An atomic boson sampler

The work addresses the challenge of scaling boson sampling beyond photonic platforms by using ultracold bosonic atoms. Boson sampling requires evolving an input Fock state of non-interacting bosons under a linear (single-particle) unitary and sampling the output occupations, a task believed to be classically intractable for sufficiently large systems. While photonic experiments have made important advances, controlling photon number, achieving low loss, and scalable verification remain difficult. Neutral atoms offer deterministic Fock-state preparation, reconfigurability, and high-fidelity detection in optical lattices. The research question is whether tools from neutral-atom platforms—optical tweezer rearrangement, rapid high-fidelity cooling, tunnel-coupled lattice evolution, and site-resolved imaging—can realize large-scale boson sampling with high indistinguishability, low loss, and programmatic control, and how to validate such experiments where full distribution verification is infeasible. The purpose is to demonstrate an atomic boson sampler with up to 180 atoms over ~1015 modes, quantify indistinguishability and dynamics, and provide tests that build confidence in many-body interference at scales challenging for classical simulation.

Prior boson sampling demonstrations have primarily used photonics, achieving increasing scale but often relying on probabilistic sources, postselection, or modified protocols such as scattershot and Gaussian boson sampling to mitigate losses and source challenges. While powerful, these approaches often require additional complexity-theory assumptions and are sensitive to loss that grows with circuit depth. Atomic platforms have a long history in quantum optics and have shown two-atom Hong–Ou–Mandel (HOM) interference and quantum walks, but large-scale many-atom, non-interacting interferometry with high state fidelity and fast cycle times has been limited by preparation speed and complexity. Quantum gas microscopes allow site-resolved preparation and detection in lattices, and optical tweezer arrays enable deterministic rearrangement and ground-state cooling of individual atoms. This work builds on: photonic boson sampling and Gaussian variants; demonstrations of atomic HOM and quantum walks; and recent tweezer-programmable lattice quantum walks, to realize fast, large-scale atomic boson sampling with validation strategies (HOM, bunching, clouding, generalized bunching) that are robust and scalable.

• Platform: Ultracold 88Sr atoms prepared in a 2D optical lattice with tunnel coupling enabling non-interacting quantum walks. Atoms are initially loaded into a 16×24 optical tweezer array with 50–75% random filling, implanted into the lattice, imaged, and then rearranged via programmable tweezers into target Fock states. Resolved sideband cooling on the 1S0→3P1 transition brings atoms to the 3D motional ground state.
• State preparation and detection: Site- and atom-resolved fluorescence imaging with typical per-site fidelity 99.8(1)%. Rearrangement success ~98% (up to 99.5%). Postselection on perfect rearrangement used for many measurements. Detection is parity-projected (light-assisted collisions) but experiments operate in regimes minimizing multi-occupancy; binning to 1D columns enables effective number resolution for the visible degree of freedom.
• Dynamics: Non-interacting single-particle Hamiltonian with nearest-neighbor tunneling J/h≈2×119 Hz and position-dependent potential V capturing lattice beam confinement; evolution U=exp(-iHt/ħ). Single-particle loss of 5.0(2)% arises from imperfect state preparation into higher in-plane bands; no additional evolution-time-dependent loss observed on millisecond scales.
• Distinguishability control: Hidden degrees of freedom (e.g., y-coordinate in a separable lattice, or time labels by combining separate runs) are used to tune visible distinguishability in 1D-binned quantum walks along x.
• Validation tests: • Two-atom HOM via 1D binning: measure coincidence ratios versus evolution time t, including near a balanced beamsplitter time t_HOM≈0.96 ms, using position labels (different y) or time labels to create distinguishable behavior. • Multi-atom bunching and clouding: quantify full bunching (all n in one site/column) and clouding (all n on same half-array) as functions of t and n. Use NN vs NNN inputs to vary sensitivity to interference. • Generalized bunching p_k: for larger 2D patterns, compute the probability all atoms appear within subsets κ of chosen size k (averaged over all κ), which is maximized by bosons. Account for parity projection and loss in analysis.
• Characterization of U: Two approaches: (i) spectroscopic calibration of lattice depths across the array to model U via band-structure calculations; (ii) direct maximum-likelihood (ML) inference of a submatrix M of U using one- and two-particle data to extract magnitudes (from single-particle walks) and relative phases (from two-particle interference), with constraints ensuring unitarity via a parameterized unitary completion.
• Simulations and statistics: Exact permanents for up to 3 particles (Glynn’s formula); Clifford–Clifford sparse sampling for larger n; models of partial distinguishability via thermal occupation of the axial (out-of-plane) mode; inclusion of calibrated single-particle loss and imaging errors; bootstrap-based confidence intervals; Monte Carlo estimators for distinguishable baselines; bias corrections for ratio estimators.
• Interactions: s-wave contact interactions estimated U_c/h≈−2π×1.7(7) Hz, ≪ J; exact simulations for 2–3 particles show negligible effect (≤10⁻⁴) on signals; inelastic three-body losses negligible on experimental timescales.

• Scale: Demonstrated boson sampling instances with up to 180 atoms distributed among 1015 lattice sites. In the central 15×15 region, U’s amplitude-squared distribution matches Porter–Thomas for ~385 outputs and phases are uniform, indicating near-Haar-like behavior locally.
• Indistinguishability: Two-atom HOM measurements yield a lower bound of 97.1±1.5% indistinguishability; with modeling of lattice non-idealities, estimate J=99.5±0.5%. Consistent results obtained without postselection and without relying on separability. Dominant distinguishability arises from imperfect axial (out-of-plane) cooling.
• Loss and detection: Single-particle loss measured at 5.0(2)% and independent of evolution time in the ms range; detection fidelity per site ~99.8(1)%. Imaging false negative P10≈0.002(1) (day-to-day ±0.002), false positive ~1e−5.
• Two- and few-body interference: 1D-binned quantum walks show clear HOM dips versus time and expected dependence on input spacing (NN vs NNN). Full bunching (n! enhancement for bosons) observed up to n=5; clouding signal measured up to n=8 at t=(n−1)·t_HOM, aligning with ideal boson predictions and distinct from distinguishable and partially distinguishable models.
• Characterization of U: ML-inferred submatrix (5×4 M) at t=1.46 ms agrees within statistical variation with spectroscopic model; method extracts magnitudes and relative phases from one- and two-particle data.
• Generalized bunching p_k: For n up to 36 and for n=180, measured p_k shows clear separation between bosonic and distinguishable behaviors, increasing with particle density n/m. Data consistent with low effective axial thermal occupation (⟨n_axial⟩≈0), inconsistent with higher temperatures (⟨n_axial⟩≥0.167).
• Large-scale partial distinguishability tests: By combining subsets of the 180-atom pattern with multiple time labels, gradually reduced interference is observed as labels increase; measured p_k and atom survival histograms agree with simulations once sufficiently distinguishable (e.g., 9 labels), supporting coherent many-body interference in the unlabeled (bosonic) case.
• Effective preparation success: Given calibrations, on an average run with 180 inputs, ~166 identical bosons are prepared, evolve, and are detected without errors; dominant deviation from ideal is the 5% single-particle loss from in-plane excitations.

The results demonstrate a neutral-atom platform achieving large-scale boson sampling with high indistinguishability, low and time-independent loss, and flexible input-state programmability. Targeted validation—HOM interference, bunching/clouding metrics, generalized bunching p_k, and direct submatrix characterization of U—collectively support that many-body interference consistent with bosonic statistics persists up to regimes that are classically hard to simulate. Compared with photonic platforms, the atomic approach benefits from deterministic Fock-state preparation, site-resolved detection, and lack of depth-dependent loss, enabling demonstrations with fewer assumptions about computational hardness. The identification and control of hidden degrees of freedom (e.g., axial motion, time labels) allow tunable distinguishability tests that qualitatively and quantitatively track expected trends, further supporting coherent dynamics. While global verification in this regime remains infeasible, the suite of tests and agreement with calibrated models build confidence that the device samples from a very large effective state space. The local near-Haar region suggests access to random-matrix-like statistics, though full Haar averaging over the entire lattice is limited by harmonic confinement. Accurate, scalable calibration or programming of U will be essential for future certifications and complexity-theoretic tests.

This work introduces an atomic boson sampler combining rapid, high-fidelity assembly of large Fock states via tweezer rearrangement, coherent non-interacting evolution in a tunnel-coupled lattice with low, time-independent loss, and high-fidelity site-resolved detection. It validates indistinguishability at the ~99.5% level, demonstrates many-body interference (bunching, clouding) up to eight atoms, characterizes submatrices of the unitary directly from one- and two-particle data, and probes generalized bunching up to 180 atoms with clear separation between bosonic and distinguishable behaviors. These capabilities, when extended with programmable local potentials, could enable Haar-averaged unitaries, stronger certifications of high-order interference, and studies of sampling complexity. Looking forward, combining these tools with controlled interactions opens routes to assembling and probing ground and excited states of Hubbard models, exploring complexity with interactions, and potentially enabling linear-optical universal quantum computing schemes through mid-circuit measurements and feedforward.

• Verification: Direct, full verification of output distributions at the demonstrated scales is infeasible; validation relies on targeted tests and calibrated models.
• Unitary family: Current dynamics arise from Hamiltonian evolution with harmonic confinement, yielding structured (not fully Haar-random) unitaries over the full lattice; only a central region is near-Haar. Efficient, scalable calibration/programming of large U remains challenging.
• Detection: Imaging is parity-projected and not inherently number resolving; mitigated via operating regimes and binning, but multi-occupancy events are not directly counted in 2D.
• Loss and preparation: A baseline single-particle loss of ~5% from in-plane excitations persists; rearrangement success ~98% introduces overhead without postselection. Although loss is time-independent on ms scales, longer evolutions could introduce additional losses.
• Hidden DOFs: Residual distinguishability primarily from axial motional excitations requires careful cooling; spatial inhomogeneities and drifts necessitate continuous calibration.
• Interactions: While negligible for reported signals, nonzero interactions can matter at high on-site occupancies or different regimes and require monitoring.