Xinbiao Wang

Wei-You Liao, Yuxuan Du, Xinbiao Wang et al.

The ongoing development of quantum processors is driving breakthroughs in scientific discovery. Despite this progress, the formidable cost of fabricating large-scale quantum processors means they will remain rare for the foreseeable future, limiting their widespread application. To address this bottleneck, we introduce the concept of predictive surrogates, which are classical learning models designed to emulate the mean-value behavior of a given quantum processor with provably computational efficiency. In particular, we propose two predictive surrogates that can substantially reduce the need for quantum processor access in diverse practical scenarios. To demonstrate their potential in advancing digital quantum simulation, we use these surrogates to emulate a quantum processor with up to 20 programmable superconducting qubits, enabling efficient pre-training of variational quantum eigensolvers for families of transverse-field Ising models and identification of non-equilibrium Floquet symmetry-protected topological phases. Experimental results reveal that the predictive surrogates not only reduce measurement overhead by orders of magnitude, but can also surpass the performance of conventional, quantum-resource-intensive approaches. Collectively, these findings establish predictive surrogates as a practical pathway to broadening the impact of advanced quantum processors.

Xinbiao Wang, Yuxuan Du, Kecheng Liu et al.

The No-Free-Lunch (NFL) theorem, which quantifies problem- and data-independent generalization errors regardless of the optimization process, provides a foundational framework for comprehending diverse learning protocols' potential. Despite its significance, the establishment of the NFL theorem for quantum machine learning models remains largely unexplored, thereby overlooking broader insights into the fundamental relationship between quantum and classical learning protocols. To address this gap, we categorize a diverse array of quantum learning algorithms into three learning protocols designed for learning quantum dynamics under a specified observable and establish their NFL theorem. The exploited protocols, namely Classical Learning Protocols (CLC-LPs), Restricted Quantum Learning Protocols (ReQu-LPs), and Quantum Learning Protocols (Qu-LPs), offer varying levels of access to quantum resources. Our derived NFL theorems demonstrate quadratic reductions in sample complexity across CLC-LPs, ReQu-LPs, and Qu-LPs, contingent upon the orthogonality of quantum states and the diagonality of observables. We attribute this performance discrepancy to the unique capacity of quantum-related learning protocols to indirectly utilize information concerning the global phases of non-orthogonal quantum states, a distinctive physical feature inherent in quantum mechanics. Our findings not only deepen our understanding of quantum learning protocols' capabilities but also provide practical insights for the development of advanced quantum learning algorithms.