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SUMMARY:Dimension lifting  in quantum computation of  partial differential
  equations and related problems - Shi Jin (Shanghai Jiao Tong University)
DTSTART:20251002T130000Z
DTEND:20251002T140000Z
UID:TALK236119@talks.cam.ac.uk
CONTACT:Georg Maierhofer
DESCRIPTION:Quantum computers are designed based on quantum mechanics prin
 ciple\, they are most suitable to solve the Schrodinger equation\, and lin
 ear PDEs (and ODEs) evolved by unitary operators.  It is important to  to 
 explore whether other problems in scientific computing\, such as ODEs\, PD
 Es\, and  linear algebra that arise in both classical and quantum systems 
 which are not unitary evolution\,  can be handled by quantum computers.  \
 n\nWe will present a systematic way to develop quantum simulation algorith
 ms for general differential equations. Our basic framework is dimension li
 fting\, that transfers non-autonomous ODEs/PDEs systems to autonomous ones
 \, nonlinear PDEs to linear ones\, and linear ones to Schrodinger type PDE
 s—coined “Schrödingerization”—with uniform evolutions. Our formul
 ation allows both qubit and qumode (continuous-variable) formulations\, an
 d their hybridizations\, and provides the foundation for analog quantum co
 mputing which are easier to realize in the near term. We will present  dim
 ension lifting techniques for quantum simulation of stochastic DEs and PDE
 s with fractional derivatives\, and quantum machine learning. A quantum si
 mulation software—“UnitaryLab”—will also be introduced.
LOCATION:Centre for Mathematical Sciences\, MR14
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