Control Framework for Distance-and Configuration-Selective NeutralAtom Gates: The Symmetric Folding Principle, Spectrally Programmed Spin Propagators and Applications to Neutral-Atom Arrays
We develop a constructive control framework for distance-and configuration-selective operations in neutral-atom arrays. The starting point is the symmetric folding principle, which reformulates propagator synthesis as a structured state-or fiber-steering problem followed by a symmetry-prescribed folded continuation of the control sequence. We specialize this principle to spectrally programmed (SU(2)) spin propagators whose action is prescribed as a function of the spectral detuning. For a driven target atom coupled to an undriven controller, the Rydberg interaction decomposes the two-atom Hamiltonian into invariant target subspaces with effective detunings (∆) and (∆ -V (ρ)). Interatomic distance is thereby converted into a spectral control parameter. Distance-selective gates can consequently be formulated as passband/stopband designs in which a chosen target rotation is produced over a prescribed distance range and the identity is produced over a separated stopband, with a finite transition region. The framework extends to one driven target and multiple conserved controller configurations, provided that the corresponding effective spectral detunings remain distinguishable.
We develop a constructive control framework for distance-and configuration-selective operations in neutral-atom arrays. The starting point is the symmetric folding principle, which reformulates propagator synthesis as a structured state-or fiber-steering problem followed by a symmetry-prescribed folded continuation of the control sequence. We specialize this principle to spectrally programmed (SU(2)) spin propagators whose action is prescribed as a function of the spectral detuning. For a driven target atom coupled to an undriven controller, the Rydberg interaction decomposes the two-atom Hamiltonian into invariant target subspaces with effective detunings (∆) and (∆ -V (ρ)). Interatomic distance is thereby converted into a spectral control parameter. Distance-selective gates can consequently be formulated as passband/stopband designs in which a chosen target rotation is produced over a prescribed distance range and the identity is produced over a separated stopband, with a finite transition region. The framework extends to one driven target and multiple conserved controller configurations, provided that the corresponding effective spectral detunings remain distinguishable.
Many quantum hardware platforms natively support either phase or exchange operations, yet converting between these two forms of control typically incurs substantial overhead. Rydberg-blockade neutral-atom arrays are highly developed for phase control, while controlled exchange is usually obtained only through depth-intensive decompositions. Here, controlled exchange is realized as a native, blockade-programmed phenomenon in a collective excited manifold. Target atoms are engineered such that two competing exchange pathways between |01> and |10> destructively interfere, while a single collective four-photon channel mediated by a symmetric Rydberg excitation remains resonant and drives a direct SWAP, with all other qubit configurations undergoing an identity action. Exchange conditionality follows from blockade: exciting a control atom to a Rydberg state shifts and blocks the target collective resonance, suppressing exchange, whereas leaving the control in the ground manifold enables exchange in a single step. Anisotropic control-target interactions give rise to selective blockade, enabling coherent programmability of exchange among specific target pairs. This yields a family of controlled-SWAP primitives with process fidelities above 99% and an order-of-magnitude reduction in circuit depth and Rydberg-state exposure time compared with decomposed implementations. The same principle generalizes to multi-control and multiplexed controlled-exchange operations, providing compact hardware-level primitives for conditional information routing in extended neutral-atom arrays. More broadly, engineering interaction-tuned near-degeneracies in collective manifolds offers a route to programmable non-diagonal multiqubit operations across quantum platforms.
Abstract Neutral atom arrays are particularly promising for large-scale quantum computing because it is possible to prepare large-scale qubit arrays. An unsolved issue is how to selectively excite one qubit deep in a 3D atomic array to Rydberg states. In this work, we show two methods for this purpose. The first method relies on a well-known result: in a dipole transition between two quantum states driven by two off-resonant fields of equal strength but opposite detunings ±Δ, the transition is characterized by two counter-rotating Rabi frequencies Ω e ± i Δ t (or ± Ω e ± i Δ t if the two fields have a π -phase difference). This pair of detuned fields lead to a time-dependent Rabi frequency 2 Ω cos ( Δ t ) (or 2 i Ω sin ( Δ t ) ), so that a full transition between the two levels is recovered. We show that when the two detuned fields are sent in different directions, one atom in a 3D optical lattice can be selectively addressed for Rydberg excitation, and when its state is restored, the state of any nontarget atoms irradiated in the light path is also restored. Moreover, we find that the Rydberg excitation by this method can significantly suppress the fundamental blockade error of a Rydberg gate, paving the way for a high-fidelity entangling gate with a commonly used quasi-rectangular pulse that is easily obtained by pulse pickers. Along the way, we find a second method for single-site Rydberg addressing in 3D, where a selected target atom can be excited to the Rydberg state while preserving the state of any nontarget atom due to a spin-echo sequence. The capability to selectively address a target atom in 3D atomic arrays for Rydberg excitation makes it possible to design a large-scale neutral-atom information processor based on the Rydberg blockade.
Rydberg-based two-qubit gate fidelities in neutral atom arrays are limited chiefly by laser intensity inhomogeneity and by detuning errors from frequency miscalibration, background-field drift, intermediate state light shift and Doppler shifts. Quantum optimal control can suppress the former, but no pulse can render a controlled-Z gate first-order insensitive to detuning. Here we show that this obstruction can be circumvented by designing Rydberg gate pulses with every leading-order detuning error relegated to single-qubit Z-rotations, which an echoed sequence removes. The resulting maximally-entangling ZZ gate has no leading-order response to arbitrary detunings on either atom, maintaining an infidelity below 10−3 within a much wider range of single-atom detunings than the time-optimal gates. We further show that a large fraction of residual error is dominated by population outside the computational subspace, which can be converted into heralded erasures. Our results significantly reduce the requirements on laser frequency stability and intensity homogeneity, field calibration and atomic temperature toward practical fault-tolerant quantum computing with neutral atoms.
Neutral atoms are promising for large-scale quantum computing, but accurate neutral-atom entanglement depends on large Rydberg interactions which strongly limit the interatomic distances. Via a phase accumulation in detuned Rabi cycles enabled by a Rydberg interaction of similar magnitude to the Rydberg Rabi frequency, we study a controlled-phase gate with an arbitrary phase and extend it to the controlled-not gate. The gates need only three steps for coupling one Rydberg state, depend on an easily accessible van der Waals interaction that naturally arises between distant atoms, and have no rotation error in the weak interaction regime. Importantly, they can work with very weak interactions so that well-separated qubits can be entangled. The gates are sensitive to the irremovable fluctuation of Rydberg interactions, but can still have a fidelity over 98% with realistic position fluctuation of qubits separated over 20 $\ensuremath{\mu}\mathrm{m}$.
Multitarget gates offer the potential to reduce gate depth in syndrome extraction for quantum error correction. Although neutral-atom quantum computers have demonstrated native multiqubit gates, existing approaches that avoid additional control or multiple atomic species have been limited to single-target gates. We propose single-control multitarget C ( Z ⊗ N ) gates on a single-species neutral-atom platform that requires no extra control and has gate durations comparable to standard C Z gates. Our approach leverages tailored interatomic distances to create an asymmetric blockade between the control and target atoms. Using a graphics processing unit-accelerated pulse synthesis protocol, we design smooth control pulses for C Z Z and C Z Z Z gates, achieving fidelities of up to 99.55 % and 99.24 % , respectively, even in the presence of simulated atom-placement errors and Rydberg-state decay. Our approach is most effective for N = 2 ( C Z Z ) and N = 3 targets ( C Z Z Z ) ; for larger , increasing spatial crowding of the targets introduces significant challenges for maintaining the required blockade asymmetry. This work presents a practical path to implementing low-overhead multitarget gates in single-species neutral-atom systems, significantly reducing the resource overhead for syndrome extraction. To motivate the impact of these gates, we apply a greedy scheduling algorithm and we demonstrate that our proposed gates can reduce the number of atom reconfiguration costs by up to 50% for color code syndrome extraction of code distances greater than 5.
We introduce a novel method to engineer sharply peaked, distance-selective interactions between neutral atoms by exploiting interaction-induced resonances within a resonantly driven Rydberg ladder system. By tuning laser parameters, a subsystem eigenstate twist rapidly and brought into degeneracy with the atomic ground state at precisely defined interatomic separations, resulting in an effective potential sharply localized around this resonance distance. Unlike previous off-resonant macrodimer-based schemes, our approach significantly enhances interaction sharpness and strength, reaching MHz scales, and provides straightforward experimental tunability without requiring sub-wavelength positional control. Analytic expressions, validated through comprehensive master-equation simulations, detail the interaction profile's amplitude, width, and resonant distance. This precise control facilitates parallel entangling gates crucial for measurement-based quantum computing and enables simulation of complex lattice Hamiltonians with customizable connectivity. Additionally, our scheme opens possibilities for novel studies in molecular physics through micrometer-scale bond-length diatomic molecules.