QUANTUM STATE DIFFUSION, LOCALIZATION AND COMPUTATION

Numerical simulation of individual open quantum systems has proven adv antages over density operator computations. Quantum state diffusion wi th a moving basis (MQSD) provides a practical numerical simulation met hod which takes full advantage of the localization of quantum states i nto wavepackets occupying small regions of classical phase space. Foll owing and extending the original proposal of Percival, Alber and Steim le, we show that MQSD can provide a further gain over ordinary QSD and other quantum trajectory methods of many orders of magnitude in compu tational space and time. Because of these gains, it is even possible t o calculate an open quantum system trajectory when the corresponding i solated system is intractable. MQSD is particularly advantageous where classical or semiclassical dynamics provides an adequate qualitative picture but is numerically inaccurate because of significant quantum e ffects. The principles are illustrated by computations for the quantum Duffing oscillator and for second-harmonic generation in quantum opti cs. Potential applications in atomic and molecular dynamics, quantum c ircuits and quantum computation are suggested.