Session K48: Strongly Driven Superconducting Systems

Displaced Frame Approach for Simulating High-Power Dispersive Readout

Dispersive readout is a ubiquitous method in the sense that the readout scheme can be applied to any type of superconducting qubits. To make the readout time shorter in the dispersive readout, one possible approach is using high-power-input light. The high-power input light increases signals from a cavity interacting with a qubit. However, the working principle of the dispersive readout is based on the perturbation theory, and the spectrum of the transmon, one of the standard implementations of qubit, is unbounded. Consequently, back actions from high-power input are nontrivial, and some numerical simulations are required to investigate these effects. The numerical simulations are heavy tasks since high-power light induces a large-amplitude coherent state that requires many Fock states for its representation. To perform the simulations efficiently, we propose an approach to simulate the dynamics in a frame where the amplitude of the coherent state almost vanishes [1]. The proposed method requires fewer Fock states compared to the same simulation in the drive frame. The proposed method enables one to access the high-power dispersive readout in the two-level system and the transmon with moderate numerical resources.

[1] S. Goto and K. Koshino, Phys. Rev. A 108, 033722 (2023)   

Theory of measurement-induced transitions in the transmon qubit, part 1.

Dispersive readout in circuit QED enables fast and high-fidelity measurements that are essential for quantum computation. However, it is a common experimental observation that increasing the measurement drive amplitude to even moderate values leads to quantum non-demolition and low-fidelity readout. Recent work suggests that this is due to ionization of the qubit to higher-energy excited states by the drive [1,2] and that this can be understood as a signature of classical chaos in the driven transmon [3]. In this work, we present a unified theoretical picture of measurement-induced transitions in the transmon qubit. We predict the critical photon number at which deleterious transitions occur, in excellent agreement with experimental results. We also use our theoretical framework to propose avenues for mitigating measurement-induced transitions.

In part 1 of this talk, we compare the transmon-resonator energy spectrum with a semiclassical model of a classically driven transmon. We identify measurement-induced transitions as arising from anticrossings in the Floquet quasi-energy spectrum and show that the anticrossings accurately predict the onset of non-QNDness. This framework also gives insight on the sensitivity of readout to gate charge fluctuations and qubit-resonator detuning.

[1] R. Shillito et al., Phys. Rev. Applied 18, 034031 (2022).

[2] M. Khezri et al., arXiv:2212.05097v1 [quant-ph] 

[3] J. Cohen et al., PRX Quantum 4, 020312 (2023).   

Theory of measurement-induced transitions in the transmon qubit, part 2

Dispersive readout in circuit QED enables fast and high-fidelity measurements that are essential for quantum computation. However, it is a common experimental observation that increasing the measurement drive amplitude to even moderate values leads to quantum non-demolition and low-fidelity readout. Recent work suggests that this is due to ionization of the qubit to higher-energy excited states by the drive [1,2] and that this can be understood as a signature of classical chaos in the driven transmon [3]. In this work, we present a unified theoretical picture of measurement-induced transitions in the transmon qubit. We predict the critical photon number at which deleterious transitions occur, in excellent agreement with experimental results. We also use our theoretical framework to propose avenues for mitigating measurement-induced transitions.

In part 2 of this talk, we discuss that the onset of QND-ness can be understood by analyzing areas of regular and chaotic motion in a fully classical phase space. This critical photon number corroborates the predictions of the quantum and semiclassical model discussed in part 1.

[1] R. Shillito et al., Phys. Rev. Applied 18, 034031 (2022).

[2] M. Khezri et al., arXiv:2212.05097v1 [quant-ph].

[3] J. Cohen et al., PRX Quantum 4, 020312 (2023).   

Anomalous dynamics of superconducting qubits coupled to strongly driven readout resonators

Experimental realization of rapid qubit readout in superconducting circuits usually relies on the application of strong readout pulses to dispersively coupled readout resonators. However, the optimal pulse strength is severely limited by the emergence of anomalous qubit dynamics in the presence of a strong readout drive. Interestingly, these anomalous dynamics cannot be explained by the Purcell decay or other conventional models of qubit dissipation. In this talk, we discuss several mechanisms for these drive-induced anomalous dynamics, from coherent multi-level or multi-photon transitions to incoherent jumps induced by the resonator photons. Using the theoretical framework of perturbative time-coarse-graining [1], we derive effective master equations for the qubit dynamics, and thereby produce simulated heterodyne histograms which are then compared with real data from transmon readout experiments. Finally, we propose some strategies for mitigating these drive-induced anomalous qubit dynamics.

 

[1] https://github.com/leonbello/QuantumGraining.jl   

Investigating readout-induced state transitions in a multimode Josephson circuit

Dispersive readout in superconducting circuits is in principle a quantum non-demolition (QND) measurement, in which the post-readout qubit state should remain in the measured eigenstate. However, unwanted state transitions are generally observed in experiments on superconducting qubits submitted to a strong readout probe tone, limiting the readout performance. Such state transition events can be classified into two types, the readout-induced energy relaxation into spurious two-level systems [1] and leakage out of qubit manifold due to non-linear transitions [2]. Both effects have been widely reported in transmon readout experiments. 

We extend these investigations into a superconducting artificial molecule consisting of two non-linear modes [3]. One of the modes has purely non-linear coupling to the readout resonator, serving as a transmon with intrinsic Purcell protection and direct readout access. The other mode mediates this non-linear coupling. We will present experimental results and preliminary theoretical understanding of the readout-induced state transitions of both types. We explain how our analysis applies to a wide choice of parameters for such multimode Josephson circuits.

[1] Thorbeck et al. arXiv:2305.10508 (2023)

[2] Sank et al. PRL 117, 190503 (2016)

[3] Gambetta et al., PRL 106, 030502 (2011)    

The effects of readout photons on the fluxonium qubit

Readout of superconducting qubits is typically performed through a readout resonator dispersively-coupled to the qubit. A standard method for improving readout fidelity is to increase the average number of photons used for readout, which should result in greater separation between the qubit-state-dependent responses of the resonator. In the transmon, however, increasing the number of photons used for readout induces unwanted qubit transitions and increases the qubit relaxation rate. While there has been significant recent interest in the fluxonium due to its high gate fidelities, the effects of readout photon number on Josephson-junction-based fluxonium have largely been unexplored. Here, we experimentally investigate the effect of increased readout photon number on the fluxonium qubit by monitoring the fluxonium state in the presence of varying numbers of readout photons. We observe an overall increase in the qubit relaxation rate with the number of readout photons and observe photon-number-dependent changes in the fluxonium transition rate. We further explore the dependence of these effects on coupling between the readout resonator and the fluxonium, and on the resonator frequency.   

Fast-switching coupler for measuring the interaction dynamics of a system formed of a flux qubit coupled to a waveguide in the ultra-strong coupling regime

The ultra-strong coupling (USC) regime of light-matter interactions, realized when the interaction rate approaches the atomic frequency, is to this day relatively unexplored experimentally. In particular, studying the time dynamics of coupled atom-field systems in the USC regime is challenging due to stringent requirements related to the short interaction times. Previously, we demonstrated a tunable coupler that controls the interaction strength between a superconducting flux qubit and a co-planar waveguide transmission line. In this talk, we discuss our theoretical and experimental work towards observation of time-domain dynamics in the USC regime with this device.

We present results of a theoretical analysis of the system, that includes the role of higher levels of the qubit circuit and a realistic model for qubit measurement. Next, we present our experimental work in progress. In our design, using control pulses sent through bias lines near the coupler, the coupling strength can be fast-tuned at sub nanosecond time scales. Measurements can be done by decoupling the qubit from the waveguide, followed by state readout using a coupled DC-SQUID. This work opens new avenues for experiments on dynamics in the spin-boson model at strong coupling and entanglement harvesting.   

Strongly-driven transmon as an incoherent noise source

Transmons are ubiquitous today in quantum computing applications. Under strong drives, which are becoming necessary for fast high fidelity operations, transmons can become structurally unstable. Due to chaotic effects, the computational manifold is no longer well separated from the remainder of the spectrum, which correlates with enhanced offset charge sensitivity and non-QND effects in readout [1,2]. In this work, we show that a coherently driven transmon can act as a source of incoherent noise driving another circuit element coupled to it. By using a full quantum model and a semiclassical analysis, we perform the noise spectroscopy of the driven transmon.   

High fidelity gates in a transmon using bath engineering for passive leakage reset

Leakage to non-computational states is one of the limiting factors which prevents fault-tolerant quantum computing. This is especially true for superconducting circuit-based architectures, where the qubits are often weakly non-linear oscillators and unwanted population transfer to higher levels cannot be ignored on energetic grounds alone.

Although several proposals have been introduced to mitigate the effect of leakage, here we theoretically explore and experimentally demonstrate a passive filtering approach to leakage in a standard transmon. By coupling the qubit to a structured environment, we engineer the decay rate of the f-state to be large and e-state to be small; any erroneous f-state population (or higher leakage population) is quickly brought back to the qubit subspace, whereas the e-state remains long-lived. Considering only energetically relevant levels, we simulate the full coupled transmon-filter system and demonstrate that it is possible to obtain both a large f-state decay rate and a high averaged gate fidelity. Our work demonstrates the possibility of passive leakage reduction as a useful tool for fault-tolerant quantum computation.   

Balanced coupling in superconducting circuits

The rotating wave approximation (RWA) is ubiquitous in the analysis of driven and coupled resonators. However, the limitations of the RWA seem to be poorly understood and in some cases the RWA disposes of essential physics. We investigate the RWA in the context of electrical resonant circuits. Using a classical Hamiltonian approach, we find that by balancing electrical and magnetic components of the resonator drive or resonator-resonator coupling, the RWA can be made to be exact. This type of balance, in which the RWA is exact, has applications in superconducting circuits where it suppresses single qubit gate error in qubits with very low frequencies, and may suppress deleterious qubit transitions caused by dispersive readout.   

High-frequency suppression of inductive coupling between flux qubit and transmission line resonator

We perform theoretical calculations to investigate the naturally occurring high-frequency cutoff in a circuit comprising a flux qubit coupled inductively to a transmission line resonator (TLR). Our results generally agree with those of past studies that considered somewhat similar circuit designs. In particular, a decoupling occurs between the qubit and the high-frequency modes. As a result, the coupling strength between the qubit and resonator modes increases with mode frequency $omega$ as $sqrt{omega}$ at low frequencies and decreases as $1/sqrt{omega}$ at high frequencies. By avoiding the approximation of ignoring the qubit-TLR coupling in certain steps in the analysis, we obtain effects not captured in previous studies. We derive expressions for the mode frequencies, coupling strengths and Lamb shift in the qubit's characteristic frequency. We identify features in the spectrum of the system that can be used in future experiments to test and validate the theoretical model.   

Capacitive coupling of persistent current qubits

Persistent current qubits are usually coupled to other elements via magnetic interactions. However, those interactions alone are only able to reproduce a small family of stoquastic models. To enlarge this family, we have analyzed the capacitive coupling between persistent current devices. First, we present a general theory to find the effective interaction in the computational subspace, which works even in the ultra-strong coupling regime. Then, we investigate several superconducting circuit designs with persistent current qubits (flux and fluxonium qubits) that, thanks to the capacitive coupling, can emulate relevant low-energy physics when coupled between them, to a waveguide or an LC mode. For instances, we will show cricuits parameters that allow to obtain an ultra-strong capacitive coupling between photons and qubit or the design of a long lived qutrit state coupled to a continuum of excitations.   

Nonlinear Space-Time Modulation for Exquisite Wavecrafting in Superconducting Quantum Systems

Noisy Intermediate-Scale Quantum Computers require control devices that generate large, coherent, and low-noise signals with minimized hardware overhead, aiming to improve the signal-to-noise ratio. By utilizing nonmagnetic and nonlinear space-time modulation of low-temperature superconductors, we can tap into unique physical phenomena that are beneficial for reducing hardware complexity. Here, we present a space-time-varying cQED system and showcase the exceptional functionalities and wave-tailoring properties that are inherent to structures driven by nonlinearity-based space-time modulation, especially in controlling superconducting transmons.   

Exact nonlinear response theory for lossy superconducting quantum circuits

Quantum systems inherently interact with their environments, typically consisting of a macroscopic number of degrees of freedom [1]. These interactions give rise

to a diverse range of phenomena, among which the most important are dissipation and decoherence [2]. In addition to the inevitable coupling to the natural environment, the study of open quantum systems is also motivated by the need to carry out measurements on real systems [3]. In such cases, the measurement apparatus itself acts as an environment, leading to decoherence. In our work we provide a formalism for calculation of electromagnetic field emitted by the superconducting circuits, which can be measured experimentally [4]. Starting from the Feynman–Vernon path integral formalism for the lossy circuits, we eliminate the influence functional by introducing auxiliary harmonic modes with complex-valued frequencies coupled to the non-linear degrees of freedom of the circuit. This results in a many-body Liouville equation for the state of the system. We propose a concept of time-averaged observables, inspired by experiment, and provide an explicit formula for producing their quasiprobability distribution. Finally, we demonstrate the applicability of our formalism through a study on the dispersive readout of a superconducting qubit.

[1] U. Weiss, Quantum dissipative systems (World Scientific, 2012)

[2] A. J. Leggett, S. Chakravarty, A. T. Dorsey, M. P. Fisher, A. Garg, and W. Zwerger, Reviews of Modern Physics 59, 1 (1987).

[3] K. Jacobs, Quantum measurement theory and its applications (Cambridge University Press, 2014).

[4] A. Blais, A. L. Grimsmo, S. Girvin, and A. Wallraff, Reviews of Modern Physics 93, 025005 (2021)