Shortcuts to adiabatic holonomic quantum computation in decoherence-free subspace with transitionless quantum driving algorithm

Abstract

By using transitionless quantum driving algorithm (TQDA), we present an efficient scheme for the shortcuts to the holonomic quantum computation (HQC). It works in decoherence-free subspace (DFS) and the adiabatic process can be speeded up in the shortest possible time. More interestingly, we give a physical implementation for our shortcuts to HQC with nitrogen-vacancy centers in diamonds dispersively coupled to a whispering-gallery mode microsphere cavity. It can be efficiently realized by controlling appropriately the frequencies of the external laser pulses. Also, our scheme has good scalability with more qubits. Different from previous works, we first use TQDA to realize a universal HQC in DFS, including not only two noncommuting accelerated single-qubit holonomic gates but also a accelerated two-qubit holonomic controlled-phase gate, which provides the necessary shortcuts for the complete set of gates required for universal quantum computation. Moreover, our experimentally realizable shortcuts require only two-body interactions, not four-body ones, and they work in the dispersive regime, which relax greatly the difficulty of their physical implementation in experiment. Our numerical calculations show that the present scheme is robust against decoherence with current experimental parameters.The decoherence-free subspace (DFS) [29-31] of a quantum system can protect the fragile quantum information against collective noises as the system undergoes a unitary evolution in its DFS. It has been demonstrated that DFS can be implemented experimentally with different physical systems [32][33][34]. In 2005, Wu et al [35] presented a theoretic scheme by combining the HQC and DFS to perform universal QC. By making the dark states of the Hamiltonian of a quantum system adiabatically evolve along a closed cyclic loop, one can acquire a Berry phase or quantum holonomy. In 2006, Zhang et al [36] and Cen et al [37] gave two schemes for HQC with DFS in trapped ions. In 2009, Oreshkov et al [38] introduced a scheme for fault-tolerant HQC on stabilizer codes. The adiabatic evolution for HQC requires a long run time. To eliminate this dilemma, Berry[39] came up with a transitionless quantum driving algorithm (TQDA), which is also outlined in slightly different manner by Demirplak and Rice [40, 41], to speed up the adiabatic quantum gates when the eigenstates of a time-dependent Hamiltonian are non-degenerate in 2009. Later, this transitionless algorithm has been gained widespread attention in both theory and experiment [42-47]. In 2010, Chen et al [42] used the TQDA to speed up adiabatic passage techniques in two-level and three-level atoms extending to the short-time domain their robustness with respect to parameter variations. In 2012, Bason et al [46] experimentally implemented the optimal high-fidelity transitionless superadiabatic protocol on Bose-Einstein condensates in optical lattices. In 2013, Zhang et al [47] implemented the acceleration of quantum adiabatic passages on the electron spin of a single NV center in diamond....

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