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An atomic boson sampler


A boson sampler implements a restricted model of quantum computing. It is defined by the ability to sample from the distribution resulting from the interference of identical bosons propagating according to programmable, non-interacting dynamics1. An efficient exact classical simulation of boson sampling is not believed to exist, which has motivated ground-breaking boson sampling experiments in photonics with increasingly many photons2,3,4,5,6,7,8,9,10,11,12. However, it is difficult to generate and reliably evolve specific numbers of photons with low loss, and thus probabilistic techniques for postselection7 or marked changes to standard boson sampling10,11,12 are generally used. Here, we address the above challenges by implementing boson sampling using ultracold atoms13,14 in a two-dimensional, tunnel-coupled optical lattice. This demonstration is enabled by a previously unrealized combination of tools involving high-fidelity optical cooling and imaging of atoms in a lattice, as well as programmable control of those atoms using optical tweezers. When extended to interacting systems, our work demonstrates the core abilities required to directly assemble ground and excited states in simulations of various Hubbard models15,16.

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Fig. 1: Assembling Fock states of bosonic atoms in a tunnel-coupled optical lattice.
Fig. 2: Multiparticle quantum walks in one dimension.
Fig. 3: Characterizing the single-particle unitary.
Fig. 4: Interference of large bosonic Fock states.

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Data availability

Experimental data used in this work are available on Zenodo at (ref. 80).

Code availability

Codes used in this work are available on Zenodo at (ref. 80).


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We thank S. Aaronson, N. Darkwah Oppong, I. H. Deutsch, J. P. D’Incao, A. V. Gorshkov and K. Mølmer for their discussions on the original manuscript and N. Cerf, L. Novo and B. Seron for their discussions on recent advancements in generalized bunching. We further thank N. Darkwah Oppong, N. E. Frattini, L. R. Liu, K. Mølmer and S. Sun for close readings of the paper. This work includes contributions from the National Institute of Standards and Technology, which are not subject to US copyright. The use of trade, product and software names is for informational purposes only and does not imply endorsement or recommendation by the US government. This work was supported by the AFOSR (FA95501910079), ARO (W911NF1910223), the National Science Foundation Physics Frontier Center at JILA (1734006) and NIST. S. Geller acknowledges support from the Professional Research Experience Program (PREP) operated jointly by NIST and the University of Colorado.

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Authors and Affiliations



A.W.Y., W.J.E., N.S. and A.M.K. contributed to developing the experiments. A.W.Y. and S. Geller performed the analysis of the results. All authors contributed to interpreting the results and preparing the paper.

Corresponding authors

Correspondence to Aaron W. Young or Adam M. Kaufman.

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S. Glancy works as a consultant for Xanadu Quantum Technologies. All other authors declare no competing interests.

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Nature thanks Loïc Henriet and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Peer reviewer reports are available.

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Extended data figures and tables

Extended Data Fig. 1 State preparation.

a, Rearrangement of atoms (blue circles) in an optical lattice (grey circles denote sites in the lattice) using optical tweezers (green) must balance several conflicting requirements, leading to the multistep algorithm described in the Methods. b, To optically cool lattice-trapped atoms with high fidelity, we use a pulsed cooling sequence involving 0.4 ms axial cooling pulses, and 0.2 ms radial cooling pulses (timing diagram pictured in lower panel). We compute the expected average thermal occupation \(\bar{n}\) as a function of time in each of three nearly-orthogonal axes of a given site in the lattice via a master equation calculation, yielding reasonable agreement with measured values in the experiment. Note that we optimize for high-fidelity cooling of the axial direction at the cost of slightly worse cooling in the radial directions.

Extended Data Fig. 2 Properties of the single particle unitary.

a, b, The single particle unitary U is depicted here for an evolution time of t = 6.45 ms, as is relevant to the measurements in Fig. 4. The finite waist of the optical lattice beams and resulting harmonic confinement means that U does not appreciably couple all sites to each other, and thus is not Haar random. c, d, U exhibits features of a Haar random matrix when considering only a 15 × 15-site region near the center of the lattice. In this region, the distribution of the norm-square of the amplitudes in U are well-captured by the Porter-Thomas distribution for 385 outputs (black line in c). The distribution of the phases in U is well-captured by the uniform distribution (black line in d). e, We perform maximum likelihood inference of a submatrix of the single-particle unitary based on one- and two-particle data (see Fig. 3), and compare the point estimate to maximum likelihood estimates of bootstrap resamples of the data, and to the spectroscopic calibration (see Supplementary Information section VI). To quantify this comparison, we compute the one- and two-particle distributions generated by the inferred parameters, and compute the total variation distances (TVDs) of these distributions, then take the maximum of the TVDs over the prepared input patterns. We call this quantity the max TVD between two sets of distributions. The depicted histogram is the max TVD between the point estimate and the maximum likelihood estimates of the bootstrap resampled data. Shown also are the max TVD between the frequencies of the data (Freq.) and the point estimate (Pt.), and that between the point estimate and the spectroscopic model (Model). The bootstrap histogram gives a sense of the size of the statistical fluctuation of the max TVD between the point estimate and the truth. The max TVD between the spectroscopic model and the point estimate is large compared to the bulk of the histogram, which is the expected behavior because statistical fluctuations in the model add to the statistical fluctuations in the point estimate.

Extended Data Fig. 3 Three particle quantum walks in one dimension.

The output distributions resulting from three particle quantum walks at evolution times of a, 1.97 ms and b, 4.23 ms are in good agreement with theory. Similar to the two particle case, each three particle output can be uniquely labelled by the coordinates of the three particles (x1, x2, x3), with x3x2x1. The probability p of measuring an output state (x1, x2, x3) is indicated by both the size and color of the circle at the corresponding coordinates. The prepared input states are marked by the red disks, and include patterns with nearest-neighbor (NN) and next-nearest-neighbor (NNN) spacing. For NN input patterns, indistinguishable bosons (Indist.) exhibit enhanced probability to lie near the leading edge of the distribution along the main diagonal (x1 = x2 = x3) in comparison to distinguishable particles (Dist.). This tendency disappears for NNN input patterns. c, d, Like in the two particle case, we can coarse-grain the three particle distributions by measuring bunching and clouding, and find good agreement with theory as a function of evolution time. All theory predictions in this figure correspond to error-free preparations of atoms with the appropriate particle statistics.

Extended Data Fig. 4 Validation of two and three particle quantum walks in one dimension.

The full output distribution after binning for a, two and b, three particles initialized at nearest-neighbor spacing, at an evolution time of tHOM and 2tHOM respectively. The grey bars are theory for error-free state preparation, evolution, and detection with parity projection, and the black points are data. The upper row corresponds to distinguishable (Dist.) atoms, and the bottom row to unlabelled, nominally indistinguishable (Indist.), atoms. The outputs are grouped by the number of collisions (1, 2, or 3 atoms on the same site) that occur after binning, indicated by the inset cartoons.

Extended Data Table 1 Comparison of large-scale boson sampling demonstrations

Supplementary information

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Young, A.W., Geller, S., Eckner, W.J. et al. An atomic boson sampler. Nature 629, 311–316 (2024).

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