Geometric quantum computation using nuclear magnetic resonance

A significant development in computing has been the discovery(1) that the c omputational power of quantum computers exceeds that of Turing machines. Ce ntral to the experimental realization of quantum information processing is the construction of fault-tolerant quantum logic gates. Their operation req uires conditional quantum dynamics, in which one sub-system undergoes a coh erent evolution that depends on the quantum state of another sub-system(2); in particular, the evolving sub-system may acquire a conditional phase shi ft. Although conventionally dynamic in origin, phase shifts can also be geo metric(3,4) Conditional geometric (or 'Berry') phases depend only on the ge ometry of the path executed, and are therefore resilient to certain types o f errors; this suggests the possibility of an intrinsically fault-tolerant way of performing quantum gate operations. Nuclear magnetic resonance techn iques have already been used to demonstrate both simple quantum information processing(5-9) and geometric phase shifts(10-12). Here we combine these i deas by performing a nuclear magnetic resonance experiment in which a condi tional Berry phase is implemented, demonstrating a controlled phase shift g ate.