We propose a protocol to realize arbitrary state synthesis and unitary operations on a qudit encoded in the collective dressed states of a Rydberg-blockaded array of three-level atoms. This system is isomorphic to the Jaynes-Cummings model and acts as a multilevel Rydberg superatom whose nonlinear spectrum can be precisely controlled through the parameters of the laser driving the intermediate-to-Rydberg transition. Control of the qudit state is possible through pulse sequences of the laser driving the ground-to-intermediate transition. The dimension of the qudit Hilbert space is scalable by adjusting the number of atoms involved in the Rydberg-blockaded array. We estimate the fidelity of our protocol for realizing arbitrary unitaries and discuss the influence of the finite lifetime of the Rydberg state. Our work paves the way for processing quantum information with Rydberg blockaded arrays of atoms as an alternative to atom qubit arrays.
We propose a protocol to realize arbitrary state synthesis and unitary operations on a qudit encoded in the collective dressed states of a Rydberg-blockaded array of three-level atoms. This system is isomorphic to the Jaynes-Cummings model and acts as a multilevel Rydberg superatom whose nonlinear spectrum can be precisely controlled through the parameters of the laser driving the intermediate-to-Rydberg transition. Control of the qudit state is possible through pulse sequences of the laser driving the ground-to-intermediate transition. The dimension of the qudit Hilbert space is scalable by adjusting the number of atoms involved in the Rydberg-blockaded array. We estimate the fidelity of our protocol for realizing arbitrary unitaries and discuss the influence of the finite lifetime of the Rydberg state. Our work paves the way for processing quantum information with Rydberg blockaded arrays of atoms as an alternative to atom qubit arrays.
Quantum devices comprised of elementary components with more than two stable levels—so-called qudits—enrich the accessible Hilbert space, enabling applications ranging from fault-tolerant quantum computing to simulating complex many-body models. While several quantum platforms are built from local elements that are equipped with a rich spectrum of stable energy levels, schemes for the efficient control and entanglement of qudits are scarce. Importantly, no experimental demonstration of multiqudit control has been achieved to date in neutral atom arrays. Here, we propose a general scheme for controlling and entangling qudits and perform a full analysis for the case of qutrits, encoded in ground and metastable states of alkaline earth atoms. We find an efficient implementation of single-qudit gates via the simultaneous driving of multiple transition frequencies. For entangling operations, we provide a concrete and intuitive recipe for the controlled- Z ( C Z ) gate for any local dimension d , realized through alternating single qudit and entangling pulses that simultaneously drive up to two Rydberg transitions. We further prove that two simultaneous Rydberg tones are, in general, the minimum necessary for implementing the C Z gate with a global drive. The pulses we use are optimally controlled, smooth, and robust to realistic experimental imperfections, as we demonstrate using extensive noise simulations. This amounts to a minimal, resource-efficient, and practical protocol for realizing a universal set of gates. Our scheme for the native control of qudits in a neutral atom array provides a high-fidelity route toward qudit-based quantum computation, ready for implementation on near-term devices.
We develop a model for quantum computation with Rydberg atom arrays, which only relies on global driving, without the need of local addressing of the qubits: any circuit is executed by a sequence of global, resonant laser pulses on a static atomic arrangement. We present two constructions: for the first, the circuit is imprinted in the trap positions of the atoms and executed by the pulses; for the second, the atom arrangement is circuit-independent, and the algorithm is entirely encoded in the global driving sequence. Our results show in particular that a quadratic overhead in atom number is sufficient to eliminate the need for local control to realize a universal quantum processor. We give explicit protocols for all steps of an arbitrary quantum computation, and discuss strategies for error suppression specific to our model. Our scheme is based on dual-species processors with atoms subjected to Rydberg blockade constraints, but it might be transposed to other setups as well.
Owing to the long lifetime of Rydberg atom, easy to operate and easy to control the interaction between Rydberg atoms, Rydberg atom has attracted considerable attention in quantum information and quantum optics fields. Specially, the anti-blockade effect, as a physical resource, can be used to implement various tasks in quantum information processing. Based on the rigid dipole blockade, an ensemble of two-level Rydberg atoms trapped in three magneto-optical traps can be regarded as a superatom. Based on the superatom model, the in-phase and anti-phase dynamics of the three-body Rydberg superatoms are studied by adjusting the numbers of atoms, and the W state and two kinds of maximal entangled states are generated simultaneously. Our work has great potential applications in coherent manipulation and quantum information processing.The numerical simulations are performed based on the superatom model and thereby the formidable obstacle that the Hilbert space dimension grows exponentially with the particle number increasing can be completely removed. As a result, the quantum control and quantum entanglement can be achieved from the single-quanta level to the mesoscopic level.
Abstract Multi-qubit quantum gates are the most important building blocks for quantum computation. In this article, we propose a scheme for realizing the Toffoli gate in a linear neutral atom array. Two ground-state hyperfine levels of the atoms are considered as qubit states. Our method relies on the strong and long-range interactions between atoms due to Rydberg excitations and the occurrence of dark states in the target qubit, with both control and target qubits being individually addressed with laser pulses. Our gate protocol enables precise control over the quantum states of individual qubits, effectively suppressing undesirable transitions to ensure high-fidelity gate performance. We also implement two-atom Rydberg antiblockade mechanism to avoid any unwanted population blockage in the control atoms to get the best fidelity. At zero temperature, the gate fidelity is estimated to be about 99.16% for realistic laser power omitting the motional state of the atoms when the interatomic distance ( l ) 6.55 μ m. We construct a C n NOT gate with n > 2 in a 2D atomic array by exploiting the n -atom Rydberg antiblockade (RAB) mechanism, which allows n atoms within the blockade radius to be simultaneously excited to the Rydberg states. In particular, we simulate C 3 NOT gate with about 98.37 % fidelity. We further analyze the gate error by decreasing the interatomic distance and find that gate fidelity improves more rapidly for larger n with increased interaction potential. We find that more than 99 % fidelity can be achieved for C 3 NOT gate for l < 6.2 μ m, implying that our proposed scheme promising and reliable for multi-qubit controlled NOT gates. For a finite temperature ( ∼ 30 μ K), including the Doppler dephasing, we simulate our gates to achieve 98.90% and 98.54 % fidelity for the Toffoli gate and C 3
In any physical platform, two ingredients are essential for quantum information processing: single-qubit control, and entangling interactions between qubits. Neutral atoms can be individually controlled with high fidelity and are resilient to environmental noise, making them attractive candidates for implementing quantum information protocols. However, achieving strong interactions remains a major obstacle. One way to increase the interaction strength between neutral atoms is to excite them into high-lying Rydberg states, which exhibit large electric dipole moments (and by extension, strong electric dipole-dipole interactions). By slowly ramping up the Rydberg level coupling in a system, one can "dress'' the atomic ground states with some Rydberg character; this maps the Rydberg dipole interaction to an effective interaction between ground states. Such Rydberg-dressed interaction is the focus of this dissertation. After describing the physics of the Rydberg-dressed interaction, we propose three protocols that demonstrate its versatility and provide a framework for considering some of the details of realistic implementation. In all three cases, Rydberg dressing --- along with some form of single-atom control --- is used to generate highly entangled states of interest. Our first proposal relates to the adiabatic model of quantum computing, in which solutions to problems are encoded in the ground states of carefully engineered Hamiltonians. The Rydberg-dressed interaction can provide nonlinear Hamiltonian terms, allowing us to encode NP-hard and other interesting problems. We model this protocol in the presence of decoherence, and find that computational fidelities of ~0.98 for four atoms should be possible with currently realistic experimental parameters. Our second proposal is also related to quantum computing, this time in the circuit model. The Rydberg-dressed interaction can be used to generate a controlled-NOT logic gate which, when interwoven with single-qubit gates, can perform universal quantum computation. Experimentally, noise due to atomic thermal motion has been a primary limitation on the fidelities of these gates. We show that a Doppler-free setup, with counterpropagating lasers, effectively suppresses this type of noise, allowing simulated fidelities of up to ~0.998 per gate. Such strong suppression is only possible because the Doppler-free configuration can harness the natural robustness of adiabatic dressing; other gate schemes using, e.g., resonant pulses, do not exhibit the same degree of improvement. Finally, we consider exploiting the many-body character of the Rydberg-dressed interaction to generate collective entanglement in mesoscopic ensembles of neutral atoms. An atomic ensemble uniformly illuminated by a single Rydberg-exciting laser is isomorphic to the well-known Jaynes-Cummings model. In addition to adapting generic Jaynes-Cummings entanglement protocols developed in other platforms, one can apply microwaves to drive entanglement in a way that is unique to the atomic platform. We prove that by allowing the microwave phase to vary in time, one can generate arbitrary symmetric states of the ensemble. While this method compares favorably with other entanglement protocols in many ways, the required frequency of phase switching presents a fundamental limitation on its effectiveness. To mitigate this, we propose a variant scheme in which parameters are chosen to only allow excitations within the system's dressed-ground subspace; this effectively cuts phase switching demands in half. All three protocols serve to illustrate the power of the Rydberg-dressed interaction and suggest directions for future study.
We study the production of arbitrary superpositions of Dicke states via optimal control. We show that N atomic hyperfine qubits, interacting symmetrically via the Rydberg blockade, are well described by the Jaynes-Cummings Hamiltonian and fully controllable by phase-modulated microwaves driving Rydberg-dressed states. With currently feasible parameters, it is possible to generate states of ∼ten hyperfine qubits in ∼1 μs, assuming a fast microwave phase switching time. The same control can be achieved with a "dressed-ground control" scheme, which reduces the demands for fast phase switching at the expense of increased total control time.