7 papers
Low-ancilla block encodings via Hamiltonian simulation
Yuxin Zhang, Changpeng Shao
Block encodings are a central primitive in quantum algorithms, but standard constructions typically require logarithmic ancilla overhead and complicated controlled operations. Rece…
Worst-case Harrow-Hassidim-Lloyd algorithm with average-case correct quantum Fourier transform
Changpeng Shao
In [\href{https://quantum-journal.org/papers/q-2022-12-07-872/}{Quantum 6, 872, 2022}], Linden and de Wolf proposed a lightweight protocol for verifying average-case correctness of…
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…
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…
Normalization of Quaternionic Polynomials in Coordinate-Free Quaternionic Variables in Conjugate-Alternating Order
Hongbo Li, Zhengyang Wang, Yue Liu +2
Quaternionic polynomials occur naturally in applications of quaternions in science and engineering, and normalization of quaternionic polynomials is a basic manipulation. Once a Gr…