Dynamics of Transmon Ionization

  1. Ross Shillito,
  2. Alexandru Petrescu,
  3. Joachim Cohen,
  4. Jackson Beall,
  5. Markus Hauru,
  6. Martin Ganahl,
  7. Adam G.M. Lewis,
  8. Guifre Vidal,
  9. and Alexandre Blais
Qubit measurement and control in circuit QED rely on microwave drives, with higher drive amplitudes ideally leading to faster processes. However, degradation in qubit coherence time
and readout fidelity has been observed even under moderate drive amplitudes corresponding to few photons populating the measurement resonator. Here, we numerically explore the dynamics of a driven transmon-resonator system under strong and nearly resonant measurement drives, and find clear signatures of transmon ionization where the qubit escapes out of its cosine potential. Using a semiclassical model, we interpret this ionization as resulting from resonances occurring at specific resonator photon populations. We find that the photon populations at which these spurious transitions occur are strongly parameter dependent and that they can occur at low resonator photon population, something which may explain the experimentally observed degradation in measurement fidelity.

Operating in a deep underground facility improves the locking of gradiometric fluxonium qubits at the sweet spots

  1. Daria Gusenkova,
  2. Francesco Valenti,
  3. Martin Spiecker,
  4. Simon Günzler,
  5. Patrick Paluch,
  6. Dennis Rieger,
  7. Larisa-Milena Pioraş-Ţimbolmaş,
  8. Liviu P. Zârbo,
  9. Nicola Casali,
  10. Ivan Colantoni,
  11. Angelo Cruciani,
  12. Stefano Pirro,
  13. Laura Cardani,
  14. Alexandru Petrescu,
  15. Wolfgang Wernsdorfer,
  16. Patrick Winkel,
  17. and Ioan M. Pop
We demonstrate flux-bias locking and operation of a gradiometric fluxonium artificial atom using two symmetric granular aluminum (grAl) loops to implement the superinductor. The gradiometric
fluxonium shows two orders of magnitude suppression of sensitivity to homogeneous magnetic fields, which can be an asset for hybrid quantum systems requiring strong magnetic field biasing. By cooling down the device in an external magnetic field while crossing the metal-to-superconductor transition, the gradiometric fluxonium can be locked either at 0 or Φ0/2 effective flux bias, corresponding to an even or odd number of trapped fluxons, respectively. At mK temperatures, the fluxon parity prepared during initialization survives to magnetic field bias exceeding 100Φ0. However, even for states biased in the vicinity of 1Φ0, we observe unexpectedly short fluxon lifetimes of a few hours, which cannot be explained by thermal or quantum phase slips. When operating in a deep-underground cryostat of the Gran Sasso laboratory, the fluxon lifetimes increase to days, indicating that ionizing events activate phase slips in the grAl superinductor.

Engineering, control and longitudinal readout of Floquet qubits

  1. Anthony Gandon,
  2. Camille Le Calonnec,
  3. Ross Shillito,
  4. Alexandru Petrescu,
  5. and Alexandre Blais
Properties of time-periodic Hamiltonians can be exploited to increase the dephasing time of qubits and to design protected one and two-qubit gates. Recently, Huang et al. [Phys. Rev.
Applied 15, 034065 (2021)] have shown that time-dependent Floquet states offer a manifold of working points with dynamical protection larger than the few usual static sweet spots. Here, we use the framework of many-mode Floquet theory to describe approaches to robustly control Floquet qubits in the presence of multiple drive tones. Following the same approach, we introduce a longitudinal readout protocol to measure the Floquet qubit without the need of first adiabatically mapping back the Floquet states to the static qubit states, which results in a significant speedup in the measurement time of the Floquet qubit. The analytical approach developed here can be applied to any Hamiltonian involving a small number of distinct drive tones, typically the study of standard parametric gates for qubits outside of the rotating-wave approximation.

Accurate methods for the analysis of strong-drive effects in parametric gates

  1. Alexandru Petrescu,
  2. Camille Le Calonnec,
  3. Catherine Leroux,
  4. Agustin Di Paolo,
  5. Pranav Mundada,
  6. Sara Sussman,
  7. Andrei Vrajitoarea,
  8. Andrew A. Houck,
  9. and Alexandre Blais
The ability to perform fast, high-fidelity entangling gates is an important requirement for a viable quantum processor. In practice, achieving fast gates often comes with the penalty
of strong-drive effects that are not captured by the rotating-wave approximation. These effects can be analyzed in simulations of the gate protocol, but those are computationally costly and often hide the physics at play. Here, we show how to efficiently extract gate parameters by directly solving a Floquet eigenproblem using exact numerics and a perturbative analytical approach. As an example application of this toolkit, we study the space of parametric gates generated between two fixed-frequency transmon qubits connected by a parametrically driven coupler. Our analytical treatment, based on time-dependent Schrieffer-Wolff perturbation theory, yields closed-form expressions for gate frequencies and spurious interactions, and is valid for strong drives. From these calculations, we identify optimal regimes of operation for different types of gates including iSWAP, controlled-Z, and CNOT. These analytical results are supplemented by numerical Floquet computations from which we directly extract drive-dependent gate parameters. This approach has a considerable computational advantage over full simulations of time evolutions. More generally, our combined analytical and numerical strategy allows us to characterize two-qubit gates involving parametrically driven interactions, and can be applied to gate optimization and cross-talk mitigation such as the cancellation of unwanted ZZ interactions in multi-qubit architectures.

Lifetime renormalization of driven weakly anharmonic superconducting qubits: II. The readout problem

  1. Alexandru Petrescu,
  2. Moein Malekakhlagh,
  3. and Hakan E. Türeci
Recent experiments in superconducting qubit systems have shown an unexpectedly strong dependence of the qubit relaxation rate on the readout drive power. This phenomenon limits the
maximum measurement strength and thus the achievable readout speed and fidelity. We address this problem here and provide a plausible mechanism for drive-power dependence of relaxation rates. To this end we introduce a two-parameter perturbative expansion in qubit anharmonicity and the drive amplitude through a unitary transformation technique introduced in Part I. This approach naturally reveals number non-conserving terms in the Josephson potential as a fundamental mechanism through which applied microwave drives can activate additional relaxation mechanisms. We present our results in terms of an effective master equation with renormalized state- and drive-dependent transition frequency and relaxation rates. Comparison of numerical results from this effective master equation to those obtained from a Lindblad master equation which only includes number-conserving terms (i.e. Kerr interactions) shows that number non-conserving terms can lead to significant drive-power dependence of the relaxation rates. The systematic expansion technique introduced here is of general applicability to obtaining effective master equations for driven-dissipative quantum systems that contain weakly non-linear degrees of freedom.

Lifetime renormalization of weakly anharmonic superconducting qubits: I. Role of number non-conserving terms

  1. Moein Malekakhlagh,
  2. Alexandru Petrescu,
  3. and Hakan E. Türeci
An outstanding challenge in superconducting quantum computing is the determination of an accurate effective model for a particular experiment. In practice, the dynamics of a superconducting
qubit in a complex electromagnetic environment can be described by an effective multimode Kerr Hamiltonian at sufficiently weak excitation. This Hamiltonian can be embedded in a master equation with losses determined by the details of the electromagnetic environment. Recent experiments indicate, however, that when a superconducting circuit is driven with microwave signals the observed relaxation rates appear to be substantially different from expectations based on the electromagnetic environment of the qubit alone. This issue has been most notorious in the optimization of superconducting qubit readout schemes. We claim here that an effective master equation with drive-power dependent parameters is the most resource-efficient approach to model such quantum dynamics. In this sequence of papers we derive effective master equations whose parameters depend on the excitation level of the circuit and the electromagnetic environment of the qubit. We show that the number non-conserving terms in the qubit nonlinearity generally lead to a renormalization of dissipative parameters of the effective master equation, while the number-conserving terms give rise to a renormalization of the system frequencies. Here, in Part I, we consider the dynamics of a transmon qubit that is prepared in an initial state of a certain excitation level, but is not driven otherwise. For two different electromagnetic environments, an infinite waveguide and an open resonator, we show that the renormalized parameters display a strong dependence on the details of the electromagnetic environment of the qubit. The perturbation technique based on unitary transformations developed here is generalized to the continuously driven case in Part II.

Fluxon-Based Quantum Simulation in Circuit QED

  1. Alexandru Petrescu,
  2. Hakan E. Türeci,
  3. Alexey V. Ustinov,
  4. and Ioan M. Pop
Long-lived fluxon excitations can be trapped inside a superinductor ring, which is divided into an array of loops by a periodic sequence of Josephson junctions in the quantum regime,
thereby allowing fluxons to tunnel between neighboring sites. By tuning the Josephson couplings, and implicitly the fluxon tunneling probability amplitudes, a wide class of 1D tight-binding lattice models may be implemented and populated with a stable number of fluxons. We illustrate the use of this quantum simulation platform by discussing the Su-Schrieffer-Heeger model in the 1-fluxon subspace, which hosts a symmetry protected topological phase with fractionally charged bound states at the edges. This pair of localized edge states could be used to implement a superconducting qubit increasingly decoupled from decoherence mechanisms.

Cutoff-free Circuit Quantum Electrodynamics

  1. Moein Malekakhlagh,
  2. Alexandru Petrescu,
  3. and Hakan E. Türeci
Any quantum-confined electronic system coupled to the electromagnetic continuum is subject to radiative decay and renormalization of its energy levels. When coupled to a cavity, these
quantities can be strongly modified with respect to their values in vacuum. Generally, this modification can be accurately captured by including only the closest resonant mode of the cavity. In the circuit quantum electrodynamics architecture, where the coupling strengths can be substantial, it is however found that the radiative decay rates are strongly influenced by far off-resonant modes. A multimode calculation accounting for the infinite set of cavity modes leads to divergences unless a cutoff is imposed. It has so far not been identified what the source of divergence is. We show here that unless gauge invariance is respected, any attempt at the calculation of circuit QED quantities is bound to diverge. We then present a theoretical approach to the calculation of a finite spontaneous emission rate and the Lamb shift that is free of cutoff.

Non-Markovian dynamics of a superconducting qubit in an open multimode resonator

  1. Moein Malekakhlagh,
  2. Alexandru Petrescu,
  3. and Hakan E. Türeci
We study the dynamics of a transmon qubit that is capacitively coupled to an open multimode superconducting resonator. Our effective equations are derived by eliminating resonator degrees
of freedom while encoding their effect in the Green’s function of the electromagnetic background. We account for the dissipation of the resonator exactly by employing a spectral representation for the Green’s function in terms of a set of non-Hermitian modes and show that it is possible to derive effective Heisenberg-Langevin equations without resorting to the rotating wave, two level or Markov approximations. A well-behaved time domain perturbation theory is derived to systematically account for the nonlinearity of the transmon. We apply this method to the problem of spontaneous emission, capturing accurately the non-Markovian features of the qubit dynamics, valid for any qubit-resonator coupling strength.

Many-Body Quantum Electrodynamics Networks: Non-Equilibrium Condensed Matter Physics with Light

  1. Karyn Le Hur,
  2. Loïc Henriet,
  3. Alexandru Petrescu,
  4. Kirill Plekhanov,
  5. Guillaume Roux,
  6. and Marco Schiró
We review recent developments concerning non-equilibrium quantum dynamics and many-body physics with light, in superconducting circuits and Josephson analogues. We start with quantum
impurity models summarizing the effect of dissipation and of driving the system. We mention theoretical and experimental efforts to characterize these non-equilibrium quantum systems. We show how Josephson junction systems can implement the equivalent of the Kondo effect with microwave photons. The Kondo effect is characterized by a renormalized light-frequency and a peak in the Rayleigh elastic transmission of a photon. We also address the physics of hybrid systems comprising mesoscopic quantum dot devices coupled to an electromagnetic resonator. Then, we discuss extensions to Quantum Electrodynamics (QED) Networks allowing to engineer the Jaynes-Cummings lattice and Rabi lattice models. This opens the door to novel many-body physics with light out of equilibrium, in relation with the Mott-superfluid transition observed with ultra-cold atoms in optical lattices. Then, we summarize recent theoretical predictions for realizing topological phases with light. Synthetic gauge fields and spin-orbit couplings have been successfully implemented with ultra-cold atoms in optical lattices — using time-dependent Floquet perturbations periodic in time, for example — as well as in photonic lattice systems. Finally, we discuss the Josephson effect related to Bose-Hubbard models in ladder and two-dimensional geometries. The Bose-Hubbard model is related to the Jaynes-Cummings lattice model in the large detuning limit between light and matter. In the presence of synthetic gauge fields, we show that Meissner currents subsist in an insulating Mott phase.