Probabilistic Design of Parametrized Quantum Circuits through Local Gate Modifications

TL;DR

The paper tackles the challenge of designing task-specific parametrized quantum circuits by introducing Localized Quantum Architecture Search (LQAS), a local, evolution-inspired refinement method that operates on gate-level modifications around a baseline ansatz. By sampling modifications with controlled probabilities and iteratively training and selecting top performers, LQAS efficiently navigates the architecture space without brute-force global searches. Empirical results on synthetic and quantum chemistry datasets show strong improvements in regression metrics, notably in DDCC where $R^2$ reaches ~0.993, while real hardware experiments reveal current hardware limitations and noise-induced gaps. The work demonstrates LQAS as a scalable, hardware-relevant approach to PQC design and provides a public codebase to facilitate further exploration and benchmarking.

Abstract

Within quantum machine learning, parametrized quantum circuits provide flexible quantum models, but their performance is often highly task-dependent, making manual circuit design challenging. Alternatively, quantum architecture search algorithms have been proposed to automate the discovery of task-specific parametrized quantum circuits using systematic frameworks. In this work, we propose an evolution-inspired heuristic quantum architecture search algorithm, which we refer to as the local quantum architecture search. The goal of the local quantum architecture search algorithm is to optimize parametrized quantum circuit architectures through a local, probabilistic search over a fixed set of gate-level actions applied to existing circuits. We evaluate the local quantum architecture search algorithm on two synthetic function-fitting regression tasks and two quantum chemistry regression datasets, including the BSE49 dataset of bond separation energies for first- and second-row elements and a dataset of water conformers generated using the data-driven coupled-cluster approach. Using state-vector simulation, our results highlight the applicability of local quantum architecture search algorithm for identifying competitive circuit architectures with desirable performance metrics. Lastly, we analyze the properties of the discovered circuits and demonstrate the deployment of the best-performing model on state-of-the-art quantum hardware.

Figures (9)

• Figure 1: An example of a four-qubit hardware-efficient circuit. The variational layer (purple) consists of parameterized rotation and entangling gates and can be repeated $k$-times. When combined with a data-encoding layer, it forms a data re-uploading layer, which can be repeated $m$-times.
• Figure 2: This figure represents the kinds of circuit-level modifications made by the sampling procedure of LQAS. The top circuit represents a member of the base population on an arbitrary iteration of LQAS. This circuit is an HEA-$2$ ansatz with 3 time depth re-encoding (HEA-2-3). The bottom circuit is a sampled ansatz that maintains the general gate configuration of the top circuit with modifications sampled ($p_\text{add} = 0.2$, $p_\text{remove} = 0.02$, $p_\text{switch}=0.1$, $p_\text{move} = 0.01$) through LQAS's ansatz modification procedure.
• Figure 3: The flow diagram above demonstrates the iterative ansatz modification process in the LQAS framework.
• Figure 4: Model evaluation of HEA-1-1 using the one-dimensional noisy quadratic function performance for the best model from each iteration over 3 iterations. Overall, iteration 3 yields the best function approximation, lowest MSE, and highest $R^2$.
• Figure 5: Comparison of the base circuit (left) and optimized circuit after three iterations of LQAS (right).