Why study geometric phase? It is an interesting phenomenon of Quantum mechanics, which can be observed in many physical systems It has interesting properties that can be exploited to increase the robustness of Quantum Computation Geometric Quantum Computation
6 Why study geometric phase? • It is an interesting phenomenon of Quantum mechanics, which can be observed in many physical systems... • It has interesting properties that can be exploited to increase the robustness of Quantum Computation: “Geometric Quantum Computation
Geometric quantum computation 100)->00)01〉-01) 10)〉10),1)-1) U =eXpRE(tdt Dynamical evolution Geometric phase Geometric gates can be more robust against different sources of noise
7 exp[ ( ) ] U = −i E t dt i Dynamical evolution Geometric phase Geometric gates can be more robust against different sources of noise | 00 | 00 ,| 01 | 01 , |10 |10 ,|11 |11 , → → → → − g Geometric quantum computation
Why geometric phase robust? Geometric phase is robust against classical fluctuation of the phase(of the first order)see for example G. D. Chiara. G. M. Palma, Phys. Rev Let.91,090404(2003) It is independent of systematic errors
8 Why geometric phase robust? • Geometric phase is robust against classical fluctuation of the phase (of the first order) see for example: G. D. Chiara, G. M. Palma, Phys. Rev. Lett. 91, 090404 (2003). ◼It is independent of systematic errors
Geometric phase in bipartite systems Almost all systems in Qip are composite If entanglement change Berry's phase what role the inter-subsystem couplings may play
9 Geometric phase in bipartite systems • Almost all systems in QIP are composite. • If entanglement change Berry’s phase. • What role the inter-subsystem couplings may play?
Berry' s phase of entangled spin pair E. Sjoqvist, Pra 62, 022109(2000 without inter-subsystem coupling) Separable pair, total BP=sum over individual BP For entangled pair, with one particle driven by the external magnetic field Initial state|H()≥=c0s个+sia geometric phase O. =T(cos a cos 8-1) B 6=arc cos[cos a cos g]
10 Berry’s phase of entangled spin pair E. Sjoqvist, PRA 62, 022109(2000)(without inter-subsystem coupling) • Separable pair, total BP=sum over individual BP. • For entangled pair, with one particle driven by the external magnetic field | (0) cos | sin | 2 2 •Initial state = + (cos cos 1) g = − •Geometric phase B S ' = arc cos[cos cos ]