Velocity-Enabled Quantum Computing with Neutral Atoms

Abstract

Realizing error-corrected logical qubits is a central goal for the current development of digital quantum computers. Neutral atoms offer the opportunity to coherently shuttle atoms for realizing efficient quantum error correction based on long-range connectivity and parallel atom transport. Nevertheless, time overheads in shuttling atoms and complex control hardware pose challenges to scaling current architectures. Here, we introduce atom velocity as a new degree of freedom in neutral-atom architectures tailored to quantum error correction. Through controlled Doppler shifts, we demonstrate velocity-selective mid-circuit state preparation and measurement on moving atoms, leaving spectator atoms unaffected. Furthermore, we achieve on-the-fly local single-qubit rotations by mapping micron-scale atom displacements to the spatial phase of global control beams. Complementing these techniques with CZ entangling gates with a fidelity of 99.86(4)%, we experimentally implement key primitives for quantum error correction and measurement-based quantum computing. We generate an eight-qubit entangled cluster state with an average stabilizer value of 0.830(4), realize an [[4,2,2]] error-detection code with 99.0(3) % logical Bell-state fidelity, and perform stabilizer measurements using a flying ancilla. By enabling selective operations on continuously moving atoms using only global beams, this velocity-enabled architecture reduces hardware overhead while minimizing shuttling and transfer delays, opening a new pathway for fast, large-scale atom-based quantum computation.

Figures (8)

• Figure 1: Velocity-enabled architecture.a Building blocks for velocity-enabled control. Controlled Doppler shifts on moving atoms define velocity zones for storage, state-preparation, and measurement. Within each velocity zone, velocity-robust local single-qubit operations are performed via on-the-fly micron-scale atom displacements. Fly-by CZ gates between atoms moving at different velocities complete the set of operations that can be performed using continuously moving atoms at any velocity zone. b An architectural overview utilizing these building blocks, featuring velocity as a new degree of freedom. Spatially separated zones used in a standard zone-based architecture are replaced with spatially co-located velocity zones addressed by global beams with controlled detunings. On-the-fly single-qubit operations and fly-by CZ gates can be performed at any velocity zone, where spatial zones for two-qubit gates (blue shading) or single-qubit gates (red modulated zone) are still well-defined. To switch between zones, atoms are accelerated to the velocity addressed by the appropriately detuned global control beam. These concepts enable efficient realization of key primitives in measurement-based quantum computing and quantum error correction. c Measurement-based computation on an entangled cluster state requires local selective readout in various measurement bases. This can be achieved in our architecture through local basis rotations via atom displacement followed by velocity-selective readout on those already moving atoms. d For quantum error correction, syndrome measurements can be performed using a flying ancilla which is first selectively excited from the ground state to the qubit manifold, then being entangled with data qubits via fly-by CZ gates, and finally selectively measured without affecting the stationary data qubits. e Level structure of $^{88}\text{Sr}$ used in our experimental demonstration with the fine-structure qubit, showing the relevant transitions for state-preparation (red), measurement (blue), single-qubit control (dark red), Rydberg excitation (purple), and depumping (turquoise) used in state-resolved detection (SRD). Beam directions and further details are given in the SI SI. f Symmetric stabilizer state benchmarking (SSB) tsai2025benchmarking of CZ gates for static atoms with (orange) and without (blue) SRD.
• Figure 2: Velocity-selective state preparation and measurement.a Atoms are moved towards or away from a 698nm clock laser at different velocities. The ground state to $^{3}\text{P}_{0}$ resonance is shifted due to the Doppler effect (top) with the expected linear dependence on velocity (bottom). b Moving selected atoms at a constant velocity of 0.03ms and matching the clock-laser detuning to the Doppler-shifted atoms, Rabi oscillations are selectively performed on the moving atoms, with nearby stationary atoms remaining in the ground state. By performing a $\pi$-pulse, selective state preparation of moving atoms into the metastable qubit manifold is achieved. c A similar concept can be applied for velocity-selective readout, where moving atoms, initially in $^{3}\text{P}_{0}$, are transferred to the ground state. Then, they are measured via a fast mid-circuit image, leaving stationary atoms in the qubit manifold unaffected. The difference in $\pi$-times between b and c is a result of the different powers used for the 698nm clock laser. d Theoretical results for velocity selectivity on a single-qubit clock transition in strontium and ytterbium and on a Raman transition with counter-propagating beams in rubidium. An analytical curve of infidelity incurred on stationary qubits for a velocity-selective $\pi$-pulse is plotted as a function of the distance traveled by the moving atoms during the pulse (top). The infidelity is independent of Rabi frequency and decreases with the distance traveled. Zeroes corresponding to detunings where stationary atoms exhibit a $2\pi$-rotation are observed and attainable for sub-µm move distances. The required velocity of the moving atoms at the first zero infidelity point is plotted as a function of Rabi frequency (bottom). e An order of magnitude faster state preparation and readout can be achieved via a three-photon transition, driven by 679, 688, and 689nm beams. A spectroscopy measurement of stationary and moving atoms is shown for a fine-tuned velocity of 0.052ms in the direction of the 688nm beam, where stationary atoms are minimally affected. f A robust transfer of atoms into the ground state can also be achieved via dissipative two-photon coupling of both qubit states into $^{3}\text{P}_{1}$, where they decay and can be imaged via a fast image. Moving atoms (round points) are depumped, whereas stationary ones remain in their state (square points). This shows the potential of velocity selectivity for qubit-reset operations.
• Figure 3: Fast local rotations via on-the-fly displacement.a The phase acquired by a qubit displaced along the Raman beams' direction ($x$) is measured in a Ramsey sequence and shows a linear trend with the expected wavelength of the FS qubit. Moving along the perpendicular direction ($y$) shows no phase shift, as expected. The effective wavelength of the FS qubit is in an intermediate regime between optical and hyperfine qubits, allowing for convenient phase control using micron-scale displacements. b Local control over qubit rotation is demonstrated in an echo sequence. Different atoms are displaced by varying distances, showing the expected shift in the Ramsey signal. In the experiment, four stationary atoms were trapped in static traps, while two columns of four atoms each were trapped in movable AOD tweezers and displaced independently. c FS echo Ramsey measurement with static and moving atoms. Thanks to the reduced sensitivity to Doppler shifts and higher Rabi frequency of the FS qubit in comparison with optical qubits, the atoms do not need to stop during the gate operation. This is demonstrated by changing the timing of the last gate in an echo sequence with respect to the atom's movement, yielding a different phase as a function of its position at the time of the gate.
• Figure 4: Cluster-state generation.a Concept of using velocity selectivity and position-dependent phases for measurement-based quantum computing. Specific atoms (blue) out of a large reservoir array are moved towards an entangling zone and selectively excited into the qubit manifold. Entangling operations are used to generate a new cluster state or grow an existing one. Atom-specific measurement bases are realized according to the position of the atoms during a final single-qubit rotation. The atoms can then be selectively measured, re-cooled and recycled to repeat the process. b We experimentally demonstrate the basic building blocks of this quantum computing approach. Eight atoms are selectively excited into the qubit manifold with four stationary atoms remaining in the ground state (not shown). The eight atoms are entangled into a linear cluster state, with stabilizers $S_i = X_i \prod_{j \in \mathcal{N}(i)} Z_j$ which consist of a Pauli $X$ gate for each qubit and Pauli $Z$ gates for its neighbors $\mathcal{N}(i)$. c The stabilizers are measured with the help of local control through atom displacements. The local $R_j$ rotations consist of an echo sequence (Fig. \ref{['fig:3']}b), with atoms displaced during the $\pi$ pulse. We obtain average stabilizer expectation values of 0.830(4) and 0.694(4) with and without state-resolved detection, respectively. d Scanning the displacement of half the atoms, the measured expectation value oscillates, giving the stabilizer value at $\lambda_{FS}/8$ displacement.
• Figure 5: Entanglement between logical qubits.a We realize a $[[4,2,2]]$ error-detection code and prepare a logical Bell state, whose fidelity is lower bounded using measurements in the $X$ (dashed box) and $Z$ bases. A fault-tolerant generation of the logical Bell state using four qubits is performed with the help of local control by atom displacement. A logical fidelity of 99.0(3)% is observed after post-selecting on the parity of the result, significantly exceeding the fidelity of individual physical Bell states prepared on pairs of physical qubits in the same sequence (b). c A flying ancilla moving at a constant velocity is used to prepare the logical $\lvert 01 \rangle\xspace_L$ state of the $[[4,2,2]]$ code. The ancilla qubit is selectively excited into the qubit manifold, performs entangling operations with all data qubits using fly-by CZ gates, and is measured with a fast image following a selective three-photon transition into the ground state. Upon measurement of the ancilla qubit in the fast image, we identify the correct state of the $[[4,2,2]]$-code with a probability of 96(2)%.