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Quantum space-depth tradeoffs for coherent block encodings
Yuxin Zhang, Changpeng Shao
Block encodings are a basic interface between quantum algorithms and linear algebra. Standard LCU constructions achieve optimal circuit depth but typically require logarithmically…
Elfs, transducers and quantum walks
Simon Apers, Jérémie Roland, Yuxin Zhang
Electric flow sampling (elfs) is a new tool in the quantum walk toolbox and a useful primitive for solving search, sampling and optimization problems on graphs. We refine this tool…
DQC1-completeness of normalized trace estimation for functions of log-local Hamiltonians
Zhengfeng Ji, Tongyang Li, Changpeng Shao +2
We study the computational complexity of estimating the normalized trace for a log-local Hamiltonian acting on qubits. This problem arises natural…
Randomized Quantum Singular Value Transformation
Xinzhao Wang, Yuxin Zhang, Soumyabrata Hazra +3
We introduce the first randomized algorithms for Quantum Singular Value Transformation (QSVT), a unifying framework for many quantum algorithms. Standard implementations of QSVT re…
Quantum singular value transformation without block encodings: Near-optimal complexity with minimal ancilla
Shantanav Chakraborty, Soumyabrata Hazra, Tongyang Li +3
We develop new algorithms for Quantum Singular Value Transformation (QSVT), a unifying framework that encapsulates most known quantum algorithms and serves as the foundation for ne…
Quantum spectral method for gradient and Hessian estimation
Yuxin Zhang, Changpeng Shao
Gradient descent is one of the most basic algorithms for solving continuous optimization problems. In [Jordan, PRL, 95(5):050501, 2005], Jordan proposed the first quantum algorithm…