We show that topological equivalence classes of circles in a two-dimensional square lattice can be used to design dynamical decoupling procedures to protect qubits attached on the edges of the lattice. Based on the ci...We show that topological equivalence classes of circles in a two-dimensional square lattice can be used to design dynamical decoupling procedures to protect qubits attached on the edges of the lattice. Based on the circles of the topologically trivial class in the original and the dual lattices, we devise a procedure which removes all kinds of local Hamiltonians from the dynamics of the qubits while keeping information stored in the homological degrees of freedom unchanged. If only the linearly independent interaction and nearest-neighbor two-qubit interactions are concerned, a much simpler procedure which involves the four equivalence classes of circles can be designed. This procedure is compatible with Eulerian and concatenated dynamical decouplings,which make it possible to implement the procedure with bounded-strength controls and for a long time period. As an application,it is shown that our method can be directly generalized to finite square lattices to suppress uncorrectable errors in surface codes.展开更多
基金supported by the National Basic Research Program of China(Grant Nos.2017YFA0303700,and 2015CB921001)the National Natural Science Foundation of China(Grant Nos.61726801,11474168,and11474181)+2 种基金in part by the Beijing Advanced Innovative Center for Future Chip(ICFC)support by the China Postdoctoral Science Foundation(Grant No.2018M631437)support by the Deutsche Forschungs Gemeinschaft(DFG)the European Research Council(ERC)(Consolidator Grant 683107/TempoQ)
文摘We show that topological equivalence classes of circles in a two-dimensional square lattice can be used to design dynamical decoupling procedures to protect qubits attached on the edges of the lattice. Based on the circles of the topologically trivial class in the original and the dual lattices, we devise a procedure which removes all kinds of local Hamiltonians from the dynamics of the qubits while keeping information stored in the homological degrees of freedom unchanged. If only the linearly independent interaction and nearest-neighbor two-qubit interactions are concerned, a much simpler procedure which involves the four equivalence classes of circles can be designed. This procedure is compatible with Eulerian and concatenated dynamical decouplings,which make it possible to implement the procedure with bounded-strength controls and for a long time period. As an application,it is shown that our method can be directly generalized to finite square lattices to suppress uncorrectable errors in surface codes.
