# Bulletin of the American Physical Society

# APS March Meeting 2020

## Volume 65, Number 1

## Monday–Friday, March 2–6, 2020; Denver, Colorado

### Session F09: General Quantum Algorithms

8:00 AM–10:48 AM,
Tuesday, March 3, 2020

Room: 106

Sponsoring
Unit:
DQI

Chair: Peter Love, Tufts Univ

### Abstract: F09.00003 : Quantum Simulation of Nonlinear Classical Dynamics*

View Presentation Abstract

#### Presenter:

Ilon Joseph

(Lawrence Livermore Natl Lab)

#### Authors:

Ilon Joseph

(Lawrence Livermore Natl Lab)

Alessandro Roberto Castelli

(Lawrence Livermore Natl Lab)

Jonathan L. DuBois

(Lawrence Livermore Natl Lab)

Vasily Geyko

(Lawrence Livermore Natl Lab)

Frank R Graziani

(Lawrence Livermore Natl Lab)

Stephen Bernard Libby

(Lawrence Livermore Natl Lab)

Jeffrey Parker

(Lawrence Livermore Natl Lab)

Yaniv J. Rosen

(Lawrence Livermore Natl Lab)

Yuan Shi

(Lawrence Livermore Natl Lab)

*N*ordinary differential equations (ODEs) within an enlarged quantum mechanical system with 2

*N*degrees of freedom. Any set of ODEs can be derived from a classical Hamiltonian that is a sum over a set of

*N*constraints, thereby yielding 2

*N*equations of motion. Quantizing the constrained system leads to a Schrodinger equation that is equal to the classical Liouville equation which ensures conservation of phase space density for the original set of ODEs. Heisenberg’s uncertainty principle is satisfied by each variable and its canonically conjugate momentum, the Lagrange multiplier, on the extended phase space. Hence, there is no uncertainty in a simultaneous measurement of any of the variables of the original ODE. An appropriate choice of Planck’s constant can be used to reduce the uncertainty in the degrees of freedom of interest to a width on the order of the level spacing. Thus, excellent fidelity to the classical system can be achieved.

*This work was performed by LLNL under US DOE contract DE-AC52-07NA27344, DOE-FES AT1030200-WA-OP SCW-1680, and LLNL-LDRD 19-FS-072 and 19-ERD-038.

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