High-order quantum algorithm for solving linear differential equations
By Dominic W. Berry. arXiv.org, 2010
364 citations recorded by the source corpus.
Linear differential equations are ubiquitous in science and engineering. Quantum computers can simulate quantum systems, which are described by a restricted type of linear differential equations. Here we extend quantum simulation algorithms to general inhomogeneous sparse linear differential equations, which describe many classical physical systems. We examine the use of high-order methods (where the error over a time step is a high power of the size of the time step) to improve the efficiency. These provide scaling close to Δt2 in the evolution time Δt. As with other algorithms of this type, the solution is encoded in amplitudes of the quantum state, and it is possible to extract global features of the solution.
Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics
View Paper: https://www.semanticscholar.org/paper/f50046196557f3898578652c2244810e779a4354
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Artificial Intelligence
- Andrew M. Childs
- Dominic W. Berry
- Guoming Wang
- Aaron Ostrander
- Jaewoo Joo
- Dieter Jaksch
- Martin Kiffner
- Michael Lubasch
In Atomic and Molecular Physics, and Optics
- Andrew M. Childs
- Guoming Wang
- Aaron Ostrander
- Dieter Jaksch
- Martin Kiffner
- Michael Lubasch
- Jaewoo Joo
- Pierre Moinier
Citations in the corpus
- Variational quantum algorithms for nonlinear problems (2019, methodology): “(S2), we use the time-dependent variational principle algorithm for MPS [13, 14].”
- Efficient quantum algorithm for dissipative nonlinear differential equations (2020, background): “1) is unstable if Re (λ1) > 0 [8, 25], we only consider the case Re (λ1) ≤ 0.”
- Quantum algorithms: an overview (2015, neutral): “These include solving large systems of di(cid:11)erential equations [62, 13], data (cid:12)tting [97] and various tasks in machine learning [65].”
- Quantum Algorithm for Linear Differential Equations with Exponentially Improved Dependence on Precision (2017, methodology): “Reference [3] solves this problem using a quantum linear systems algorithm (QLSA) to implement linearmultistepmethods,which represent the differential equationswith a systemof linear equations by discretizing time.”