Digital Control of a Superconducting Qubit Using a Josephson Pulse Generator at 3 K.

Scaling of quantum computers to fault-tolerant levels relies critically on the integration of energy-efficient, stable, and reproducible qubit control and readout electronics. In comparison to traditional semiconductor-control electronics (TSCE) located at room temperature, the signals generated by rf sources based on Josephson-junctions (JJs) benefit from small device sizes, low power dissipation, intrinsic calibration, superior reproducibility, and insensitivity to ambient fluctuations. Previous experiments to colocate qubits and JJ-based control electronics have resulted in quasiparticle poisoning of the qubit, degrading the coherence and lifetime of the qubit. In this paper, we digitally control a 0.01-K transmon qubit with pulses from a Josephson pulse generator (JPG) located at the 3-K stage of a dilution refrigerator. We directly compare the qubit lifetime T 1, the coherence time T 2 * , and the thermal occupation P th when the qubit is controlled by the JPG circuit versus the TSCE setup. We find agreement to within the daily fluctuations of ±0.5 µs and ±2 µs for T 1 and T 2 * , respectively, and agreement to within the 1% error for P th. Additionally, we perform randomized benchmarking to measure an average JPG gate error of 2.1 × 10-2. In combination with a small device size (< 25 mm2) and low on-chip power dissipation (≪100 µW), these results are an important step toward demonstrating the viability of using JJ-based control electronics located at temperature stages higher than the mixing-chamber stage in highly scaled superconducting quantum information systems.

Tunable resonant and nonresonant interactions between a phase qubit and LC resonator.

We use a flux-biased radio frequency superconducting quantum interference device (rf SQUID) with an embedded flux-biased direct current SQUID to generate strong resonant and nonresonant tunable interactions between a phase qubit and a lumped-element resonator. The rf SQUID creates a tunable magnetic susceptibility between the qubit and resonator providing resonant coupling strengths from zero to near the ultrastrong coupling regime. By modulating the magnetic susceptibility, nonresonant parametric coupling achieves rates >100 MHz. Nonlinearity of the magnetic susceptibility also leads to parametric coupling at the subharmonics of the qubit-resonator detuning.

Sideband cooling of micromechanical motion to the quantum ground state.

The advent of laser cooling techniques revolutionized the study of many atomic-scale systems, fuelling progress towards quantum computing with trapped ions and generating new states of matter with Bose-Einstein condensates. Analogous cooling techniques can provide a general and flexible method of preparing macroscopic objects in their motional ground state. Cavity optomechanical or electromechanical systems achieve sideband cooling through the strong interaction between light and motion. However, entering the quantum regime--in which a system has less than a single quantum of motion--has been difficult because sideband cooling has not sufficiently overwhelmed the coupling of low-frequency mechanical systems to their hot environments. Here we demonstrate sideband cooling of an approximately 10-MHz micromechanical oscillator to the quantum ground state. This achievement required a large electromechanical interaction, which was obtained by embedding a micromechanical membrane into a superconducting microwave resonant circuit. To verify the cooling of the membrane motion to a phonon occupation of 0.34 ± 0.05 phonons, we perform a near-Heisenberg-limited position measurement within (5.1 ± 0.4)h/2π, where h is Planck's constant. Furthermore, our device exhibits strong coupling, allowing coherent exchange of microwave photons and mechanical phonons. Simultaneously achieving strong coupling, ground state preparation and efficient measurement sets the stage for rapid advances in the control and detection of non-classical states of motion, possibly even testing quantum theory itself in the unexplored region of larger size and mass. Because mechanical oscillators can couple to light of any frequency, they could also serve as a unique intermediary for transferring quantum information between microwave and optical domains.

Circuit cavity electromechanics in the strong-coupling regime.

Demonstrating and exploiting the quantum nature of macroscopic mechanical objects would help us to investigate directly the limitations of quantum-based measurements and quantum information protocols, as well as to test long-standing questions about macroscopic quantum coherence. Central to this effort is the necessity of long-lived mechanical states. Previous efforts have witnessed quantum behaviour, but for a low-quality-factor mechanical system. The field of cavity optomechanics and electromechanics, in which a high-quality-factor mechanical oscillator is parametrically coupled to an electromagnetic cavity resonance, provides a practical architecture for cooling, manipulation and detection of motion at the quantum level. One requirement is strong coupling, in which the interaction between the two systems is faster than the dissipation of energy from either system. Here, by incorporating a free-standing, flexible aluminium membrane into a lumped-element superconducting resonant cavity, we have increased the single-photon coupling strength between these two systems by more than two orders of magnitude, compared to previously obtained coupling strengths. A parametric drive tone at the difference frequency between the mechanical oscillator and the cavity resonance dramatically increases the overall coupling strength, allowing us to completely enter the quantum-enabled, strong-coupling regime. This is evidenced by a maximum normal-mode splitting of nearly six bare cavity linewidths. Spectroscopic measurements of these 'dressed states' are in excellent quantitative agreement with recent theoretical predictions. The basic circuit architecture presented here provides a feasible path to ground-state cooling and subsequent coherent control and measurement of long-lived quantum states of mechanical motion.

rf-SQUID-mediated coherent tunable coupling between a superconducting phase qubit and a lumped-element resonator.

We demonstrate coherent tunable coupling between a superconducting phase qubit and a lumped-element resonator. The coupling strength is mediated by a flux-biased rf SQUID operated in the nonhysteretic regime. By tuning the applied flux bias to the rf SQUID we change the effective mutual inductance, and thus the coupling energy, between the phase qubit and resonator. We verify the modulation of coupling strength from 0 to 100 MHz by observing modulation in the size of the splitting in the phase qubit's spectroscopy, as well as coherently by observing modulation in the vacuum Rabi oscillation frequency when on resonance. The measured spectroscopic splittings and vacuum Rabi oscillations agree well with theoretical predictions.