Quantum algorithms for linear differential equation and phase estimation via Lindbladians
Naixu Guo | Centre for Quantum Technologies (CQT)
In this talk I will present two recent works about Lindbladian based quantum algorithms. In the first work, we propose a new quantum algorithm for solving ODEs by harnessing open quantum systems. Solving linear ordinary differential equations (ODE) is one of the most promising applications for quantum computers to demonstrate exponential advantages. The challenge is to simulte the non-unitary dynamics. Specifically, we propose a novel technique called non-diagonal density matrix encoding. Combined with the state-of-the-art quantum Lindbladian simulation algorithms, our algorithm achieve near-optimal dependence on all parameters under a plausible input model.
In the second work, we make an attempt to bridge Quantum phase estimation (QPE) and Lindbladian dynamics. Certain simple Lindbladian processes can be adapted to perform QPE-type tasks. However, unlike previous QPE algorithms, these Lindbladian evolutions are restricted to standard quantum limit complexity. This indicates that, different from Hamiltonian dynamics, the natural dissipative evolution speed of such Lindbladians does not saturate the fundamental quantum limit.
We confirm this by presenting a quantum algorithm that achieves quadratic fast-forwarding. The mechanism is fundamentally different from the fast-forwarding examples of Hamiltonian dynamics. As a bonus, this fast-forwarded simulation naturally serves as a new Heisenberg-limit QPE algorithm. Therefore, our work explicitly bridges the standard quantum limit-Heisenberg limit transition to the fast-forwarding of dissipative dynamics.
About the speaker
Naixu Guo is currently a fourth-year PhD student at Centre for Quantum Technologies(CQT), National University of Singapore. He is advised by Patrick Rebentrost and Miklos Santha. Previously, he graduated from Kyoto University and Osaka University. His research interests mainly include quantum algorithms, quantum machine learning, and AI for quantum.
Location
QNC 1201