Title: QuBS: Combinatorial Quantum Brain Surgeon on Quantum Annealers
Primary area: optimization
Keywords: QUBO form, quantum machine learning, Hessian, quantum optimization

Abstract: Quantum Neural Networks (QNNs) are parameterized quantum circuits trained for machine learning tasks. Sparse QNNs are desired since: 1) their limited entanglement topologies are less likely to approximate 2-design unitaries and affected by training issues such as barren plateaus; and 2) they reduce susceptibility to decoherence and cumulative operational errors---a critical requirement for high-fidelity execution on near-term quantum hardware. This necessitates a method to prune QNNs with minimal fidelity loss. Existing techniques predominantly rely on Euclidean-space heuristics, such as Pauli rotation strengths or their gradients, to serve as proxies for QNN operation importance. However, these approaches are misaligned with the Hilbert-space dynamics and fundamentally ignore the non-commutativity of quantum operations (i.e. inter-parameter correlations). In response to existing limitations, we propose *QuBS*, a novel framework that explicitly accounts for the QNN's Hilbert-space evolution. *QuBS* approximates the non-commutativity effects of QNN pruning up to 2nd order. The core of *QuBS* involves searching for an optimal sparse subnetwork by solving a Quadratic Unconstrained Binary Optimization (QUBO) problem. Given the NP-hard nature of QUBOs (unsolvable in polynomial time classically), which become intractable for classical solvers as problem size grows, we leverage quantum annealers---an emerging machine leveraging adiabatic Hamiltonian evolution to seek high-quality solutions for QUBOs; this evolution is performed on the order of microseconds per anneal, enabling rapid sampling of the solution space. We further propose an iterative variant of *QuBS* to enable pruning large-scale QNNs with constrained computational resources provided by the annealer. We evaluate *QuBS* on pre-trained QNNs designed for image classification and benchmark it against established protocols. We show that *QuBS* consistently outperforms existing baselines with up to 30 percent improvement in retained classification accuracy at high sparsity levels.