Bulletin of the American Physical Society
APS March Meeting 2022
Volume 67, Number 3
Monday–Friday, March 14–18, 2022; Chicago
Session A36: Superconducting Qubits: cQED Design ToolsRecordings Available

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Sponsoring Units: DQI Chair: Alexander McDonald, University of Chicago Room: McCormick Place W194A 
Monday, March 14, 2022 8:00AM  8:12AM 
A36.00001: Design of interacting superconducting quantum circuits with quasilumped models Yehan Liu, Zlatko K Minev, Thomas G McConkey, Jay M Gambetta The remarkable growth in the field of quantum information processing increasingly requires precise, widely applicable, and modular methods that can model the quantum electrodynamics of the physical circuits, including their moresubtle renormalization effects. Here, we present a practical demonstration of a computationally efficient method satisfying these criteria. The method, referred to as the quasilumped model of circuit quantum electrodynamics, and implemented in Qiskit Metal, partitions a quantum device into compact lumped or quasidistributed cells. The composite system is then reduced and mapped to a set of simple subsystem building blocks and their pairwise interactions. We demonstrate the versatility of this approach by several examples in a full stack workflow, from device layout to electromagnetic simulation, then to Hamiltonian analysis and ultimately to time evolution simulation. 
Monday, March 14, 2022 8:12AM  8:24AM 
A36.00002: A fluxbased 3D electrodynamic modeling approach to superconducting circuits and materials Dzung Pham, Wentao Fan, Kanupriya Sinha, Hakan E Tureci The fluxbased description of superconducting lumpedelement circuits has enjoyed tremendous success in studying the fundamental physics of superconducting devices and circuits as well as their computational modeling. We extend fluxbased electrodynamic field theory of superconductors to two and threedimensional materials and fields. Starting with Maxwell's equations and superconducting order parameter equations, we derive equations of motion for gaugeinvariant flux fields describing the dynamics of hybridized lightmatter fields. The formulation utilizes a dualmesh construction with flux fields and currents living on edges and charges living on nodes, enabling accurate chargeconserving dynamics. We demonstrate its application to the Meissner effect and flux quantization in 3D superconducting structures. 
Monday, March 14, 2022 8:24AM  8:36AM 
A36.00003: Simulation of Parametrically Coupled Qubits with Qiskit Metal and pyEPR Zachary L Parrott, Xiaoyue Jin, Taewan Noh, Raymond W Simmonds Various forms of circuit simulation can be an indispensable tool in designing superconducting qubit experiments. Before committing to a particular device, fixed after fabrication, simulations can be used to explore design tradeoffs in order to optimize the desired circuit behavior. In addition, simulations can be used to help diagnose unexplained results in existing experiments. In this talk, we discuss the open source Qiskit Metal toolkit and the energy participation ratio (EPR) method for simulating various ongoing experiments of parametrically coupled circuits. By sweeping various design parameters, we can predict how these parameters influence the circuit's mode frequencies and relevant features such as static crosscouplings between these modes. Through comparisons with existing measured devices we are able to identify what design parameters strongly influence the device characteristics we wish to adjust and how to optimize them. Additionally we can assess what dynamics or behaviors are not being properly modelled or accounted for, as well as identify key features that should not be omitted in traditional lumped element design approaches. Finally we will discuss how we can use this simulation framework to inform the design of future devices and experiments within our group. 
Monday, March 14, 2022 8:36AM  8:48AM 
A36.00004: A diagrammatic approach to compute effective Hamiltonians of driven superconducting circuits: Part I Xu Xiao, Jayameenakshi Venkatraman, Rodrigo G Cortiñas, Shoumik Chowdhury, Michel H Devoret Superconducting circuits submitted to microwave drives have proven to be a promising means to realize novel parametric interactions described by an effective, timeindependent Hamiltonian. A key challenge in controlling such interactions is to develop a systematic and computationally efficient approach for obtaining the Hamiltonian terms beyond the rotatingwaveapproximation. We have constructed a diagrammatic bookkeeping tool to compute the effective Hamiltonian of a driven nonlinear oscillator to arbitrary order. The physical intuition associated with our Feynmanlike diagrams allows the corresponding Hamiltonian terms to be written down directly, whereas simple counting of topologically distinct diagrams yields the coefficients associated with those terms. Underlying this diagrammatic approach is a quantum averaging method that treats, in a way we believe is novel, on equal footing both classical and quantum nonlinear dynamics. In Part I, we introduce the diagrammatic approach through pedagogical examples and discuss its underlying physical intuition. 
Monday, March 14, 2022 8:48AM  9:00AM 
A36.00005: A diagrammatic approach to compute effective Hamiltonians of driven superconducting circuits: Part II Jayameenakshi Venkatraman, Xu Xiao, Rodrigo G Cortiñas, Shoumik Chowdhury, Michel H Devoret Superconducting circuits submitted to microwave drives have proven to be a promising means to realize novel parametric interactions described by an effective, timeindependent Hamiltonian. A key challenge in controlling such interactions is to develop a systematic and computationally efficient approach for obtaining the Hamiltonian terms beyond the rotatingwaveapproximation. We have constructed a diagrammatic bookkeeping tool to compute the effective Hamiltonian of a driven nonlinear oscillator to arbitrary order. The physical intuition associated with our Feynmanlike diagrams allows the corresponding Hamiltonian terms to be written down directly, whereas simple counting of topologically distinct diagrams yields the coefficients associated with those terms. Underlying this diagrammatic approach is a quantum averaging method that treats, in a way we believe is novel, on equal footing both classical and quantum nonlinear dynamics. Basing ourselves on Part I, in Part II we present novel parametric processes predicted by the diagrams and show that they agree with a full numerical diagonalization. 
Monday, March 14, 2022 9:00AM  9:12AM 
A36.00006: Modeling the effects of 1/f dephasing noise on a coherently driven qubit Peter Groszkowski, Alireza Seif, Jens Koch, Aashish Clerk Accurately describing the impact of highly nonMarkovian 1/f dephasing noise on superconducting qubits via simple modelling tools is challenging even if the noise is treated as being classical. Typical approaches are to either perform a bruteforce numerical average over many noise realizations, or use adhoc timelocal master equations whose validity is often not clear. In this talk, we use a generalized cumulant expansion to rigorously derive an effective timelocal Lindblad style master equation that describes the evolution of a driven qubit subject to classical 1/f dephasing noise. We find that the effective dissipation in this master equation is explicitly timedependent, and also has a form that depends both on the driving as well as the noise spectral density. Our analysis reveals that over a large set of experimentally relevant parameters, our effective description leads to evolution that can be substantially more accurate than other more commonly used approximation techniques. 
Monday, March 14, 2022 9:12AM  9:24AM 
A36.00007: "Integrating Quantum Processor Device and Control Optimization in a Gradientbased Framework" Xiaotong Ni, Huihai Zhao, Lei Wang, Feng Wu, Jianxin Chen A quantum processor design workflow goes through multiple steps, each of which plays a crucial role in the final performance of the device. This work demonstrates that the figure of merit reflecting a design goal can be made differentiable for parameters from the device and the control. In addition, we can compute the gradient of the design objective in a single reverse run, then utilize the gradient to optimize the design and the control parameters jointly and efficiently, extending the scope of quantum optimal control to superconducting device design. To the best of our knowledge, this work is the first attempt to extend gradient optimization to superconducting device design. We also demonstrate the viability of reverse gradientbased joint optimization over device and control parameters through a few examples. 
Monday, March 14, 2022 9:24AM  9:36AM 
A36.00008: Coherence dynamics of a photondressed qubit Maksym Liul, Sergey Shevchenko, Franco Nori, Io Chun Hoi, ChinYeh Chen, ChihHsun Chien We consider a capacitivelyshunted charge qubit in front of a mirror [1], affected by two signals: probe and dress signals. By varying the parameters of these signals and then analyzing the probe signal (reflected by the mirror) it is possible to explore the system properties. A similar system has been considered recently [1] but only a stationary picture was measured and described theoretically. The difference between the previous and the current configuration is in decreasing the qubit coupling to the environment, allowing to decrease the system decoherence time and perform timedomain measurements. We describe our system by solving both Bloch equations and rate equations. The obtained timedependent occupation probabilities are related to the experimentally measured values. The study of this type of dynamics opens up new horizons for better understanding of the system properties and underlying physical processes such as LandauZenerStückelbergMajorana (LZSM) transitions. 
Monday, March 14, 2022 9:36AM  9:48AM 
A36.00009: How to correctly account for timevarying fluxes in superconducting circuits Ahmed Kenawy, Fabian Hassler, David P DiVincenzo, RomanPascal Riwar Timevarying fluxes are a ubiquitous tool to control superconducting hardware. Surprisingly, however, the existing literature has never fully accounted for the electromotive force induced by the magnetic field. Here, we propose a general recipe to construct a lowenergy Hamiltonian, taking as input only the circuit geometry and the solution of the external magnetic fields. We apply this recipe to the example of a dc SQUID and show that the assignment of individual capacitances to each Josephson junction is possible only if we permit those capacitances to be negative, timedependent, or even momentarily singular. Such anomalous capacitances lead, among others, to a strong enhancement of qubit relaxation rates. Then, we tackle the problem of driven topological quantum circuits, focusing on two weakly coupled Kitaev chains and study how the electromotive force modifies the timedependent fractional Josephson effect. 
Monday, March 14, 2022 9:48AM  10:00AM 
A36.00010: Quantum Fluctuations in Electrical Multiport Linear Systems Iñigo L Egusquiza, Adrian Parra Rodriguez We present an extension of the classical NyquistThevenin theorem for multiport classical electrical networks by Twiss [1] to the quantum case. Conversely, we extend the quantum fluctuationdissipation result [2,3] for one port electrical systems to the multiport case, both reciprocal and nonreciprocal. Our results are extended to lossy systems by depicting resistive components as continuous limits of purely lossless lumpedelement networks. Simple circuit examples are analyzed, including a linear system lacking a direct impedance representation. 
Monday, March 14, 2022 10:00AM  10:12AM 
A36.00011: Automated precise multiparameter estimation for quantum devices Thomas M Stace, Michael Hush, Andre Carvalho Hardware built for quantum computing is designed with an ideal model in mind. However, physically realised systems may have additional elements whose effects on the rest of the system are typically accounted for in effective models. In such cases, there is ambiguity in which model “correctly” describes the system  the effective model, or a more complete physical model that includes the dynamics in a larger Hilbert space. We present an efficient method for fitting Hamiltonian parameters using automated differentiation in a flexible graph representation for quantum models. Our approach works with noisy experimental data and is able to make statistical estimates of the parameter uncertainty. We demonstrate these approaches with an example where a coupling resonator is used to mediate multiqubit gates between superconducting qubits. We compare an effective model that eliminates the coupling resonator with a more fundamental model that retains the full dynamics and Hilbert space of the qubitcouplerqubit system. Using our model fitting techniques we are able to use information criteria to compare amongst models based on accuracy and predictive power, in the presence of noise and parameter uncertainty. This has implications for hardware system identification and design cycles. 
Monday, March 14, 2022 10:12AM  10:24AM 
A36.00012: Inconsistencies in the Quantization of Singular Superconducting Circuits Martin Rymarz, David P DiVincenzo The theory of circuit quantum electrodynamics successfully describes superconducting circuits based on the Hamiltonian formalism of quantum mechanics. In the process, mathematical descriptions of an electrical network at hand might involve effective models, which, however, can easily lead to singular Lagrangians that describe constrained systems in which not all variables are independent. 
Monday, March 14, 2022 10:24AM  10:36AM 
A36.00013: KQCircuits, an opensource package for drawing automation of superconducting quantum processors. Alessandro Landra, Johannes Heinsoo, Sinan Inel, David Janzso, Máté Jenei, Janne Kotilahti, Caspar F OckeloenKorppi, Jukka Räbinä, Niko Savola In the last decade, research in the field of superconducting circuits has increased significantly, notably driven by its utility in quantum computing. One of the first tasks, often among the steepest in difficulty, consists of accurately laying out the desired quantum circuits and connectivity in a lithography mask file. This is usually done in an adhoc manner, and new researchers must go through this process with suboptimal outcome and poor scalability. 
Monday, March 14, 2022 10:36AM  10:48AM 
A36.00014: A Surface Integral Equation Method for the Superconducting Quantum Device Tian Xia, Feng Wu, HsiangSheng Ku, Hao Deng, Jianjun Chen, Ran Gao, Xiaotong Ni, Qi Ye, Wenlong Yu, Xiaohang Zhang, Jingwei Zhou, Jianxin Chen, Chunqing Deng, HuiHai Zhao Computing the Hamiltonian of a superconducting quantum device from its layout is a necessary step for making use of the device as a quantum processor. A conventional approach is to use the finite element method (FEM) to extract the linear capacitance matrix from the electrostatic simulation for the circuit quantization. However, this method is computationally intensive for largescale systems. In particular, the calculations of the surface losses, quantified by the participation ratios, have been computationally challenging for arbitrary designs due to the difficulties to capture the singular electrical field in such a multiscale problem. Here, we apply a much more accurate and efficient method, the surface integral equation (SIE) method. It only requires the discretization of the conductive surfaces, as opposed to the discretization of the truncated volume in the FEM. Consequently, the number of unknowns is greatly reduced, resulting in a significant saving in the simulation time. We further introduce a nonconformal mesh scheme to reinforce a large mesh density near the superconductor boundaries without affecting the interior mesh density. As a result, the electric field singularity is much better captured with only slight increases in the computational time and the memory usages. We benchmark our method with an analytically solvable coplanar capacitor. To achieve the same accuracy in the computation of the capacitance matrix and the participation ratios, our method is accelerated by tens or hundreds of times respectively, compared to the FEM simulations. This method paves the way for the accurate and efficient design optimization of the superconducting quantum devices. 
Monday, March 14, 2022 10:48AM  11:00AM 
A36.00015: Hamiltonian of a flux qubitLC oscillator circuit in the deepstrongcoupling regime Fumiki Yoshihara, Sahel Ashhab, Tomoko Fuse, Motoaki Bamba, Kouichi Semba We derive the Hamiltonian of a superconducting circuit that comprises a singleJosephsonjunction flux qubit inductively coupled to an LC oscillator, and we compare the derived circuit Hamiltonian with the quantum Rabi Hamiltonian [1]. The energy level structure of the circuit Hamiltonian can be fitted well by the quantum Rabi Hamiltonian even when the qubitoscillator circuit is in the deepstrongcoupling regime [2]. We also show that although the circuit Hamiltonian can be transformed via a unitary transformation to a Hamiltonian containing a capacitive coupling term, the resulting circuit Hamiltonian cannot be approximated by the capacitivecoupling variant of the quantum Rabi Hamiltonian even for relatively weak coupling. This difference between the flux and charge gauges follows from the properties of the qubit Hamiltonian eigenstates. 
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