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Explore a novel hybrid quantum-classical approach to representing quantum states through this 18-minute conference talk from the Quantum Techniques in Machine Learning (QTML) 2025 conference. Discover the multiple-basis representation method, which expresses quantum states as linear combinations of states that are sparse in given bases specified by quantum circuits. Learn how this representation bridges classical simulation capabilities with quantum computational advantages, particularly for depth-limited quantum circuits accessible on current hardware. Examine the expressivity of multiple-basis representation states and their relationship to classical simulability of quantum circuits, including how they encompass both matrix-product states and stabilizer states while extending beyond these frameworks. Investigate practical applications including ground state approximation, simulation of deeper quantum computations using shallow circuit bases, and tomographical protocols for state description. Understand how this approach enables simultaneous utilization of multiple hardware-friendly bases, providing a natural framework for hybrid computational methods suitable for near-term quantum devices and opening new pathways for quantum-classical computational synergy.
