Fast and Robust Geometric Two-Qubit Gates for Superconducting Qubits and Beyond

  1. F. Setiawan,
  2. Peter Groszkowski,
  3. and Aashish A. Clerk
Quantum protocols based on adiabatic evolution are remarkably robust against imperfections of control pulses and system uncertainties. While adiabatic protocols have been successfully
implemented for quantum operations such as quantum state transfer and single-qubit gates, their use for geometric two-qubit gates remains a challenge. In this paper, we propose a general scheme to realize robust geometric two-qubit gates in multi-level qubit systems where the interaction between the qubits is mediated by an auxiliary system (such as a bus or coupler). While our scheme utilizes Stimulated Raman Adiabatic Passage (STIRAP), it is substantially simpler than STIRAP-based gates that have been proposed for atomic platforms, requiring fewer control tones and ancillary states, as well as utilizing only a generic dispersive interaction. We also show how our gate can be accelerated using a shortcuts-to-adiabaticity approach, allowing one to achieve a gate that is both fast and relatively robust. We present a comprehensive theoretical analysis of the performance of our two-qubit gate in a parametrically-modulated superconducting circuits comprising two fluxonium qubits coupled to an auxiliary system.

Scqubits: a Python package for superconducting qubits

  1. Peter Groszkowski,
  2. and Jens Koch
scqubits is an open-source Python package for simulating and analyzing superconducting circuits. It provides convenient routines to obtain energy spectra of common superconducting qubits,
such as the transmon, fluxonium, flux, cos(2ϕ) and the 0-π qubit. scqubits also features a number of options for visualizing the computed spectral data, including plots of energy levels as a function of external parameters, display of matrix elements of various operators as well as means to easily plot qubit wavefunctions. Many of these tools are not limited to single qubits, but extend to composite Hilbert spaces consisting of coupled superconducting qubits and harmonic (or weakly anharmonic) modes. The library provides an extensive suite of methods for estimating qubit coherence times due to a variety of commonly considered noise channels. While all functionality of scqubits can be accessed programatically, the package also implements GUI-like widgets that, with a few clicks can help users both create relevant Python objects, as well as explore their properties through various plots. When applicable, the library harnesses the computing power of multiple cores via multiprocessing. scqubits further exposes a direct interface to the Quantum Toolbox in Python (QuTiP) package, allowing the user to efficiently leverage QuTiP’s proven capabilities for simulating time evolution.

Control and Coherence Time Enhancement of the 0- π Qubit

  1. Agustin Di Paolo,
  2. Arne L. Grimsmo,
  3. Peter Groszkowski,
  4. Jens Koch,
  5. and Alexandre Blais
Kitaev’s 0-π qubit encodes quantum information in two protected, near-degenerate states of a superconducting quantum circuit. In a recent work, we have shown that the coherence
times of a realistic 0-π device can surpass that of today’s best superconducting qubits [Groszkowski et al., New Journal of Physics 20 043053 (2018)]. Here we address controllability of the 0-π qubit. Specifically, we investigate the potential for dispersive control and readout, and introduce a new, fast and high-fidelity single-qubit gate that can interpolate smoothly between logical X and Z. We characterize the action of this gate using a multi-level treatment of the device, and analyze the impact of circuit element disorder and deviations in control and circuit parameters from their optimal values. Furthermore, we propose a cooling scheme to decrease the photon shot-noise dephasing rate, which we previously found to limit the coherence times of 0-π devices within reach of current experiments. Using this approach, we predict coherence time enhancements between one and three orders of magnitude, depending on parameter regime.

Quantum control of an oscillator using stimulated nonlinearity

  1. Andrei Vrajitoarea,
  2. Ziwen Huang,
  3. Peter Groszkowski,
  4. Jens Koch,
  5. and Andrew A. Houck
Superconducting circuits extensively rely on the Josephson junction as a nonlinear electronic element for manipulating quantum information and mediating photon interactions. Despite
continuing efforts in designing anharmonic Josephson circuits with improved coherence times, the best photon lifetimes have been demonstrated in microwave cavities. Nevertheless, architectures based on quantum memories need a qubit element for addressing these harmonic modules at the cost of introducing additional loss channels and limiting process fidelities. This work focuses on tailoring the oscillator Hilbert space to enable a direct Rabi drive on individual energy levels. For this purpose we implement a flux-tunable inductive coupling between two linear resonators using a superconducting quantum interference device. We dynamically activate a three-wave mixing process through parametric flux modulation in order to selectively address the lowest eigenstates as an isolated two-level system. Measuring the Wigner function confirms we can prepare arbitrary states confined in the single photon manifold, with measured coherence times limited by the oscillator intrinsic quality factor. This architectural shift in engineering oscillators with stimulated nonlinearity can be exploited for designing long-lived quantum modules and offers flexibility in studying non-equilibrium physics with photons in a field-programmable simulator.

Coherence properties of the 0-π qubit

  1. Peter Groszkowski,
  2. A. Di Paolo,
  3. A. L. Grimsmo,
  4. A. Blais,
  5. D.I. Schuster,
  6. A. A. Houck,
  7. and Jens Koch
Superconducting circuits rank among the most interesting architectures for the implementation of quantum information processing devices. The recently proposed 0-π qubit [Brooks et
al., Phys. Rev. A 87, 52306 (2013)] promises increased protection from spontaneous relaxation and dephasing. In practice, this ideal behavior is only realized if the parameter dispersion among nominally identical circuit elements vanishes. In this paper we present a theoretical study of the more realistic scenario of slight variations in circuit elements. We discuss how the coupling to a spurious, low-energy mode affects the coherence properties of the 0-π device, investigate the relevant decoherence channels, and present estimates for achievable coherence times in multiple parameter regimes.

Universal stabilization of a parametrically coupled qubit

  1. Yao Lu,
  2. Srivatsan Chakram,
  3. Nelson Leung,
  4. Nathan Earnest,
  5. Ravi K. Naik,
  6. Ziwen Huang,
  7. Peter Groszkowski,
  8. Eliot Kapit,
  9. Jens Koch,
  10. and David I. Schuster
We autonomously stabilize arbitrary states of a qubit through parametric modulation of the coupling between a fixed frequency qubit and resonator. The coupling modulation is achieved
with a tunable coupler design, in which the qubit and the resonator are connected in parallel to a superconducting quantum interference device. This allows for quasi-static tuning of the qubit-cavity coupling strength from 12 MHz to more than 300 MHz. Additionally, the coupling can be dynamically modulated, allowing for single photon exchange in 6 ns. Qubit coherence times exceeding 20 μs are maintained over the majority of the range of tuning, limited primarily by the Purcell effect. The parametric stabilization technique realized using the tunable coupler involves engineering the qubit bath through a combination of photon non-conserving sideband interactions realized by flux modulation, and direct qubit Rabi driving. We demonstrate that the qubit can be stabilized to arbitrary states on the Bloch sphere with a worst-case fidelity exceeding 80 %.

Transient dynamics of a superconducting nonlinear oscillator

  1. P. Bhupathi,
  2. Peter Groszkowski,
  3. M.P. DeFeo,
  4. Matthew Ware,
  5. Frank K. Wilhelm,
  6. and B. L. T. Plourde
We investigate the transient dynamics of a lumped-element oscillator based on a dc superconducting quantum interference device (SQUID). The SQUID is shunted with a capacitor forming
a nonlinear oscillator with resonance frequency in the range of several GHz. The resonance frequency is varied by tuning the Josephson inductance of the SQUID with on-chip flux lines. We report measurements of decaying oscillations in the time domain following a brief excitation with a microwave pulse. The nonlinearity of the SQUID oscillator is probed by observing the ringdown response for different excitation amplitudes while the SQUID potential is varied by adjusting the flux bias. Simulations are performed on a model circuit by numerically solving the corresponding Langevin equations incorporating the SQUID potential at the experimental temperature and using parameters obtained from separate measurements characterizing the SQUID oscillator. Simulations are in good agreement with the experimental observations of the ringdowns as a function of applied magnetic flux and pulse amplitude. We observe a crossover between the occurrence of ringdowns close to resonance and adiabatic following at larger detuning from the resonance. We also discuss the occurrence of phase jumps at large amplitude drive. Finally, we briefly outline prospects for a readout scheme for superconducting flux qubits based on the discrimination between ringdown signals for different levels of magnetic flux coupled to the SQUID.