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Quantum Derivative Pricing for SPDEs via BDSDE Representation
Xinmiao Li, Yanqiao Wang, Rundi Lu +2
We study quantum speedups of derivative pricing for stochastic partial differential equation (SPDE) models through their backward doubly stochastic differential equation (BDSDE) re…
A Unified Frequency Principle for Quantum and Classical Machine Learning
Rundi Lu, Ruiqi Zhang, Weikang Li +3
Quantum neural networks constitute a key class of near-term quantum learning models, yet their training dynamics remain not fully understood. Here, we present a unified theoretical…
Taming Barren Plateaus in Arbitrary Parameterized Quantum Circuits without Sacrificing Expressibility
Zhenyu Chen, Yuguo Shao, Zhengwei Liu +1
Quantum algorithms based on parameterized quantum circuits (PQCs) have enabled a wide range of applications on near-term quantum devices. However, existing PQC architectures face s…
Diagnosing Quantum Circuits: Noise Robustness, Trainability, and Expressibility
Yuguo Shao, Zhenyu Chen, Zhaohui Wei +1
Achieving practical quantum advantage on near-term noisy hardware is a central goal of quantum computation. However, without efficient pre-execution diagnostics, circuit design and…
BELT: Block Encoding of Linear Transformation on Density Matrices
Fuchuan Wei, Rundi Lu, Yuguo Shao +3
Linear maps that are not completely positive play a crucial role in the study of quantum information, yet their non-completely positive nature renders them challenging to realize p…
Infinite-dimensional Extension of the Linear Combination of Hamiltonian Simulation: Theorems and Applications
Rundi Lu, Hao-En Li, Zhengwei Liu +1
We generalize the Linear Combination of Hamiltonian Simulation (LCHS) formula [An, Liu, Lin, Phys. Rev. Lett. 2023] to simulate time-evolution operators in infinite-dimensional spa…