Quantum computing of semiclassical formulas

2008/01/30 by Bertrand Georgeot, B. Georgeot, Olivier Giraud +1
Computer Science · Mathematics · Physics and Astronomy · #Algorithm #Computation #Mathematics #Observable #Physics #Quadratic equation #Quantum #Quantum Computing Algorithms and Architecture #Quantum algorithm #Quantum chaos and dynamical systems #Quantum computer #Quantum many-body systems #Quantum mechanics #Semiclassical physics #nlin.CD #quant-ph

paper · pdf · doi:10.1103/physreve.77.046218

published as Phys. Rev. E 77, 046218 (2008) · 8 pages, 1 figure

arxiv created 2008/01/30 · openalex publication_date 2008/04/25 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

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.

Citations

• Periodic Orbits and Classical Quantization Conditions
• Quantum mechanical computers
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