Lattice field theory for superconducting circuits

TL;DR

Predicting large superconducting circuits from first principles is challenging due to many-body dynamics. The paper introduces a general ab-initio lattice-field-theory method for circuit-QED, casting dynamics in a Euclidean path-integral and extracting the spectrum from two-point correlators while preserving full local U(1) Hilbert spaces. It demonstrates three fluxonium studies: reproducing tensor-network results, exploring impedance- and gate-disorder-driven dephasing, and revealing ground-capacitance effects on qubit properties, with a reweighting strategy enabling efficient disorder averaging. This approach provides a scalable, truncation-free framework for energies, matrix elements, and coherence-related observables in complex superconducting circuits, offering a powerful tool for device design, prototyping, and experimental interpretation.

Abstract

Large superconducting quantum circuits have a number of important applications in quantum computing. Accurately predicting the performance of these devices from first principles is challenging, as it requires solving the many-body Schrödinger equation. This work introduces a new, general ab-initio method for analyzing large quantum circuits based on lattice field theory, a tool commonly applied in nuclear and particle physics. This method is competitive with state-of-the-art techniques such as tensor networks, but avoids introducing systematic errors due to truncation of the infinite-dimensional Hilbert space associated with superconducting phases. The approach is applied to fluxonium, a specific many-component superconducting qubit with favorable qualities for quantum computation. A systematic study of the influence of impedance on fluxonium is conducted that parallels previous experimental studies, and ground capacitance effects are explored. The qubit frequency and charge noise dephasing rate are extracted from statistical analyses of charge noise, where thousands of instantiations of charge disorder in the Josephson junction array of a fixed fluxonium qubit are explicitly averaged over at the microscopic level. This is difficult to achieve with any other existing method.

Figures (9)

• Figure 1: Fluxonium: (left) Lumped-element circuit model of fluxonium (right) Microscopic circuit model of fluxonium. Description: The microscopic model of fluxonium considered here involves phase differences across junctions $\theta_i$, ground capacitances, and identical array junctions. The lumped-element model approxiates the Josephson junction array as a linear inductor. Notation: The variables $C^b,C^b_g,E_J^b$ are the capacitance, ground capacitance and Josephson energy of the small junction, while $C^a,C^a_g,E_J^a$ are the same for the array junctions. The model studied includes $N$ array junctions and an external flux $\Phi_{\text{ext}}$ threading the loop.
• Figure 2: Effective frequency plot: Plot of the cosh-corrected effective frequency, Eq.$~$ (\ref{['eq:cosh-corr-discrete-eff-freq']}), for the qubit parameters of Eq.$~$ (\ref{['eq:tn-comp-params']}) for the interpolating operator $\mathcal{O} = \sum_x \text{sin}\theta_x$ for the ensemble with the coarsest lattice spacing in \ref{['tab:cont-lim-details']}. Eleven equally spaced gate charges are considered, with the blue data corresponding to $n_{g} = 0$ and the orange to $n_{g} = 1/2$, and error-bars have been estimated with $100$ bootstrap resamplings of the Monte Carlo data.
• Figure 3: Continuum limit extrapolation: (a) Qubit frequency as a function of lattice spacing for the system defined in Eq.$~$ (\ref{['eq:tn-comp-params']}). Computations are performed at 11 equally-spaced points between $n_g=0$ (light blue) and $n_g=1/2$ (light orange points). Error bars are statistical. The flatness of the curves indicate very small lattice spacing artifacts. (b) Lattice spacing error of the qubit frequency, i.e. the difference between individual simulations and the continuum limit, for $n_g \in \{0.00,0.25,0.40\}$. The observed quadratic dependence is expected from theory. Color coding is the same as in the top panel. Points are slightly shifted horizontally for visibility.
• Figure 4: Tensor network comparison: Qubit frequency as a function of gate charge $n_g$ for the system defined in Eq.$~$ (\ref{['eq:tn-comp-params']}). Continuum-extrapolated lattice results are shown with pink circles while TN results are denoted by gray triangles, and have been slightly shifted in $n_g$ for viewing convenience. Uncertainties on the lattice calculations are statistical while those on TN result from a webplot digitization of the figures reported in Ref. Di_Paolo_2021.
• Figure 5: Qubit frequency distributions: Histogram of qubit frequencies for the device parameters in Table \ref{['tab:fluxonium-parameters']}. The $z=0.135$ distribution (not shown) has such large spread that it is approximately uniform on the scale of this figure. Histograms are generated from 1024 random draws of the gate charge distribution where all $n_{gx}$ are drawn independently and uniformly over the interval $[0,1)$. Data shown is for fixed $\Delta t = 5$ ps.