Quantum computing of semiclassical formulas

Bertrand Georgeot (1, 2) , Olivier Giraud (1)

1 ICQ - Cohérence Quantique (LPT)
2 LPT - Laboratoire de Physique Théorique

We show that semiclassical formulas such as the Gutzwiller trace formula can be implemented on a quantum computer more efficiently than on a classical device. We give explicit quantum algorithms which yield quantum observables from classical trajectories, and which alternatively test the semiclassical approximation by computing classical actions from quantum evolution. The gain over classical computation is in general quadratic, and can be larger in some specific cases.

Domaines: Physique Quantique [quant-ph]

Bertrand Georgeot, Olivier Giraud. Quantum computing of semiclassical formulas. Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, 2008, 77, pp.046218. ⟨10.1103/PhysRevE.77.046218⟩. ⟨hal-00344141⟩