On the Transfer of Knowledge in Quantum Algorithms

TL;DR

The paper addresses how to reuse knowledge across tasks in quantum algorithms by creating a unified ToK framework with a joint notation that bridges classical Transfer Learning/Optimization and quantum computing. It classifies transfer strategies, proposes a structured taxonomy, and demonstrates three use cases—reverse annealing, multitasking QAOA, and sequential VQE—that illustrate potential gains in performance and generalization. The work provides a sequencing of when, what, and how to transfer in QC and discusses challenges, such as negative transfer and hardware limitations, with practical guidance. Overall, ToK is shown to reduce resource demands and accelerate problem-solving in NISQ-era QC and beyond, provided hardware advances continue.

Abstract

Quantum computing is poised to transform computational paradigms across science and industry. As the field evolves, it can benefit from established classical methodologies, including promising paradigms such as Transfer of Knowledge (ToK). This work serves as a brief, self-contained reference for ToK, unifying its core principles under a single formal framework. We introduce a joint notation that consolidates and extends prior work in Transfer Learning and Transfer Optimization, bridging traditionally separate research lines and enabling a common language for knowledge reuse. Building on this foundation, we classify existing ToK strategies and principles into a structured taxonomy that helps researchers position their methods within a broader conceptual map. We then extend key transfer protocols to quantum computing, introducing two novel use cases--reverse annealing and multitasking Quantum Approximate Optimization Algorithm (QAOA)--alongside a sequential Variational Quantum Eigensolver (VQE) approach that supports and validates prior findings. These examples highlight ToK's potential to improve performance and generalization in quantum algorithms. Finally, we outline challenges and opportunities for integrating ToK into quantum computing, emphasizing its role in reducing resource demands and accelerating problem-solving. This work lays the groundwork for future synergies between classical and quantum computing through a shared, transferable knowledge framework.

Figures (8)

• Figure 1: Transfer of knowledge philosophy.
• Figure 2: A schematic overview of the quantum algorithms employed. (a) Quantum annealing. Figures (b)-(c) illustrate the architecture of the variational algorithms utilized. Both algorithms can be systematically divided into the following stages: i) state initialization, ii) state manipulation, iii) measurement, and iv) a classical optimization subroutine. (b) The QAOA protocol applies a sequence of parameterized layers, alternating between the driver Hamiltonian $H_B$ and the problem Hamiltonian $H_C$, to an initial mixed state. (c) The VQE algorithm evolves an arbitrary initial state $|\Psi_0\rangle$ through a parameterized ansatz $\mathcal{U}(\theta)$, tailored to approximate the target ground state.
• Figure 3: Boxplot showing the results obtained for UC1, related to the experiments on Reverse Annealing. The leftmost boxplot shows the baseline results obtained via forward annealing, while the rightmost boxplot illustrates a case of negative transfer, using as input an instance entirely unrelated to MaxCut_50.
• Figure 4: Schematic structure of the Transfer-QAOA algorithm. This multitasking approach leverages the optimization stage of QAOA to enable information sharing across multiple MaxCut instances. The algorithm compares the cost functions of the $k-$ instances with the parameters optimized in different cases, facilitating the transfer of information between instances when the cost function of one graph is improved by the optimization parameters of another.
• Figure 5: Success probability for the different MaxCut instances. The figure compares the statistical values and their errors for the various multitasking approaches proposed in this article, highlighting the benefits of the transfer protocol in the QAOA algorithm, particularly in the transfer-static-QAOA.