Non-adiabatic holonomic quantum computation (NHQC) has been developed to shorten the construction times of geometric quantum gates. However, previous NHQC gates require the driving Hamiltonian to satisfy a set of rather restrictive conditions, reducing the robustness of the resulting geometric gates against control errors. Here we show that non-adiabatic geometric gates can be constructed in an extensible way, called NHQC+, for maintaining both flexibility and robustness. Consequently, this approach makes it possible to incorporate most of the existing optimal control methods, such as dynamical decoupling, composite pulses, and shortcut to adiabaticity, into the construction of single-looped geometric gates. Furthermore, this extensible approach of geometric quantum computation can be applied to various physical platform such as superconducting qubits and nitrogen-vacancy centers. Specifically, we performed numerical simulation to show how the noise robustness in the recent experimental implementations [Phys. Rev. Lett. 119, 140503 (2017)] and [Nat. Photonics 11, 309 (2017)] can be significantly improved by our NHQC+ approach. These results cover a large class of new techniques combing the noise robustness of both geometric phase and optimal control theory.

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....

Neutrino oscillation is an important physical phenomenon in elementary particle physics, and its nonclassical features can be revealed by the Leggett-Garg inequality. It shows that its quantum coherence can be sustained over astrophysical length scales. In this work, we investigate the measure of quantumness in experimentally observed neutrino oscillations via the nonlocal advantage of quantum coherence (NAQC), quantum steering, and Bell nonlocality. From various neutrino sources, ensembles of reactor and accelerator neutrinos are analyzed at distinct energies, such as Daya Bay (0.5 km and 1.6 km) and MINOS (735 km) collaborations. The NAQC of two-flavor neutrino oscillation is characterized experimentally compared to the theoretical prediction. It exhibits non-monotonously evolutive phenomenon with the increase of energy. Furthermore, it is found that the NAQC is a stronger quantum correlation than quantum steering and Bell nonlocality even in the order of km. Hence, for an arbitrary bipartite neutrino-flavor state with achieving a NAQC, it must be also a steerable and Bell nonlocal state. The results might offer an insight into the neutrino oscillation for the further applications on quantum information processing.

Three-level quantum systems, which possess some unique characteristics beyond two-level ones, such as electromagnetically induced transparency, coherent trapping, and Raman scatting, play important roles in solid-state quantum information processing. Here, we introduce an approach to implement the physically feasible threelevel transitionless quantum driving with multiple Schrödinger dynamics (MSDs). It can be used to control accurately population transfer and entanglement generation for three-level quantum systems in a nonadiabatic way. Moreover, we propose an experimentally realizable hybrid architecture, based on two nitrogen-vacancycenter ensembles coupled to a transmission line resonator, to realize our transitionless scheme which requires fewer physical resources and simple procedures, and it is more robust against environmental noises and control parameter variations than conventional adiabatic passage techniques. All these features inspire the further application of MSDs on robust quantum information processing in experiment.

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Xue-Ke Song (), Qing Ai (), Jing Qiu (), and Fu-Guo Deng ()

Neutrino oscillation represents an intriguing physical phenomenon where the quantumness can be maintained and detected over a long distance. Previously, the non-classical character of neutrino oscillation was tested with the Leggett-Garg inequality, where a clear violation of the classical bound was observed [J. A. Formaggio et al., Phys. Rev. Lett. 117, 050402 (2016)]. However, there are several limitations in testing neutrino oscillations with the Leggett-Garg inequality. In particular, the degree of violation of the Leggett-Garg inequality cannot be taken as a "measure of quantumness". Here we focus on quantifying the quantumness of experimentallyobserved neutrino oscillation, using the tools of recently-developed quantum resource theory. We analyzed ensembles of reactor and accelerator neutrinos at distinct energies from a variety of neutrino sources, including Daya Bay (0.5 km and 1.6 km), Kamland (180 km), MINOS (735 km), and T2K (295 km). The quantumness of the three-flavoured neutrino oscillation is characterized within a 3σ range relative to the theoretical prediction. It is found that the maximal coherence was observed in the neutrino source from the Kamland reactor. However, even though the survival probability of the Daya Bay experiment did not vary significantly (dropped about 10 percent), the coherence recorded can reach up to 40 percent of the maximal value. These results represent the longest distance over which quantumness were experimentally determined for quantum particles other than photons.Introduction.-The phenomenon of neutrino oscillation was proposed for more than half a century [1,2]. Since then, compelling experimental evidences of the transitions between different neutrino flavors have been obtained from different sources, including solar [3,4], atmosphere [5], reactor [6,7] and accelerator neutrinos [8][9][10][11]. In the three-generation neutrino framework, neutrinos and antineutrinos are produced simultaneously and detected in three different flavors, namely electron e, muon µ, and tau τ leptons. The flavor states are linear combination of the mass states [12,13]. Neutrino oscillation implies that a given flavor may change into another flavor during the propagating, caused by the nonzero neutrino mass and neutrino mixing. Recently, a number of refined measurements and analyses on the oscillations parameters have been presented [14][15][16][17]. However, the justification of neutrino oscillation is based on a crucial assumption that the different neutrino states are well coherent during its propagating; this assumption of quantum coherence still needs to be verified carefully, as it leads to considerable constrains in ultra-high energy or astronomical scales [18,19]. Furthermore, to explore the possibility of utilizing neutrino oscillations for future applications in quantum information processing, an important step is to verify the "quantumness" in neutrino oscillations.

Neutrino oscillation is deemed as an interesting physical phenomenon and shows the nonclassical features made apparently by the Leggett–Garg inequality. The uncertainty principle is one of the fundamental features that distinguishes the quantum world to its classical counterpart. And the principle can be depicted in terms of entropy, which forms the so-called entropic uncertainty relations (EUR). In this work, the entropic uncertainty relations that are relevant to the neutrino-flavor states are investigated by comparing the experimental observation of neutrino oscillations to predictions. From two different neutrino sources, we analyze ensembles of reactor and accelerator neutrinos for different energies, including measurements performed by the Daya Bay collaboration using detectors at 0.5 and 1.6 km from their source, and by the MINOS collaboration using a detector with a 735km distance to the neutrino source. It is found that the entropy-based uncertainty conditions strengths exhibits non-monotonic evolutions as the energy increases. We also quantify the systemic quantumness measured by quantum correlation, and derive the intrinsic relationship between quantum correlation and EUR. Furthermore, we utilize EUR as a criterion to detect entanglement of neutrino-flavor state. Our results could illustrate the potential applications of neutrino oscillations on quantum information processing in the weak-interaction processes.