247 citations · 806 across the 13 of their papers we have counts for
13 papers
Dense outputs from quantum simulations
Jin-Peng Liu, Lin Lin
The quantum dense output problem is the process of evaluating time-accumulated observables from time-dependent quantum dynamics using quantum computers. This problem arises frequen…
Towards provably efficient quantum algorithms for large-scale machine-learning models
Junyu Liu, Minzhao Liu, Jin-Peng Liu +5
Large machine learning models are revolutionary technologies of artificial intelligence whose bottlenecks include huge computational expenses, power, and time used both in the pre-…
Linear combination of Hamiltonian simulation for nonunitary dynamics with optimal state preparation cost
Dong An, Jin-Peng Liu, Lin Lin
We propose a simple method for simulating a general class of non-unitary dynamics as a linear combination of Hamiltonian simulation (LCHS) problems. LCHS does not rely on convertin…
Escaping From Saddle Points Using Asynchronous Coordinate Gradient Descent
Marco Bornstein, Jin-Peng Liu, Jingling Li +1
Large-scale non-convex optimization problems are expensive to solve due to computational and memory costs. To reduce the costs, first-order (computationally efficient) and asynchro…
Quantum differential equation solvers: limitations and fast-forwarding
Dong An, Jin-Peng Liu, Daochen Wang +1
We study the limitations and fast-forwarding of quantum algorithms for linear ordinary differential equation (ODE) systems with a particular focus on non-quantum dynamics, where th…
Quantum Algorithms for Sampling Log-Concave Distributions and Estimating Normalizing Constants
Andrew M. Childs, Tongyang Li, Jin-Peng Liu +2
Given a convex function , the problem of sampling from a distribution is called log-concave sampling. This task has wide app…
Efficient quantum algorithm for nonlinear reaction-diffusion equations and energy estimation
Dong An, Di Fang, Stephen Jordan +3
Nonlinear differential equations exhibit rich phenomena in many fields but are notoriously challenging to solve. Recently, Liu et al. [1] demonstrated the first efficient quantum a…
Quantum simulation of real-space dynamics
Andrew M. Childs, Jiaqi Leng, Tongyang Li +2
Quantum simulation is a prominent application of quantum computers. While there is extensive previous work on simulating finite-dimensional systems, less is known about quantum alg…
Quantum-accelerated multilevel Monte Carlo methods for stochastic differential equations in mathematical finance
Dong An, Noah Linden, Jin-Peng Liu +3
Inspired by recent progress in quantum algorithms for ordinary and partial differential equations, we study quantum algorithms for stochastic differential equations (SDEs). Firstly…
Efficient quantum algorithm for dissipative nonlinear differential equations
Jin-Peng Liu, Herman Øie Kolden, Hari K. Krovi +3
Nonlinear differential equations model diverse phenomena but are notoriously difficult to solve. While there has been extensive previous work on efficient quantum algorithms for li…
Solving generalized eigenvalue problems by ordinary differential equations on a quantum computer
Changpeng Shao, Jin-Peng Liu
Many eigenvalue problems arising in practice are often of the generalized form $A\x=λB\x$. One particularly important case is symmetric, namely are Hermitian and is posi…
High-precision quantum algorithms for partial differential equations
Andrew M. Childs, Jin-Peng Liu, Aaron Ostrander
Quantum computers can produce a quantum encoding of the solution of a system of differential equations exponentially faster than a classical algorithm can produce an explicit descr…
Quantum spectral methods for differential equations
Andrew M. Childs, Jin-Peng Liu
Recently developed quantum algorithms address computational challenges in numerical analysis by performing linear algebra in Hilbert space. Such algorithms can produce a quantum st…