A Theoretical Study On Single-loop And Spin Clusters Geometric Quantum Computing

One of the most important problems in the field of the physical implementation of quantum computer is to find a way to precisely control quantum operations on a set of two-level systems. These days, due to geometric quantum computation has a degree of stability against a class of error in nature, so it have been attracting more and more interests. Theoretically, a pure geometric phase quantum gate can be achieved based on adiabatic geometric phase. But the adiabatic condition is not satisfied in many realistic cases. To solve this problem, AA phase was suggested to complete geometric quantum gates. These gates have the faster gate-operation time and intrinsic geometric features of the geometric phase. However the total phase in a nonadiabatic cyclic evolution generally consists of both the geometric and dynamical phases. Therefore we wish to remove the dynamic phase and get the nonadiabatic geometric phase. One of these scenario is a multi-loop scheme, in which the evolution is driven by the Hamiltonian along the time-reversal path of the first-period loop during the second period. At last, the dynamic phase is canceled and the geometric phase do not. But the gates may not be practical by using the magnetic field and need rotate the field to adjust the cyclical initial states. In the recent, there is a single-loop proposal. Comparing with the existing multi-loop geometric approach, this scenario may simplify the gate operation and shorten the gate-operation time. Yet in this way, the geometric phase is constant. In fact, the set of universal quantum gates were controlled by angle of initial . state, but not the geometric phase, which will constrain the physical implementation of quantum computation. Therefore, we propose another way for analytically constructing a universal set of geometric quantum gates using a single-loop scenario. Our method contains the advantages of both single-loop scenario and multi-loop scheme, and avoids part of their negative aspects. In this scheme, geodesic evolution loop is selected so that no dynamic phase is involved. In contrast with previous scenarios, our method not only...