PIRSA:23040079

Exponential quantum speedup in simulating coupled classical oscillators

Wiebe, N. (2023). Exponential quantum speedup in simulating coupled classical oscillators. Perimeter Institute. https://pirsa.org/23040079

Wiebe, Nathan. Exponential quantum speedup in simulating coupled classical oscillators. Perimeter Institute, Apr. 19, 2023, https://pirsa.org/23040079 

          @misc{ pirsa_PIRSA:23040079,
            doi = {10.48660/23040079},
            url = {https://pirsa.org/23040079},
            author = {Wiebe, Nathan},
            keywords = {Quantum Information},
            language = {en},
            title = {Exponential quantum speedup in simulating coupled classical oscillators},
            publisher = {Perimeter Institute},
            year = {2023},
            month = {apr},
            note = {PIRSA:23040079 see, \url{https://pirsa.org}}
          }

Nathan Wiebe University of Toronto

DOI 10.48660/23040079
Collection
Talk Type Scientific Series
Subject

Abstract

We present a quantum algorithm for simulating the classical dynamics of 2^n coupled oscillators (e.g.,  masses coupled by springs). Our approach leverages a mapping between the Schrodinger equation and Newton's equations for harmonic potentials such that the amplitudes of the evolved quantum state encode the momenta and displacements of the classical oscillators. When individual masses and spring constants can be efficiently queried, and when the initial state can be efficiently prepared, the complexity of our quantum algorithm is polynomial in n, almost linear in the evolution time, and sublinear in the sparsity. As an example application, we apply our quantum algorithm to efficiently estimate the kinetic energy of an oscillator at any time, for a specification of the problem that we prove is BQP-complete. Thus, our approach solves a potentially practical application with an exponential speedup over classical computers. Finally, we show that under similar conditions our approach can efficiently simulate more general classical harmonic systems with 2^n modes.

Zoom link:  https://pitp.zoom.us/j/91882209363?pwd=UndJRVdaZW04RGtpL0M2SE52RDJwZz09