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Layerwise Federated Learning for Heterogeneous Quantum Clients using Quorus

Jason Han, Nicholas S. DiBrita, Daniel Leeds, Jianqiang Li, Jason Ludmir, Tirthak Patel

TL;DR

Quorus tackles the challenge of training quantum models across private clients with heterogeneous circuit depths by introducing layerwise losses and reverse distillation in a federated setting. It offers multiple hardware-aware designs (Layerwise, Ancilla/Blocking, Funnel) to balance shot budget, qubit count, and midcircuit capabilities, while ensuring synchronized objectives among clients. Empirical results show up to a 12.4% improvement in testing accuracy over Q-HeteroFL and higher gradient magnitudes for deeper clients, with validation on IBM QPUs that underscores real-world viability. Collectively, Quorus provides a practical, noise-aware QFL framework that enables scalable quantum machine learning across diverse hardware, supported by open-source implementations. The work advances depth-heterogeneous quantum collaboration, paving the way for privacy-preserving and resource-aware quantum learning on near-term devices.

Abstract

Quantum machine learning (QML) holds the promise to solve classically intractable problems, but, as critical data can be fragmented across private clients, there is a need for distributed QML in a quantum federated learning (QFL) format. However, the quantum computers that different clients have access to can be error-prone and have heterogeneous error properties, requiring them to run circuits of different depths. We propose a novel solution to this QFL problem, Quorus, that utilizes a layerwise loss function for effective training of varying-depth quantum models, which allows clients to choose models for high-fidelity output based on their individual capacity. Quorus also presents various model designs based on client needs that optimize for shot budget, qubit count, midcircuit measurement, and optimization space. Our simulation and real-hardware results show the promise of Quorus: it increases the magnitude of gradients of higher depth clients and improves testing accuracy by 12.4% on average over the state-of-the-art.

Layerwise Federated Learning for Heterogeneous Quantum Clients using Quorus

TL;DR

Quorus tackles the challenge of training quantum models across private clients with heterogeneous circuit depths by introducing layerwise losses and reverse distillation in a federated setting. It offers multiple hardware-aware designs (Layerwise, Ancilla/Blocking, Funnel) to balance shot budget, qubit count, and midcircuit capabilities, while ensuring synchronized objectives among clients. Empirical results show up to a 12.4% improvement in testing accuracy over Q-HeteroFL and higher gradient magnitudes for deeper clients, with validation on IBM QPUs that underscores real-world viability. Collectively, Quorus provides a practical, noise-aware QFL framework that enables scalable quantum machine learning across diverse hardware, supported by open-source implementations. The work advances depth-heterogeneous quantum collaboration, paving the way for privacy-preserving and resource-aware quantum learning on near-term devices.

Abstract

Quantum machine learning (QML) holds the promise to solve classically intractable problems, but, as critical data can be fragmented across private clients, there is a need for distributed QML in a quantum federated learning (QFL) format. However, the quantum computers that different clients have access to can be error-prone and have heterogeneous error properties, requiring them to run circuits of different depths. We propose a novel solution to this QFL problem, Quorus, that utilizes a layerwise loss function for effective training of varying-depth quantum models, which allows clients to choose models for high-fidelity output based on their individual capacity. Quorus also presents various model designs based on client needs that optimize for shot budget, qubit count, midcircuit measurement, and optimization space. Our simulation and real-hardware results show the promise of Quorus: it increases the magnitude of gradients of higher depth clients and improves testing accuracy by 12.4% on average over the state-of-the-art.

Paper Structure

This paper contains 19 sections, 1 theorem, 7 equations, 11 figures, 6 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Related Work
  4. Design and Approach
  5. Quorus Workflow
  6. Ansatz Designs and Selection
  7. Quantum Classifier Design
  8. Experimental Evaluation
  9. Analysis of Quorus's Functionality
  10. Conclusion
  11. Acknowledgement
  12. Further Preliminaries
  13. Proof that the Quorus-Ancilla Circuit is Equivalent to the Quorus-Blocking Circuit
  14. Details of Our Experimental Methodology
  15. Q-HeteroFL Framework
  16. ...and 4 more sections

Key Result

Proposition 1

Let $U$ be an $n$-qubit unitary and let $\ket{\psi}=U\ket{0}^{\otimes n}$. Write $\ket{\psi}$ as where the first ket is qubit $0$, $\ket{\phi_b}$ are normalized states of the remaining $n-1$ qubits, and $|\alpha|^2+|\beta|^2=1$. Consider two procedures: (A) Direct measurement. Measure qubit $0$ in the computational ($Z$) basis. The probabilities are $p_b=\|(\ket{b}\!\bra{b}\otimes I)\ket{\psi}\ P

Figures (11)

  • Figure 1: Depiction of the overall setup of our depth-heterogeneous quantum FL framework. Our setup utilizes the realistic scenario of a classical network for sending and receiving parameters, and each client has a quantum computer that can run circuits of varying depths.
  • Figure 2: We evaluate three ansätze for Quorus: (1) The staircase ansatz, (2) the V-shaped ansatz, and (3) the alternating ansatz, which switches between staircase and V-shaped layers (not shown).
  • Figure 3: The difference between classical and quantum layerwise classifiers. Measurements collapse quantum data, and thus an altered state is passed to the next layer.
  • Figure 4: The Quorus-Layerwise design. The circuit must be run $L$ times, where $L$ is the number of layers.
  • Figure 5: The Quorus-Ancilla design. The circuit is only run once, but requires an ancilla qubit per layer, and also dephases the first qubit.
  • ...and 6 more figures

Theorems & Definitions (1)

  • Proposition 1: Ancilla--measurement equals measuring the control