Nonadiabatic geometric quantum computation protected by dynamical decoupling via the XXZ Hamiltonian

Nonadiabatic geometric quantum computation protected by dynamical decoupling combines the robustness of nonadiabatic geometric gates and the decoherence-resilience feature of dynamical decoupling. Solid-state systems provide an appealing candidate for the realization of nonadiabatic geometric quantum computation protected dynamical decoupling since the solid-state qubits are easily embedded in electronic circuits and scaled up to large registers. In this paper, we put forward a scheme of nonadiabatic geometric quantum computation protected by dynamical decoupling via the XXZ Hamiltonian, which not only combines the merits of nonadiabatic geometric gates and dynamical decoupling but also can be realized in a number of solid-state systems, such as superconducting circuits and quantum dots.

Topological dynamical decoupling

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.

Dynamical decoupling of electron spins in phosphorus-doped silicon

Quantum coherence is an important enabling feature underpinning quantum computation. However, because of couplings with its noisy surrounding environment, qubits suffer from the decoherence effects. The dynamical decoupling (DD) technique uses pulse-induced qubit flips to effectively mitigate couplings between qubits and environment. Optimal DD eliminates dephasing up to a given order with the minimum number of pulses. In this paper, we first introduce our recent work on prolonging electron spin coherence in γ-irradiated malonic acid crystals and analyze different decoherence mechanisms in this solid system. Then we focus on electron spin relaxation properties in another system, phosphorous-doped silicon (Si:P) crystals. These properties have been investigated by pulse electron paramagnetic resonance (EPR). We also investigate the performance of the dynamical decoupling technique on this system. Using 8-pulse periodic DD, the coherence time can be extended to 296 μs compared with 112 μs with one-pulse control.