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arXiv:2608.30631

Deterministic Universal Logical Gates for Finite-Energy GKP Qubits in Trapped Neutral Atoms

Alok Kumar, Aaron N. Raja, Diksha Thapliyal, Ishitwa Kumar Das, Ajay Wasan1

quant-phSubmitted Aug 31, 2026• Announced Sep 1, 2026• 0 citations
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Abstract

We present a universal logical gate set for finite-energy Gottesman-Kitaev-Preskill (GKP) qubits encoded in the harmonic motional states of trapped neutral atoms. Internal electronic states serve as ancilla for implementing state-dependent conditional displacements in phase space, enabling arbitrary single-qubit phase gates. A Transient Rydberg excitation-mediated atomic dipole-dipole interaction enables a controlled-Z gate without invoking the blockade mechanism. The gates operate under magic-trapping conditions, allowing continuous trapping throughout the gate sequence, thereby preserving the motional encoding without intermediate measurement or feedforward. We assess the experimental feasibility of the proposed protocols using neutral $^{88}\mathrm{Sr}$ atoms and obtain average gate fidelities of $0.986$ for single-qubit phase gates and $0.985$ for the controlled-Z gate at a finite squeezing parameter of $Δ=0.25$ (12 dB of squeezing), increasing to $0.997$ and $0.995$ respectively as $Δ$ reaches $0.1$. These results provide a route toward universal, measurement-free logical control of motional GKP qubits in neutral-atom architectures.

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We present a universal logical gate set for finite-energy Gottesman-Kitaev-Preskill (GKP) qubits encoded in the harmonic motional states of trapped neutral atoms. Internal electronic states serve as ancilla for implementing state-dependent conditional displacements in phase space, enabling arbitrary single-qubit phase gates. A Transient Rydberg excitation-mediated atomic dipole-dipole interaction enables a controlled-Z gate without invoking the blockade mechanism. The gates operate under magic-trapping conditions, allowing continuous trapping throughout the gate sequence, thereby preserving the motional encoding without intermediate measurement or feedforward. We assess the experimental feasibility of the proposed protocols using neutral 88Sr^{88}\mathrm{Sr}88Sr atoms and obtain average gate fidelities of 0.9860.9860.986 for single-qubit phase gates and 0.9850.9850.985 for the controlled-Z gate at a finite squeezing parameter of Δ=0.25Δ=0.25Δ=0.25 (12 dB of squeezing), increasing to 0.9970.9970.997 and 0.9950.9950.995 respectively as ΔΔΔ reaches 0.10.10.1. These results provide a route toward universal, measurement-free logical control of motional GKP qubits in neutral-atom architectures.
Bosonic quantum error correction codes encode logical qubits in the Hilbert space of one or multiple harmonic oscillators. A prominent class of bosonic codes is that of Gottesman-Kitaev-Preskill (GKP) codes of which implementations have been demonstrated with trapped ions and microwave cavities. In this paper, we investigate theoretically the preparation and error correction of a GKP qubit in a vibrational mode of a neutral atom stored in an optical dipole trap. This platform has recently shown remarkable progress in simultaneously controlling the motional and electronic degrees of freedom of trapped atoms. The protocols we develop make use of motional states and, additionally, internal electronic states of the trapped atom to serve as an ancilla qubit. We compare optical tweezer arrays and optical lattices and find that the latter provide more flexible control over the confinement in the out-of-plane direction, which can be utilized to optimize the conditions for the implementation of GKP codes. Concretely, the different frequency scales that the harmonic oscillators in the axial and radial lattice directions exhibit and a small oscillator anharmonicity prove to be beneficial for robust encodings of GKP states. Finally, we underpin the experimental feasibility of the proposed protocols by numerically simulating the preparation of GKP qubits in an optical lattice with realistic parameters.
The realisation of a universal quantum computer at scale promises to deliver a paradigm shift in information processing, providing the capability to solve problems that are intractable with conventional computers. A key limiting factor of realising fault-tolerant quantum information processing (QIP) is the large ratio of physical-to-logical qubits that outstrip device sizes available in the near future. An alternative approach proposed by Gottesman, Kitaev, and Preskill (GKP) encodes a single logical qubit into a single harmonic oscillator, alleviating this hardware overhead in exchange for a more complex encoding. Owing to this complexity, current experiments with GKP codes have been limited to single-qubit encodings and operations. Here, we report on the experimental demonstration of a universal gate set for the GKP code, which includes single-qubit gates and -- for the first time -- a two-qubit entangling gate between logical code words. Our scheme deterministically implements energy-preserving quantum gates on finite-energy GKP states encoded in the mechanical motion of a trapped ion. This is achieved by a novel optimal control strategy that dynamically modulates an interaction between the ion's spin and motion. We demonstrate single-qubit gates with a logical process fidelity as high as 0.960 and a two-qubit entangling gate with a logical process fidelity of 0.680. We also directly create a GKP Bell state from the oscillators' ground states in a single step with a logical state fidelity of 0.842. The overall scheme is compatible with existing hardware architectures, highlighting the opportunity to leverage optimal control strategies as a key accelerant towards fault tolerance.
Abstract Conventional approaches towards creating a large-scale, fault-tolerant quantum computer require an error correction scheme that uses multiple physical qubits to encode one logical qubit of protected quantum information. A key limiting factor in realizing error-corrected quantum information processing is the large ratio of physical-to-logical qubits required by many error correction codes, outstripping the size of near-term devices. The Gottesman–Kitaev–Preskill (GKP) code offers hardware efficiency at the cost of increased encoding complexity by encoding a logical qubit into a single quantum harmonic oscillator. Building on earlier demonstrations of GKP-encoded operations, we realize an entangling gate on GKP logical qubits. Our experiments use an optimal control strategy that deterministically implements a universal set of energy-preserving logical gates on finite-energy GKP states encoded in the mechanical motions of a trapped ion. We also directly generate a GKP Bell state starting from vacuum. Our approach is compatible with existing hardware architectures, demonstrating the potential for optimal control techniques with advanced encoding schemes to accelerate the path towards large-scale fault-tolerant quantum information processing.
Bosonic quantum error correction codes encode logical qubits in the Hilbert space of one or multiple harmonic oscillators. A prominent class of bosonic codes is that of Gottesman-Kitaev-Preskill (GKP) codes of which implementations have been demonstrated with trapped ions and microwave cavities. In this paper, we investigate theoretically the preparation and error correction of a GKP qubit in a vibrational mode of a neutral atom stored in an optical dipole trap. This platform has recently shown remarkable progress in simultaneously controlling the motional and electronic degrees of freedom of trapped atoms. The protocols we develop make use of motional states and, additionally, internal electronic states of the trapped atom to serve as an ancilla qubit. We compare optical tweezer arrays and optical lattices and find that the latter provide more flexible control over the confinement in the out-of-plane direction, which can be utilized to optimize the conditions for the implementation of GKP codes. Concretely, the different frequency scales that the harmonic oscillators in the axial and radial lattice directions exhibit and a small oscillator anharmonicity prove to be beneficial for robust encodings of GKP states. Finally, we underpin the experimental feasibility of the proposed protocols by numerically simulating the preparation of GKP qubits in an optical lattice with realistic parameters.
We demonstrate a method for encoding Gottesman–Kitaev–Preskill (GKP) error-correcting qubits with single ultracold atoms trapped in individual sites of a deep optical lattice. Using quantum optimal control protocols, we demonstrate the generation of GKP qubit states with 10 dB squeezing, which is the current minimum allowable squeezing level for use in surface code error correction. States are encoded in the vibrational levels of the individual lattice sites and generated via phase modulation of the lattice potential. Finally, we provide a feasible experimental protocol for the realization of these states. Our protocol opens up possibilities for generating large arrays of atomic GKP states for continuous-variable quantum information.
We demonstrate a method for encoding Gottesman-Kitaev-Preskill (GKP) error-correcting qubits with single ultracold atoms trapped in individual sites of a deep optical lattice. Using quantum optimal control protocols, we demonstrate the generation of GKP qubit states with 10 dB squeezing, which is the current minimum allowable squeezing level for use in surface code error correction. States are encoded in the vibrational levels of the individual lattice sites and generated via phase modulation of the lattice potential. Finally, we provide a feasible experimental protocol for the realization of these states. Our protocol opens up possibilities for generating large arrays of atomic GKP states for continuous-variable quantum information.