Microstructural Topology as a Prescriptor for Quantum Coherence: Towards A Unified Framework for Decoherence in Superconducting Qubits

Abstract

In superconducting quantum circuits, decoherence improvements are frequently obtained through process interventions that simultaneously modify surface chemistry, microstructural topology, and device geometry, leaving mechanistic attribution structurally underdetermined. Predictive materials engineering requires measurable structural statistics to be separated from geometry-dependent coupling coefficients into independently testable factors. We introduce the concept of classical and quantum microstructure. In that context, we formulate a channel-wise separable framework for decoherence in superconducting transmon qubits in which each loss channel is described by a reduced prescriptor. Here, a channel-specific microstructural state variable is determined independently of device geometry, and a geometry-dependent coupling functional is computable from field solutions without reference to surface chemistry. We derive this product form from a spatially resolved kernel representation and establish a perturbative separability criterion that defines the regime where independent variation of the variables is valid. The framework specifies five prescriptor classes for dominant loss pathways in transmon-class devices. Falsifiability is operationalized through a pre-committed 2x2 experimental protocol in which the variables must satisfy independent ratio checks within propagated uncertainty. A Minimum-Dataset Specification standardizes reporting for cross-laboratory inference. Part I establishes the conceptual and mathematical architecture; coordinated experimental validation is reserved for Part II.

Figures (4)

• Figure 1: Classical versus quantum microstructure. (a) Classical microstructure: ensemble-averaged structural features govern amplitude-based observables such as bulk resistivity $\rho$, RMS roughness $\sigma$, and mean critical current density $J_c$. (b) Quantum microstructure: coherence is governed by a statistically sparse population of structurally severe defect configurations - atomic edge cusps hosting two-level systems (TLS), strained grain boundaries, adsorbed spin clusters - whose coupling to the qubit mode is superlinear in local structural severity. These rare, strongly coupled sites motivate distribution-resolved descriptors such as the curvature second moment $\mu_2$, which may correlate more strongly with coherence observables than ensemble averages. This distinction determines which statistics are predictive, not merely descriptive.
• Figure 2: Prescriptor framework overview. (a) Physical transmon device with five representative loss channels. (b) Extraction of channel-specific microstructural state variables $\rho_j$ from witness-sample measurements, independent of device geometry. (c) Computation of geometry-dependent coupling functionals $G_j$ from finite-element field solutions, independent of surface chemistry. (d) Framework illustration and Part II validation target: comparing the predicted scalar prescriptor $\Pi_j = \rho_j G_j$ against independently measured observables. The vertical division between panels (b) and (c) represents the structural independence of $\rho_j$ and $G_j$, validated experimentally via the $2\!\times\!2$ protocol of Sec. \ref{['sec:falsifiability']}.
• Figure 3: Prescriptor I extraction pipeline (illustrative schematic - not experimental data): format for Part II validation. (a) FIB-SEM curvature histograms for a process-split series with trench-edge etch depth varied $0$-$30$ nm; the series produces $\mu_2$ values spanning a controlled range at fixed device geometry. (b) Schematic correlation of $T_1$ with three candidate microstructural predictors: $\mu_2$ (second curvature moment), $\mu_1$ (first curvature moment), and $R_{\text{RMS}}$ (RMS roughness). (c) Pre-committed model-discrimination matrix. Success criterion: $R^2(T_1, \mu_2) > R^2(T_1, R_{\text{RMS}})$ at 95% confidence across the full etch-depth split series. Failure of this criterion would indicate that curvature is not a sufficient reduced descriptor in this processing regime.
• Figure 4: Schematic of the $2\times2$ separability protocol. Rows correspond to materials treatments that vary the channel-specific microstructural state variable $\rho_j$ while nominally holding geometry fixed; columns correspond to device geometries that vary the coupling functional $G_j$ while nominally holding the materials treatment fixed. Each cell defines a pre-committed prescriptor $\Pi_{mn}=\rho_{j,m}G_{j,n}$ and an independently measured observable $O^{\mathrm{meas}}_{mn}$. The row-ratio check tests the materials axis and the column-ratio check tests the geometry axis. Agreement of both checks within propagated uncertainty supports the separable reduced-order model in the tested operating regime.