We propose a fast scheme to generate Schrödinger cat states in a superconducting resonator using a continuously driven qubit without resorting to the dispersive regime, two-photondrives, or engineered two-photon dissipation. We provide analysis for when the qubit is on and off resonance from the drive. We extend our analysis to account for a third level in a weakly-anharmonic qutrit. We also discuss the case of a strongly-anharmonic qutrit. Throughout the paper, we corroborate our analytical results with numerical simulations in the presence of energy relaxation and dephasing of the qubit and resonator using realistic experimental parameters.
Superconducting quantum computing is experiencing a tremendous growth. Although major milestones have already been achieved, useful quantum-computing applications are hindered by avariety of decoherence phenomena. Decoherence due to two-level systems (TLSs) hosted by amorphous dielectric materials is ubiquitous in planar superconducting devices. We use high-quality quasilumped element resonators as quantum sensors to investigate TLS-induced loss and noise. We perform two-tone experiments with a probe and pump electric field; the pump is applied at different power levels and detunings. We measure and analyze time series of the quality factor and resonance frequency for very long time periods, up to 1000 h. We additionally carry out simulations based on the TLS interacting model in presence of a pump field. We find that loss and noise are reduced at medium and high power, matching the simulations, but not at low power.
Amorphous dielectric materials have been known to host two-level systems (TLSs) for more than four decades. Recent developments on superconducting resonators and qubits enable detailedstudies on the physics of TLSs. In particular, measuring the loss of a device over long time periods (a few days) allows us to investigate stochastic fluctuations due to the interaction between TLSs. We measure the energy relaxation time of a frequency-tunable planar superconducting qubit over time and frequency. The experiments show a variety of stochastic patterns that we are able to explain by means of extensive simulations. The model used in our simulations assumes a qubit interacting with high-frequency TLSs, which, in turn, interact with thermally activated low-frequency TLSs. Our simulations match the experiments and suggest the density of low-frequency TLSs is about three orders of magnitude larger than that of high-frequency ones.
Today’s quantum computers are comprised of tens of qubits interacting with each other and the environment in increasingly complex networks. In order to achieve the best possibleperformance when operating such systems, it is necessary to have accurate knowledge of all parameters in the quantum computer Hamiltonian. In this article, we demonstrate theoretically and experimentally a method to efficiently learn the parameters of resonant interactions for quantum computers consisting of frequency-tunable superconducting qubits. Such interactions include, for example, those to other qubits, resonators, two-level state defects, or other unwanted modes. Our method is based on a significantly improved swap spectroscopy calibration and consists of an offline data collection algorithm, followed by an online Bayesian learning algorithm. The purpose of the offline algorithm is to detect and roughly estimate resonant interactions from a state of zero knowledge. It produces a square-root reduction in the number of measurements. The online algorithm subsequently refines the estimate of the parameters to comparable accuracy as traditional swap spectroscopy calibration, but in constant time. We perform an experiment implementing our technique with a superconducting qubit. By combining both algorithms, we observe a reduction of the calibration time by one order of magnitude. We believe the method investigated will improve present medium-scale superconducting quantum computers and will also scale up to larger systems. Finally, the two algorithms presented here can be readily adopted by communities working on different physical implementations of quantum computing architectures.
In this Note, I show an algorithmic method to find the energy and, thus, the Hamiltonian of an arbitrary electrical circuit based on the so-called incidence matrix and the circuit’stotal power. This method does not require to find any Lagrangian; instead, it is based on the concept of generalized linear momenta for the kinetic and co-kinetic energy of a circuit. The method can account for superconducting loops by a simple extension of Faraday-Henry-Neumann’s law. Auxiliary (i.e., parasitic) circuit elements are required to deal with circuits with an incomplete set of generalized velocities resulting in an incomplete set of canonical coordinates. This method can be readily automatized to obtain the Hamiltonian of arbitrarily complicated circuits. I also show how to quantize the circuit associated with a resonator capacitively coupled with a qubit.
Quantum computers are close to become a practical technology. Solid-state implementations based, for example, on superconducting devices strongly rely on the quality of the constituentmaterials. In this work, we fabricate and characterize superconducting planar resonators in the microwave range, made from aluminum films on silicon substrates. We study two samples, one of which is unprocessed and the other cleaned with a hydrofluoric acid bath and by heating at 880∘C in high vacuum. We verify the efficacy of the cleaning treatment by means of scanning transmission electron microscope imaging of samples‘ cross sections. From 3 h-long resonator measurements at ≈10 mK and with ≈10 photonic excitations, we estimate the frequency flicker noise level using the Allan deviation and find an approximately tenfold noise reduction between the two samples; the cleaned sample shows a flicker noise power coefficient for the fractional frequency of ≈0.23×10−15. Our preliminary results follow the generalized tunneling model for two-level state defects in amorphous dielectric materials and show that suitable cleaning treatments can help the operation of superconducting quantum computers.
Quantum bits (qubits) with long coherence times are an important element for the implementation of medium- and large-scale quantum computers. In the case of superconducting planar qubits,understanding and improving qubits‘ quality can be achieved by studying superconducting planar resonators. In this Paper, we fabricate and characterize coplanar waveguide resonators made from aluminum thin films deposited on silicon substrates. We perform three different substrate treatments prior to aluminum deposition: One chemical treatment based on a hydrofluoric acid clean, one physical treatment consisting of a thermal annealing at 880 degree Celsius in high vacuum, one combined treatment comprising both the chemical and the physical treatments. We first characterize the fabricated samples through cross-sectional tunneling electron microscopy acquiring electron energy loss spectroscopy maps of the samples‘ cross sections. These measurements show that both the chemical and the physical treatments almost entirely remove native silicon oxide from the substrate surface and that their combination results in the cleanest interface. We then study the quality of the resonators by means of microwave measurements in the „quantum regime“, i.e., at a temperature T~10 mK and at a mean microwave photon number ⟨n ph⟩∼1. In this regime, we find that both surface treatments independently improve the resonator’s intrinsic quality factor and that the highest quality factor is obtained for the combined treatment, Qi∼0.8 million. Finally, we find that the TLS quality factor averaged over a time period of 3 h is ∼3 million at ⟨n ph⟩∼10, indicating that substrate surface engineering can potentially reduce the TLS loss below other losses such as quasiparticle and vortex loss.
A practical quantum computer requires quantum bit (qubit) operations with low error rates in extensible architectures. We study a packaging method that makes it possible to addresshundreds of superconducting qubits by means of three-dimensional wires: The large-scale quantum socket. A qubit chip is housed in a superconducting box, where both box and chip dimensions lead to unwanted modes that can interfere with qubit operations. We theoretically analyze these interference effects in the context of qubit coherent leakage. We propose two methods to mitigate the resulting errors by detuning the resonance frequency of the modes from the qubit frequency. We perform detailed electromagnetic field simulations indicating that the resonance frequency of the modes increases with the number of installed three-dimensional wires and can be engineered to be significantly higher than the highest qubit frequency. Finally, we show preliminary experimental results towards the implementation of a large-scale quantum socket.
Extensible quantum computing architectures require a large array of quantum devices operating with low error rates. A quantum processor based on superconducting quantum bits can bescaled up by stacking microchips that each perform different computational functions. In this article, we experimentally demonstrate a thermocompression bonding technology that utilizes indium films as a welding agent to attach pairs of lithographically-patterned chips. We perform chip-to-chip indium bonding in vacuum at 190∘C with indium film thicknesses of 150nm. We characterize the dc and microwave performance of bonded devices at room and cryogenic temperatures. At 10mK, we find a dc bond resistance of 515nΩmm2. Additionally, we show minimal microwave reflections and good transmission up to 6.8GHz in a tunnel-capped, bonded device as compared to a similar uncapped device. As a proof of concept, we fabricate and measure a set of tunnel-capped superconducting resonators, demonstrating that our bonding technology can be used in quantum computing applications.
Quantum computing architectures are on the verge of scalability, a key requirement for the implementation of a universal quantum computer. The next stage in this quest is the realizationof quantum error correction codes, which will mitigate the impact of faulty quantum information on a quantum computer. Architectures with ten or more quantum bits (qubits) have been realized using trapped ions and superconducting circuits. While these implementations are potentially scalable, true scalability will require systems engineering to combine quantum and classical hardware. One technology demanding imminent efforts is the realization of a suitable wiring method for the control and measurement of a large number of qubits. In this work, we introduce an interconnect solution for solid-state qubits: The quantum socket. The quantum socket fully exploits the third dimension to connect classical electronics to qubits with higher density and better performance than two-dimensional methods based on wire bonding. The quantum socket is based on spring-mounted micro wires the three-dimensional wires that push directly on a micro-fabricated chip, making electrical contact. A small wire cross section (~1 mmm), nearly non-magnetic components, and functionality at low temperatures make the quantum socket ideal to operate solid-state qubits. The wires have a coaxial geometry and operate over a frequency range from DC to 8 GHz, with a contact resistance of ~150 mohm, an impedance mismatch of ~10 ohm, and minimal crosstalk. As a proof of principle, we fabricated and used a quantum socket to measure superconducting resonators at a temperature of ~10 mK.