Abstract
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.
| Language | English |
|---|---|
| Article number | 105301 |
| Pages | 1-17 |
| Number of pages | 17 |
| Journal | Journal of Physics A: Mathematical and Theoretical |
| Volume | 47 |
| Issue number | 10 |
| DOIs | |
| Publication status | Published - 19 Feb 2014 |
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High-order quantum algorithm for solving linear differential equations. / Berry, Dominic W.
In: Journal of Physics A: Mathematical and Theoretical, Vol. 47, No. 10, 105301, 19.02.2014, p. 1-17.Research output: Contribution to journal › Article › Research › peer-review
TY - JOUR
T1 - High-order quantum algorithm for solving linear differential equations
AU - Berry, Dominic W.
PY - 2014/2/19
Y1 - 2014/2/19
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=84894849729&partnerID=8YFLogxK
U2 - 10.1088/1751-8113/47/10/105301
DO - 10.1088/1751-8113/47/10/105301
M3 - Article
VL - 47
SP - 1
EP - 17
JO - Journal of Physics A: Mathematical and Theoretical
T2 - Journal of Physics A: Mathematical and Theoretical
JF - Journal of Physics A: Mathematical and Theoretical
SN - 1751-8113
IS - 10
M1 - 105301
ER -