An atomic boson sampler

Boson sampling, a restricted model of quantum computing, involves sampling from the distribution resulting from the interference of identical bosons under programmable, non-interacting dynamics. Classical simulation of this process is believed to be intractable for sufficiently large systems, motivating experimental demonstrations. Previous experiments using photons have faced challenges in generating and reliably evolving specific photon numbers with low loss, often employing probabilistic techniques or modifications to standard boson sampling. This research explores an alternative approach using ultracold bosonic atoms, which are more amenable to preparation in Fock states and offer advantages in terms of state preparation and control. The ability to efficiently sample from the probability distribution generated by a boson sampler is considered a significant milestone toward demonstrating quantum computational supremacy. The researchers aim to demonstrate large-scale boson sampling using ultracold atoms, addressing the challenges of state preparation, evolution under non-interacting dynamics, and high-fidelity detection.

The paper reviews previous boson sampling experiments, primarily focusing on photonic implementations. It highlights the challenges faced in photonic systems, such as the difficulty in generating and reliably evolving specific numbers of photons with low loss. The probabilistic nature of photon generation and the inherent loss in optical circuits have led to the use of postselection techniques or modifications to the standard boson sampling problem in several prior works. The researchers discuss alternative approaches employing ultracold atoms, referencing past demonstrations of two-atom interference and the potential of quantum gas microscopy for preparing and detecting large numbers of atoms in optical lattices. However, it also points out the limitations of existing atomic approaches, such as low state fidelities and long cycle times.

The experiment utilizes ultracold ⁸⁸Sr atoms in a two-dimensional tunnel-coupled optical lattice. State preparation involves loading a thermal cloud of atoms into an optical tweezer array, imaging the atoms, and rearranging them into desired patterns using optical tweezers. High-fidelity optical cooling is then employed to cool the atoms to their three-dimensional motional ground state. The atoms then evolve in the lattice under a single-particle Hamiltonian, which describes tunneling between adjacent lattice sites and a position-dependent potential. The evolution results in a quantum walk, and the final atom positions are measured using high-fidelity site-resolved imaging. The experiment incorporates several key techniques: fast and programmable atom preparation using optical tweezers (hundreds of milliseconds), low-loss propagation in the lattice (5.0(2)% loss, independent of evolution time), and high-fidelity atom position detection (~99.8(1)% per site). The indistinguishability of the atoms is a critical factor, so several tests are employed, including Hong-Ou-Mandel (HOM) interference experiments involving up to eight atoms. The single-particle unitary evolution is characterized using data from one and two-atom quantum walks and spectroscopic measurements. The researchers also introduce and perform tests to quantify bunching features for a range of atom numbers, providing evidence of bosonic behavior. The Hamiltonian evolution creates a quantum walk; the many-atom evolution is related to the permanent of a matrix derived from the single-particle unitary. The complexity of computing the permanent is a key element in the argument for the intractability of classical simulation of the process. Different methods of partitioning between visible and hidden degrees of freedom (DOFs) are used, allowing tests of indistinguishability using 1D quantum walks along one axis while treating the other axis as a hidden DOF. A maximum likelihood (ML) fit of the unitary is performed using one- and two-atom data for direct characterization of the unitary evolution. Generalized bunching probability is used to assess bosonic behavior in larger atom numbers, by assessing the probability of all atoms ending up in an arbitrary subset of sites.

The experiment achieves high fidelity in atom preparation, evolution, and detection. The measured indistinguishability of the atoms is 99.5±1.5%, which is high enough to observe the bunching behavior expected for bosons. The single-particle unitary is directly characterized using both one- and two-atom quantum walk data with the maximum likelihood (ML) procedure, confirming the effectiveness of this technique for unitary characterization. The results demonstrate a clear separation between the experimental observations for indistinguishable bosons and distinguishable particles in several tests, including bunching and clouding experiments with up to eight atoms. The generalized bunching probability, applied to larger atom numbers, shows a clear separation between bosonic and distinguishable behavior. The largest input patterns used in this work contain 180 atoms, with the output distribution spanning a 10^15 dimensional Hilbert space. While direct verification is impossible at this scale, the consistency of the results with the predictions for indistinguishable bosons supports the claim that the experiment indeed samples from this large state space. Simulations with partially distinguishable atoms, produced by combining experiments with different atom subsets, further validate the bosonic behavior of the system. By analyzing the generalized bunching probabilities, this study also reveals a lower limit for the thermal occupation of the out-of-plane motional DOFs.

The results address the research question by demonstrating the feasibility of large-scale boson sampling with ultracold atoms. The high fidelity of the experimental apparatus and the successful application of various tests of indistinguishability support the claim that the experiment is indeed sampling from a computationally hard problem. The results are significant as they represent a major advancement in boson sampling experiments. Unlike photonics experiments, the ultracold atom approach exhibits low loss that is independent of evolution time, enabling the study of boson sampling with fewer assumptions regarding the hardness of classical simulation. The development and application of multiple tests, including the generalized bunching technique, to characterize the system's performance, further increase the robustness of these results. The study demonstrates a significant improvement over previous boson sampling experiments in scalability and experimental capabilities, while also addressing the need for robust verification methods at large scales.

This work presents a novel approach to large-scale boson sampling using ultracold atoms and optical tweezers, achieving high fidelity in all stages of the experiment. The diverse tests performed confirm indistinguishability and bosonic behavior at a scale previously unreachable. Future research directions include using optical tweezers for flexible programmability of the unitary, performing high-fidelity mid-circuit measurements, and extending the techniques to explore interacting systems and Hubbard models for condensed matter physics simulations. Furthermore, improved unitary calibration techniques are needed to certify boson sampling in the many-particle regime.

Direct verification of boson sampling remains computationally infeasible for the system sizes studied. While various tests strongly suggest bosonic behavior, the absence of direct verification constitutes a limitation. The applied unitary is not Haar-random but rather has some additional structure that could, in principle, facilitate efficient classical simulation. While the observed low loss is independent of evolution time, this is limited by the current experimental duration, and it is anticipated that this will limit the scalability in the long term. The relatively slow dynamics of the system compared to the speed of current atomic measurement techniques limits the speed at which the experiment can be run.