Nonadiabatic holonomic quantum computation has received increasing attention due to its robustness against control errors as well as high-speed realization. Several schemes of its implementation have been put forward based on various physical systems, each of which has some particular merits. In this paper, we put forward an alternative scheme of nonadiabatic holonomic quantum computation, in which a universal set of quantum gates is realized based on Rydberg superatoms. A Rydberg superatom is a mesoscopic atomic ensemble that allows for only a single Rydberg excitation shared by many atoms within a blockade radius and can be used to generate the collective states to encode the qubits. In our scheme, the qubit is encoded into two collective ground states of Rydberg superatoms and the interaction between two long-range Rydberg superatoms is mediated by a microwave cavity with the aid of two additional collective Rydberg states. Different from the previous schemes, which are based on the systems in the microscope scale, the present scheme is based on atomic ensembles in the mesoscopic scale. Besides the common merits of nonadiabatic holonomic quantum computation such as the robustness and the speediness, the Rydberg-superatom-based scheme has the following particular merits: the long coherence time of Rydberg states and the operability of the mesoscopic systems.
Nonadiabatic holonomic quantum computation has received increasing attention due to its robustness against control errors as well as high-speed realization. Several schemes of its implementation have been put forward based on various physical systems, each of which has some particular merits. In this paper, we put forward an alternative scheme of nonadiabatic holonomic quantum computation, in which a universal set of quantum gates is realized based on Rydberg superatoms. A Rydberg superatom is a mesoscopic atomic ensemble that allows for only a single Rydberg excitation shared by many atoms within a blockade radius and can be used to generate the collective states to encode the qubits. In our scheme, the qubit is encoded into two collective ground states of Rydberg superatoms and the interaction between two long-range Rydberg superatoms is mediated by a microwave cavity with the aid of two additional collective Rydberg states. Different from the previous schemes, which are based on the systems in the microscope scale, the present scheme is based on atomic ensembles in the mesoscopic scale. Besides the common merits of nonadiabatic holonomic quantum computation such as the robustness and the speediness, the Rydberg-superatom-based scheme has the following particular merits: the long coherence time of Rydberg states and the operability of the mesoscopic systems.
Nonadiabatic holonomic gates provide an effective means to perform high-speed and error-resilient manipulation of quantum states. It is practically important to realize nonadiabatic holonomic multiqubit controlled gates since multiqubit controlled gates are widely used in quantum information processing. Rydberg atoms are an appealing physical system for the realization of nonadiabatic holonomic multiqubit controlled gates as the Rydberg-mediated interaction is beneficial to couple two qubits. In this paper, we put forward a scheme for the realization of nonadiabatic holonomic multiqubit controlled gates based on Rydberg atoms, where an (n+1)-qubit controlled-$(\mathrm{n}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbf{\ensuremath{\sigma}})$ gate can be realized by $(2n\ensuremath{-}1)$ basic operations. Moreover, the effective coupling between two qubits is in the first-order strength of Rabi frequencies, which allows for the implementation of quantum gates within a short duration.
Quantum computation is much more effective than classical computation in solving many problems such as factoring large integers and searching unsorted databases. However, such effectiveness relies on the ability to perform universal high-fidelity quantum gates. One main challenge in achieving such high-fidelity gates is to reduce control errors of a quantum system. To overcome this problem, various proposals of fault-tolerant quantum computation are proposed. A promising one of such proposals is nonadiabatic holonomic quantum computation. Nonadiabatic holonomic quantum computation is realized by using a quantum system with a subspace satisfying both the cyclic evolution and parallel transport conditions. For an N dimensional quantum system with Hamiltonian H(t) and evolution operator U(t)=Texp[−i∫0tH(t')dt'] , if there exists a time-dependent L dimensional subspace S(t) spanned by the orthonormal vectors {|ϕk(t)〉=U(t)|ϕk(0)〉}k=1L that satisfy the two conditions: (1) ∑k=1L|ϕk(τ)〉〈ϕk(τ)|= ∑k=1L|ϕk(0)〉〈ϕk(0)| , with τ being the evolution period, and (2) 〈ϕk(t)|H(t)|ϕl(t)〉=0, k,l=1,2,⋯,L, then the unitary transformation U(τ) is a holonomic gate on the L dimensional subspace S(0) spanned by {|ϕk(0)〉}k=1L . The work of realizing nonadiabatic holonomic gate is to build a physical system with a Hamiltonian satisfying both the cyclic evolution condition and the parallel transport condition. Nonadiabatic holonomic quantum computation is based on nonadiabatic non-Abelian geometric phases. Since nonadiabatic non-Abelian geometric phases are only dependent on evolution paths but independent of evolution details, nonadiabatic holonomic gates are robust against control errors. Besides, nonadiabatic holonomic gates do not require the long run-time evolution that is necessary for adiabatic holonomic gates. Due to the merits of both robustness against control errors and high-speed realization, nonadiabatic holonomic quantum computation has received increasing attention in theory and experiment. Various schemes of nonadiabatic holonomic quantum computation have been proposed based on different physical systems, and a number of these schemes have been experimentally demonstrated with nuclear magnetic resonance systems, nitrogen-vacancy center systems, and superconducting systems. The progress of nonadiabatic holonomic quantum computation is also reflected in the improvement of the methods of designing quantum gates. The single-shot scheme, single-loop multiple-pulse scheme and composite gate scheme of nonadiabatic quantum gate are based on the improved methods. In particular, the single-shot scheme simplifies the operation of the one-qubit gate, so that the operation of any one-qubit gate, which needs to be realized by combining two non-commuting π-rotation gate in the original scheme, can be simply realized by a single-shot operation. In this paper, we propose a scheme of nonadiabatic holonomic quantum computation with atom-cavity system. The universal set of quantum gates in our scheme consists of an arbitrary one-qubit nonadiabatic holonomic gate and a two-qubit nonadiabatic holonomic controlled-PHASE gate. To realize the arbitrary one-qubit gate, we use two resonant laser pulses and an off-resonant laser pulse to drive a single four-level atom. With the aid of Stark shifts, the one-qubit gate can be performed in one-step only by changing the Rabi frequencies and the phases of the laser pulses. To realize the two-qubit controlled-PHASE gate, we use two off-resonant laser pulses to drive the two four-level atoms in the cavity. The transitions between the two-atom ground state and the two-atom auxiliary state is facilitated by exchanging virtual photons through a common cavity mode. In this process, the effective two-atom transition is disentangled from the cavity mode and therefore the two-qubit gate is insensitive to the cavity decay.
Abstract We propose a scheme for realizing nonadiabatic holonomic quantum computation within a decoherence-free subspace using Rydberg atoms. By employing large-detuned lasers and the Rydberg antiblockade condition, we construct an effective Hamiltonian that couples logical states in a three-atom decoherence-free subspace while ensuring that the Rydberg states remain unpopulated. This approach significantly suppresses decoherence caused by atomic spontaneous emission and mitigates the mechanical effects and sensitivity to interatomic distance variations associated with Rydberg excitations. We demonstrate the realization of both conventional and single-loop single-logical-qubit holonomic gates with high fidelity. Furthermore, by utilizing an asymmetric encoding method, in which the control logical qubits employ Rydberg-state encoding to provide the required conditional blockade, we extend the scheme to construct universal two- and three-logical-qubit holonomic gates, offering a robust and scalable approach for quantum information processing.
Nonadiabatic holonomic quantum computation in decoherence-free subspaces has attracted increasing attention recently, as it allows for high-speed implementation and combines both the robustness of holonomic gates and the coherence stabilization of decoherence-free subspaces. Since the first protocol of nonadiabatic holonomic quantum computation in decoherence-free subspaces, a number of schemes for its physical implementation have been put forward. However, all previous schemes require two noncommuting gates to realize an arbitrary one-qubit gate, which doubles the exposure time of gates to error sources as well as the resource expenditure. In this paper, we propose an alternative protocol for nonadiabatic holonomic quantum computation in decoherence-free subspaces, in which an arbitrary one-qubit gate in decoherence-free subspaces is realized by a single-shot implementation. The present protocol not only maintains the merits of the original protocol but also avoids the extra work of combining two gates to implement an arbitrary one-qubit gate and thereby reduces the exposure time to various error sources.
We propose a nonadiabatic non-Abelian geometric quantum operation scheme to realize universal quantum computation with mesoscopic Rydberg atoms. A single control atom entangles a mesoscopic ensemble of target atoms through long-range interactions between Rydberg states. We demonstrate theoretically that both the single-qubit and two-qubit quantum gates can achieve high fidelities around or above 99.9 in ideal situations. Besides, to address the experimental issue of Rabi frequency fluctuation (Rabi error) in Rydberg atom and ensemble, we apply the dynamical-invariant-based zero systematic-error sensitivity (ZSS) optimal control theory to the proposed scheme. Our numerical simulations show that the average fidelity could be 99.98 for single ensemble qubit gate and 99.94 for two-qubit gate even when the Rabi frequency of the gate laser acquires 10 fluctuations. We also find that the optimized scheme can also reduce errors caused by higher order perturbation terms in deriving the Hamiltonian of the ensemble atoms. To address the experimental issue of decoherence error between the ground state and Rydberg levels in Rydberg ensemble, we introduce a dispersive coupling regime between Rydberg and ground levels, based on which the Rydberg state is adiabatically discarded. The numerical simulation demonstrate that the quantum gate is enhanced. By combining strong Rydberg atom interactions, nonadiabatic geometric quantum computation, dynamical invariant and optimal control theory together, our scheme shows another route to construct fast and robust quantum gates with mesoscopic atomic ensembles. Our study contributes to the ongoing effort in developing quantum information processing with Rydberg atoms trapped in optical lattices or tweezer arrays.
Nonadiabatic holonomic quantum computation, focusing mainly on implementing universal single- and two-qubit gates, commonly suffers gate fidelity losses inevitably due to the presence of systematic errors. Here we propose to realize fast holonomic multiqubit controlled~(CN-NOT) Rydberg atom gates. Uniquely, the gate time is independent of the control qubit number N. We show that the fast gate is largely immune to laser parameter fluctuations and motional dephasing. The high tolerance of systematic errors can be further enhanced through optimal pulse engineering. The proposed protocol is intrinsically different from typical schemes based on Rydberg blockade or antiblockade, and moreover can be implemented alternatively with superconducting circuits. Our study paves a new way to build robust multiqubit gates with Rydberg atoms trapped in optical arrays or superconducting circuits, and hence contributes to current efforts in developing scalable quantum computation with trapped atoms and fabricable superdonducting devices.