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Gate construction of block-encoding for Hamiltonians needed for simulating partial differential equations

Nikita Guseynov ^*

Xiajie Huang ^†

Nana Liu^‡

University of Michigan-Shanghai Jiao Tong University Joint Institute, Shanghai 200240, China

School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai 200240, China

Institute of Natural Sciences, School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai 200240; China Ministry of Education Key Laboratory in Scientific and Engineering Computing, Shanghai Jiao Tong University, Shanghai 200240 China; Shanghai Artificial Intelligence Laboratory, Shanghai, China; and University of Michigan-Shanghai Jiao Tong University Joint Institute, Shanghai 200240, China

^*Contact author: guseynov.nm@gmail.com
^†Contact author: xj.huang@sjtu.edu.cn
^‡Contact author: nana.liu@quantumlah.org

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Articles Citing

Gate construction of block-encoding for Hamiltonians needed for simulating partial differential equations

Quantum Sampling and Moment Estimation for Transformed Gaussian Random Fields

Quantum linear system solvers: A survey of algorithms and applications

Quantum finite element algorithm for solving Euler–Bernoulli and heat transfer PDEs with Dirichlet, Neumann, and Robin boundary conditions

Quantum framework for simulating linear PDEs with Robin boundary conditions

Fourier space readout method for efficiently recovering functions encoded in quantum states

Performance evaluation of variational quantum eigensolver and quantum dynamics algorithms on the advection-diffusion equation

Linear-combination-of-unitaries decomposition for the Laplace operator

An efficient explicit implementation of a near-optimal quantum algorithm for simulating linear dissipative differential equations

Toward end-to-end quantum simulation of rapidly distorted turbulence

Binary Tree Block Encoding of Classical Matrix

Quantum random feature method for solving partial differential equations

Optical quantum computing

Scalable quantum computational science: A perspective from block-encodings and polynomial transformations

Quantum Computing for Boundary-Aware Computational Mechanics: A Review and Variational Finite Element Perspective

No title available

Quantum wave simulation with sources and loss functions

Quantum dynamics simulation of the advection-diffusion equation

Quantum circuits for partial differential equations in Fourier space

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