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PAS-QFL: Personalized Ansatz Selection for Quantum Federated Learning under Client Data Heterogeneity

Jindi Wu, Qun Li

arXiv:2608.14995v1quant-phcs.AIcs.DC

TL;DR

Under heterogeneous, class-imbalanced client data, fixed quantum neural-network ansatzes may not suit all clients, while fully individualized structures hinder parameter aggregation. PAS-QFL separates shared and client-specific ansatzes and improves average Macro-F1 over fixed-structure QFL baselines across most evaluated settings.

  • Problem

    Existing QFL methods commonly use one ansatz for all clients, despite client-dependent ansatz suitability under class-imbalanced non-IID data.

  • Method

    PAS-QFL selects a stable shared ansatz for aggregation and a client-specific private ansatz as a personalized decision head, uploading only shared parameters.

  • Results

    PAS-QFL improves average Macro-F1 over fixed-structure baselines across most evaluated settings, reaching 94.00 versus 86.00 and 78.70 on FM-2 with five clients.

  • Takeaways & Limitations

    The results identify private-ansatz structure as an important personalization dimension for QFL under heterogeneous client data.

Abstract

from arXiv · show

Quantum federated learning (QFL) lets multiple quantum clients collaboratively train quantum neural networks (QNNs) without sharing private local data. However, existing QFL methods commonly assume that all clients use the same ansatz, overlooking how heterogeneous client data affects ansatz suitability. Under class-imbalanced non-IID data, different clients may favor different ansatz structures, so a fixed ansatz can lead to unstable and unfair performance across clients. In this paper, we propose PAS-QFL, a Personalized Ansatz Selection framework for QFL under client data heterogeneity. Rather than treating the ansatz as a monolithic structure, PAS-QFL decomposes each client QNN into a globally shared ansatz and a client-specific private ansatz, and personalizes the structure of the private ansatz rather than only its parameters. The shared ansatz is placed first and selected by a stability-aware cross-client criterion so that its parameters can be reliably aggregated, while the private ansatz serves as a personalized decision head, selected per client by local Macro-F1 to adapt the shared representation to its local data. During training, each client updates both its shared and private parameters locally but uploads only the shared parameters, so federated aggregation stays well-defined while each client keeps its own private structure. PAS-QFL uses Macro-F1 as the primary selection metric to avoid misleading accuracy under class imbalance. Experiments on heterogeneous QFL tasks show that PAS-QFL improves average Macro-F1 over the existing fixed-ansatz QFL baselines, demonstrating the value of personalizing the ansatz structure for practical QFL.

I. INTRODUCTION

PAS-QFL addresses client-dependent ansatz suitability in class-imbalanced non-IID QFL by decomposing each client QNN into a globally shared ansatz and a client-specific private ansatz. It selects the shared structure for stable cross-client aggregation and personalizes the private decision head per client.

  • Motivation: Existing QFL methods commonly impose one ansatz and aggregate the same parameters across clients, simplifying aggregation but limiting heterogeneous-client adaptation.Ansatz design simultaneously shapes local quantum representations and defines the parameterized decision structure whose parameters are federated.
  • PAS-QFL: PAS-QFL decomposes each client QNN into a globally shared ansatz followed by a client-specific private ansatz that acts as a personalized decision head.The framework personalizes private ansatz structure rather than only private parameters, addressing the fixed-architecture limitation of many personalized QFL designs.
  • PAS-QFL: The shared ansatz is selected for stable cross-client performance so its parameters can be meaningfully aggregated, while private ansatz structures remain client-local.During federated training, clients update shared and private parameters locally but upload only shared parameters; private structures and parameters are never shared.
  • Motivation: Under non-IID data, no single ansatz consistently performs best across heterogeneous clients, causing performance instability in QFL.Client profiling with ansatzes having different entanglement structures found markedly different Macro-F1 profiles.
  • Evaluation: PAS-QFL demonstrates consistent performance advantages over homogeneous and fixed-private QFL baselines under non-IID data.The introduction identifies this evaluation as evidence for the framework’s advantages under heterogeneous client data.

II. RELATED WORK

Related QFL research addresses client heterogeneity through aggregation and parameter personalization, while other approaches support structural heterogeneity using shared and private model components. These studies establish the value of personalization and model heterogeneity in QFL.

  • Weighted aggregation assigns client-specific weights based on local data distribution, reliability, or quality.
  • Personalized approaches regularize local updates so clients adapt parameters to their data while remaining consistent with the global model.
  • Shared-local QFL designs aggregate a shared global component while keeping each client’s personalized local component private.
  • Quorus supports heterogeneous quantum clients with different hardware capabilities and varying circuit depths through layerwise losses.

III. MOTIVATION AND PROBLEM STATEMENT · IV. PAS-QFL DESIGN

PAS-QFL addresses client-dependent ansatz suitability in heterogeneous, class-imbalanced QFL by selecting a shared ansatz for aggregation and a private ansatz per client. Its architecture separates a globally shared representation from personalized quantum decision heads, using validation Macro-F1 to guide selection.

  • III. MOTIVATION AND PROBLEM STATEMENT: PAS-QFL profiles a pool of same-qubit ansatzes whose entanglement patterns include linear, reverse-linear, pairwise, full, star, symmetric, and circular structures.The study simulates N = 9 clients using 5-qubit QNNs and 400 local Fashion-MNIST-derived binary-classification samples.
  • III. MOTIVATION AND PROBLEM STATEMENT: Client-wise profiling shows that validation Macro-F1 sensitivity to ansatz choice varies substantially across clients, establishing client-dependent ansatz suitability under class-imbalanced non-IID data.Some clients are relatively insensitive, whereas others show large gaps between their best and worst ansatzes.
  • III. MOTIVATION AND PROBLEM STATEMENT: Ansatz-wise profiling reveals different cross-client stability levels, motivating shared-ansatz selection that considers stability rather than average performance alone.Some ansatzes perform consistently, while others are strong for certain clients but degrade for others.
  • III. MOTIVATION AND PROBLEM STATEMENT: PAS-QFL selects one common shared ansatz S ∈ A and one client-specific private ansatz P_i ∈ A to maximize average Macro-F1 while preserving aggregable shared structure.The shared ansatz must remain structurally identical across clients so federated aggregation is well-defined.
  • IV. PAS-QFL DESIGN: PAS-QFL decomposes each client QNN into a globally shared ansatz and a client-specific private ansatz, personalizing architecture while preserving a federated component.For client i, the circuit includes encoded input data, a local copy of the shared ansatz S(θ_i), and a private ansatz P_i(ϕ_i).
  • IV. PAS-QFL DESIGN: The shared ansatz precedes the private component and supplies common parameters for aggregation, while the private ansatz follows it as a personalized quantum decision head.This ordering separates the common federated block from local adaptation.
  • IV. PAS-QFL DESIGN: PAS-QFL profiles every candidate locally using validation Macro-F1, forms a client-ansatz profiling matrix, and selects each client’s private ansatz from client-wise results.Each client trains a standalone local QNN for every candidate ansatz before private-structure selection.

A. Client-Specific Private Ansatz Selection

PAS-QFL selects each client’s private ansatz from local profiling results using validation Macro-F1, allowing personalization of both private parameters and private-layer architecture. The selected private ansatz remains local during federated training, while only shared parameters are eligible for aggregation.

  • Private ansatz selection: PAS-QFL selects a client-specific private ansatz from local profiling results using validation Macro-F1 obtained under the profiling budget.Fi(a) measures the validation Macro-F1 when client i trains candidate ansatz a as a standalone local QNN.
  • Private ansatz selection: A high local validation Macro-F1 indicates that an ansatz’s circuit structure and entanglement pattern match the client’s local decision behavior.The private component functions as a client-specific quantum decision head.
  • Private ansatz selection: Because client data are heterogeneous and class-imbalanced, different clients may select different private ansatz structures.This personalizes the private-layer architecture rather than only its parameters.
  • Private ansatz selection: The selected private ansatz is placed after the shared ansatz and remains local to its client during federated training.Private parameters are updated locally with shared-parameter copies, but neither private structures nor private parameters are uploaded or aggregated.

B. Stability-Aware Shared Ansatz Selection

PAS-QFL selects one shared ansatz for all clients using cross-client performance and stability because its parameters are aggregated during federated training. The selection penalizes variability in client performance while balancing mean Macro-F1 against cross-client spread.

  • B. Stability-Aware Shared Ansatz Selection: The shared ansatz is chosen for stable cross-client collaboration because all clients use it and its parameters are aggregated during federated training.Selection considers overall performance and stability across heterogeneous clients rather than performance on only a few clients.
  • B. Stability-Aware Shared Ansatz Selection: PAS-QFL scores each candidate ansatz using its cross-client mean Macro-F1 penalized by its cross-client spread.The score is computed from the same profiling matrix used to evaluate candidate ansatzes.
  • B. Stability-Aware Shared Ansatz Selection: λ ≥0 controls the trade-off between average performance and cross-client stability.When λ = 0, the highest mean Macro-F1 is selected; larger λ penalizes ansatzes with greater performance variation across clients.

C. Federated Training

PAS-QFL federates training over a fixed shared ansatz while keeping each client’s private ansatz local. Clients update both parameter sets locally, upload only shared parameters, and enable well-defined FedAvg aggregation across heterogeneous private structures.

  • Federated Training: Selected shared and private ansatz structures remain fixed during training, while their parameters are optimized locally.Each client trains the full model on its local data.
  • Federated Training: At each communication round, the server broadcasts global shared parameters, which clients use to initialize their local shared parameters.Client i initializes its local shared parameters as θ_i^t = θ̄^t.
  • Federated Training: Clients update shared and private-head parameters locally, then upload only updated shared parameters to the server.Private ansatz structures and parameters remain local and are never transmitted.
  • Federated Training: The server aggregates uploaded shared parameters using FedAvg, reducing to equal-weight averaging when all clients have the same local training size.FedAvg weights client updates by each client’s number of local training samples n_i.
  • Federated Training: Because all uploaded parameters belong to the same shared ansatz, aggregation remains well-defined while clients retain different private quantum decision-head structures.Private structures and parameters are neither aggregated nor transmitted.

V. EVALUATION

PAS-QFL is evaluated with Qiskit-based simulations across noiseless and noisy settings, heterogeneous client counts, and class-imbalanced non-IID data. The evaluation compares local, fixed-ansatz federated, fixed-private-ansatz, and personalized-ansatz training settings.

  • Evaluation setup: Qiskit-based simulations use noiseless settings to isolate ansatz-selection effects and noisy settings to examine robustness under NISQ noise.The evaluation includes systems with 5 and 9 clients, class ratios from 1:9 to 9:1, and 5-qubit QNNs.
  • Datasets and tasks: The benchmark covers binary and four-class classification on both Fashion-MNIST and MNIST: FM-2, FM-4, M-2, and M-4.The four tasks combine dataset and class-count variation under the heterogeneous QFL setting.
  • Compared methods: Four training settings are compared: Local, Fix-all, Fix-pri, and PAS-QFL.Local performs independent client training; Fix-all uses one shared ansatz; Fix-pri fixes an identical private ansatz; PAS-QFL selects shared and client-specific structures.
  • Compared methods: PAS-QFL selects the shared ansatz with a stability-aware criterion and the private ansatz per client, uploading and aggregating only shared parameters.The personalized private ansatz and its parameters remain local.

A. Overall Performance

PAS-QFL achieves competitive or superior average Macro-F1 across heterogeneous QFL tasks, client scales, and noiseless or noisy simulations, with especially large gains on challenging multi-class tasks. Its advantage comes from combining a stable shared ansatz with client-specific private ansatz selection, although flexibility does not always improve performance on simpler noisy binary classification.

  • Noiseless simulation: PAS-QFL outperforms FIX-ALL and FIX-PRI on all four tasks in the 5-client noiseless setting.On FM-2, average Macro-F1 rises to 94.00 from 86.00 and 78.70; on M-4, it reaches 75.00 from 70.70 and 66.70.
  • Noiseless simulation: 73.29 average Macro-F1 on FM-4 with 9 noiseless clients exceeds 68.09 for FIX-ALL and 52.92 for FIX-PRI.PAS-QFL remains competitive on FM-2 and performs more strongly on FM-4, M-2, and M-4.
  • Noisy simulation: 64.06 average Macro-F1 on FM-4 with 5 noisy clients exceeds 58.05 for FIX-ALL and 58.88 for FIX-PRI.PAS-QFL improves over both fixed-structure baselines on all four tasks in this setting.
  • Noisy simulation: 72.36 average Macro-F1 on FM-4 with 9 noisy clients exceeds 60.04 for FIX-ALL and 52.21 for FIX-PRI.PAS-QFL also outperforms the fixed-structure baselines on M-2 and M-4, but is lower on FM-2.
  • Interpretation: PAS-QFL’s gains are largest on challenging multi-class tasks, while added private-head flexibility does not improve FM-2 with 9 noisy clients.The paper attributes the FM-2 limitation possibly to stable fixed structures already capturing binary classification and noisy local updates adding variance.
  • Design motivation: PAS-QFL selects a stable shared ansatz for aggregation and client-specific private ansatzes for local decision adaptation.This addresses the limited adaptability of homogeneous QFL and fixed-private personalized QFL under heterogeneous clients.

B. Effect of Personalized Private Ansatz Selection

PAS-QFL’s gains arise from selecting personalized private ansatz structures, not merely from adding locally trainable private parameters. On FM-2 with five clients, this structure-level personalization outperforms fixed-private architectures and better adapts to heterogeneous local data.

  • Private ansatz selection: PAS-QFL achieves the highest average Macro-F1 of 94.00, surpassing all fixed-private variants on FM-2 with five clients.The comparison uses pairwise ansatz as the shared layer, while fixed-private baselines share one private architecture but train private parameters locally.
  • Private ansatz selection: The best fixed-private baseline reaches 84.67 with the linear ansatz, while other fixed private structures range from 65.42 to 83.54.The wide spread shows that private ansatz structure substantially affects client-level adaptation.
  • Private ansatz selection: No single fixed private ansatz matches PAS-QFL, which selects each client’s private ansatz through local profiling.Different clients can therefore use different private ansatz structures as personalized quantum decision heads.

C. Effect of Stability-Aware Shared Ansatz Selection

Stability-aware shared ansatz selection materially affects federated performance: with private ansatzes fixed, PAS-QFL’s Pairwise shared ansatz achieves the highest average Macro-F1, supporting its role as a stable common structure for aggregation.

  • Experimental setup: The experiment varies only the shared ansatz while fixing PAS-QFL’s personalized private ansatzes and federated training procedure, isolating the shared structure’s effect.The setting uses FM-2 with 5 clients.
  • Shared ansatz comparison: 94.00 average Macro-F1 is achieved by PAS-QFL’s Pairwise shared ansatz, outperforming the other shared ansatz candidates.Fig. 7 reports lower performance for the other shared ansatzes.
  • Role of shared structure: The shared ansatz remains important because its parameters form the common component aggregated across clients, even when private ansatzes are personalized.The observed performance spread demonstrates that private personalization does not eliminate the shared structure’s influence.
  • Role of shared structure: PAS-QFL’s profiling-based stability-aware criterion selects a shared structure more compatible with cross-client aggregation, strengthening overall federated performance.This complements private ansatz personalization, which supports client-specific local adaptation.

VI. CONCLUSION

PAS-QFL personalizes quantum federated learning under client data heterogeneity by selecting stable shared ansatzes for aggregation and client-specific private ansatzes as personalized quantum decision heads. This enables ansatz-level personalization while keeping aggregated parameters structurally consistent across clients.

  • PAS-QFL is a personalized ansatz selection framework for quantum federated learning under client data heterogeneity.
  • The framework profiles candidate ansatzes across clients to select a stable shared ansatz for federated aggregation.
  • Each client receives a client-specific private ansatz that acts as a personalized quantum decision head.
  • Ansatz-level personalization preserves structurally consistent aggregated parameters across clients.
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