We have designed and fabricated a Al/AlO$_{x}$/Al dc SQUID phase qubit on a sapphire substrate with a qubit junction area of 0.4 $\mu$m$^2$. The qubit junction is shunted with a 1 pF interdigitated capacitor, and is isolated from the bias leads by an LC filter and an inductive isolation network using a larger Josephson junction. Our previous device (A. Przybysz \textit{et al.}, IEEE Trans. on Appl. Supercond., 2011) with similar parameters had its relaxation time $T_{1}$ limited by coupling to the microwave line. To reduce this coupling, we adopted a coplanar stripline design and verified the coupling strength using finite element model microwave simulations. We will discuss our design, the microwave simulations, estimates for the overall coherence time due to losses and noise from various sources, the device fabrication process, and progress towards testing the device.   

Large tunable inductance of the decorated Josephson chain

We discuss the new design of a tunable superconductive inductance made from the decorated frustrated Josephson junction chains frustrated by magnetic field. We show that for the optimal choice of parameters the inductance of this chain varies in a very wide range as a function of the magnetic field. The resulting plasma frequency may exceed the value of quantum resistance, $\sqrt{L/C}\gg h/(2e)^2$ that characterizes superinductance. The important distinction of this design from the chain of dc-SQUIDs loops is the absence of phase slips at all magnetic fields. We present the results of the extensive numerical simulations that confirm these expectations.   

Driven dynamics of a qubit tunably coupled to a harmonic oscillator

We have investigated the driven dynamics of a superconducting flux qubit that is tunably coupled to a microwave resonator. We find that the qubit experiences an additional oscillating field mediated by off-resonant driving of the resonator, leading to unanticipated, strong modifications of the qubit Rabi frequency. Low-frequency noise in the coupling parameter translates to an effective noise in the amplitude of the drive field, causing a reduction of the coherence time during driven evolution. The noise can be mitigated with the rotary-echo pulse sequence, which, for driven systems, is analogous to the Hahn-echo sequence.   

Phase gate operation on a flux qubit via the readout SQUID line

Detuning a superconducting qubit from its rotating frame is one means to implement a phase gate operation. For superconducting flux qubits, this detuning can be realized by changing the magnetic flux threading the qubit loop, .e.g., by the mutual coupling from a nearby microwave antenna. In this work, we demonstrate an alternative approach: we implement a phase gate by pulsing a current through the readout DC SQUID. While the DC SQUID acts as a qubit flux sensor for readout, we in turn may use it as an actuator to impose the phase-gate flux shift. Using this pulsed current approach, we demonstrated Ramsey-type free-induction with more than 20 oscillation periods. We also studied the impact of the first phase gate on subsequent, sequential phase gates.   

Progress towards a metastable superconducting qubit

We will report on progress towards the demonstration of a metastable RF SQUID (MRFS) qubit, which has the potential to exhibit excited-state lifetimes many orders of magnitude longer than present-day superconducting qubits, while retaining long enough coherence times to allow gate error rates as low as $\sim 10^{-5}$. These properties result from the two main characteristics of the MRFS qubit: (i) its two lowest levels are essentially macroscopically distinct persistent-current states, which can be strongly decoupled from high-frequency electromagnetic fluctuations (in contrast to most superconducting qubits whose levels are approximately those of a nonlinear LC oscillator and are thus strongly coupled); and (ii) its extremely large inductance makes it only weakly sensitive to low-frequency magnetic flux noise.   

Quantum gates by qubit frequency modulation in circuit QED

Several types of two-qubit gates have been realized experimentally in circuit QED. These are based, for example, on tuning the pair of qubits in resonance with each other [Majer, Nature 449, 443-447 (2007)] or on a microwave pulse on one qubit at the transition frequency of a second qubit [Chow, Phys. Rev. Lett. 107, 080502 (2011)]. Another realization is based on a sequence of blue-sideband transitions generated by microwave pulses [Leek, Phys. Rev. B 79, 180511(R) (2009)]. Here, we propose a different approach relying on oscillations of the qubit frequency using a flux-bias line. We explain how frequency modulation leads to tunable qubit-resonator and qubit-qubit interactions. We also show how this form of quantum control leads to faster (first-order) sideband transitions and consider applications to two-qubit gates.   

Transmon qubit coupled to a quasi-lumped element resonator

We report on the design, fabrication and measurement of an Al/AlO$_{\mbox{x}}$/Al transmon qubit coupled to a quasi-lumped element superconducting resonator. Our resonator, which has a resonant frequency of $\approx 5.4\,$GHz, and a loaded quality factor $Q_l \approx 30,000$ is, in turn, coupled to a transmission line. The qubit is designed to have $E_J/E_c > 30$ to significantly decrease the sensitivity to low-frequency charge noise. The coupling of the qubit to the resonator is designed to be $g/2\pi> 100\, $MHz. We report and discuss preliminary spectroscopic measurements and coherence measurements of the qubit.   

Fast, coherent control of the tunable coupling qubit

We present results of time domain measurements on a tunable coupling qubit (TCQ) coupled to a superconducting coplanar waveguide resonator. The TCQ has the benefit of independently tunable qubit frequency and cavity-qubit coupling. We show that the TCQ's frequency and coupling can be dynamically controlled in tens of nanoseconds by using two on-chip flux control lines. Using this dynamic control, Rabi oscillations were measured at various coupling strengths showing that the coupling can be reduced by a factor greater than 1500. To measure qubit coherence at low coupling, the TCQ was tuned to a high coupling region, excited by a~synchronized~pi-pulse and then returned to the zero coupling region where the qubit state was measured. ~Coherence times of several microseconds were measured and are comparable to other superconducting qubits   

Transferring the state of a quantum register to a single oscillator: a simple circuit verses numerical optimization

We consider the problem of swapping a quantum state between a register of qubits and a single quantum oscillator. We design a mesoscopic quantum circuit to do this, using an off-resonant interaction, based on the concept of coherent feedback control. We consider an explicit realization of this circuit, and perform simulations of its performance. We then take a different approach, in which we couple the register directly to the resonator, including inter-qubit couplings and local controls, and use numerical optimization to search for a control protocol that will achieve the swap with very high fidelity. Our results show that the protocols found using numerical searches are superior in speed and fidelity to the manually-designed circuit. We also explore how the time and complexity of the protocols increases with the problem size.   

Gradiometric persistent current flux qubit with tunable tunnel coupling

The persistent current flux qubit is a Josephson junction based superconducting circuit exhibiting a strong anharmonicity in combination with excellent coherence times of more than 10\,$\mu$s. However, quantum coherence decreases drastically away from an optimal point and a controlled design of the transition frequency at this point is demanding with respect to fabrication stability. Here, we present the spectroscopic analysis of a gradiometric flux qubit, where the tunnel coupling can be tuned from a few hundreds of Megahertz to several Gigahertz.   

Large dispersive shift in superconducting flux qubit

We study dispersive readout in superconducting flux qubits which are capacitively coupled to a superconducting cavity with $\sim$ 10 GHz resonant frequency $f_r$. To discriminate the state of the qubit precisely, large magnitude of the dispersive shift $\chi$ is desirable. For the two-level system, $\chi$ is given by $g^2/\Delta$ where $g$ is the coupling strength and $\Delta$ is the detuning between the qubit and the cavity. For the multilevel system such as superconducting qubits, however, this formula is modified due to the contributions from higher levels [1]. It has been pointed out that if $f_r$ lies between 01 and 12 transition frequencies of the qubit ($f_{01}$ and $f_{12}$, respectively), $|\chi|$ becomes large because of constructive contributions from different levels [1]. Our flux qubit has $f_{01}=$ 5 GHz and $f_{12}=$ 15 GHz at the optimal flux bias, thus satisfying this condition. Moreover, because of the large anharmonicity ($|f_{12} - f_{01}|$) of the flux qubit, we can easily make $g$ as large as $\sim$ 100 MHz, while staying in the deep dispersive limit. Both of these enhance $|\chi|$ and we have obtained $\chi$ of 80 MHz at the optimal flux bias, which agrees well with the prediction by the energy band calculation. [1] J. Koch et al., PRA 76, 042319 (2007)