Geometric quantum computation using nuclear magnetic resonance

Abstract

A significant development in computing has been the discovery¹ that the computational power of quantum computers exceeds that of Turing machines. Central to the experimental realization of quantum information processing is the construction of fault-tolerant quantum logic gates. Their operation requires conditional quantum dynamics, in which one sub-system undergoes a coherent evolution that depends on the quantum state of another sub-system²; in particular, the evolving sub-system may acquire a conditional phase shift. Although conventionally dynamic in origin, phase shifts can also be geometric^3,4. Conditional geometric (or ‘Berry’) phases depend only on the geometry of the path executed, and are therefore resilient to certain types of errors; this suggests the possibility of an intrinsically fault-tolerant way of performing quantum gate operations. Nuclear magnetic resonance techniques have already been used to demonstrate both simple quantum information processing^5,6,7,8,9 and geometric phase shifts^10,11,12. Here we combine these ideas by performing a nuclear magnetic resonance experiment in which a conditional Berry phase is implemented, demonstrating a controlled phase shift gate.