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arXiv:2307.06936 · Nature

An atomic boson sampler

Aaron W. Young, Shawn Geller, William J. Eckner, Nathan Schine, Scott Glancy, Emanuel H. Knill, Adam M. Kaufman

Published May 8, 2024• 40 citations
arXivHTMLPDF

Abstract

Abstract 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 ac- cording to programmable, non-interacting dynamics [1]. Here, we demonstrate a new combination of tools for implementing boson sampling using ultracold atoms in a two-dimensional, tunnel-coupled optical lattice. These tools include fast and programmable preparation of large ensembles of nearly identical bosonic atoms (99.5+0.5 −1.6% indistinguishability) by means of rearrangement with optical tweezers and high-fidelity optical cooling, propagation for variable evolution time in the lattice with low loss (5.0(2) %, independent of evolution time), and high fidelity detection of the atom positions after their evolution (typically 99.8(1) %). With this system, we study specific instances of boson sampling involving up to 180 atoms distributed among ∼ 1000 sites in the lattice. Direct verifi- cation of a given boson sampling distribution is not feasible in this regime. Instead, we introduce and perform targeted tests to determine the indistinguishability of the prepared atoms, to char- acterize the applied family of single particle unitaries, and to observe expected bunching features due to interference for a large range of atom numbers. When extended to interacting systems, our work demonstrates the core capabilities required to directly assemble ground and excited states in simulations of various Hubbard models [2, 3].

DOI
10.1038/s41586-024-07304-4

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Abstract 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 ac- cording to programmable, non-interacting dynamics [1]. Here, we demonstrate a new combination of tools for implementing boson sampling using ultracold atoms in a two-dimensional, tunnel-coupled optical lattice. These tools include fast and programmable preparation of large ensembles of nearly identical bosonic atoms (99.5+0.5 −1.6% indistinguishability) by means of rearrangement with optical tweezers and high-fidelity optical cooling, propagation for variable evolution time in the lattice with low loss (5.0(2) %, independent of evolution time), and high fidelity detection of the atom positions after their evolution (typically 99.8(1) %). With this system, we study specific instances of boson sampling involving up to 180 atoms distributed among ∼ 1000 sites in the lattice. Direct verifi- cation of a given boson sampling distribution is not feasible in this regime. Instead, we introduce and perform targeted tests to determine the indistinguishability of the prepared atoms, to char- acterize the applied family of single particle unitaries, and to observe expected bunching features due to interference for a large range of atom numbers. When extended to interacting systems, our work demonstrates the core capabilities required to directly assemble ground and excited states in simulations of various Hubbard models [2, 3].
Sampling from a quantum distribution can be exponentially hard for classical computers and yet could be performed efficiently by a noisy intermediate-scale quantum device. A prime example of a distribution that is hard to sample is given by the output states of a linear interferometer traversed by N identical boson particles. Here, we propose a scheme to implement such a boson-sampling machine with ultracold atoms in a polarization-synthesized optical lattice. We experimentally demonstrate the basic building block of such a machine by revealing the Hong-Ou-Mandel interference of two bosonic atoms in a four-mode interferometer. To estimate the sampling rate for large N , we develop a theoretical model based on a master equation that accounts for particle losses, but does not include technical errors. Our results show that atomic samplers have the potential to achieve a quantum advantage over today's best supercomputers with N ≳ 40 . Published by the American Physical Society 2024
Ultracold atoms in optical lattices can provide faithful analog realizations of the Hubbard model and many of its variants. Recently, these simulators have been augmented with improved programmable controls that enable new routes to state preparation, new kinds of dynamics, and, by extension, access to new observables. I will discuss two examples where such tools have enabled simulations that challenge classical numerical techniques: first, a sampling problem involving non-interacting bosons on a lattice that is closely related to boson sampling; and second, the preparation of low temperature equilibrium states of interacting spinful fermions on a lattice. These simulations have the potential to enhance our understanding of quantum many body physics, including practical problems of interest in material design relating to strongly correlated quantum materials. However, fully harnessing their capabilities in the regime where exact classical numerical simulations are absent requires new, precision probes of the relevant microscopic or thermodynamic quantities.
Experiments with ultracold atoms in optical lattices provide outstanding opportunities to realize exotic quantum states due to a high degree of tunability and control. In this thesis, I present experiments that extend this control from global parameters to the level of individual particles. \n\nUsing a quantum gas microscope for 87Rb, we have developed a single-site addressing scheme based on digital amplitude holograms. The system self-corrects for aberrations in the imaging setup and creates arbitrary beam profiles. We are thus able to shape optical potentials on the scale of single lattice sites and control the dynamics of individual atoms. \n\nWe study the role of quantum statistics and interactions in the Bose-Hubbard model on the fundamental level of two particles. Bosonic quantum statistics are apparent in the Hong-Ou-Mandel interference of massive particles, which we observe in tailored double-well potentials. These underlying statistics, in combination with tunable repulsive interactions, dominate the dynamics in single- and two-particle quantum walks. We observe highly coherent position-space Bloch oscillations, bosonic bunching in Hanbury Brown-Twiss interference and the fermionization of strongly interacting bosons.\n\nMany-body states of indistinguishable quantum particles are characterized by large-scale spatial entanglement, which is difficult to detect in itinerant systems. Here, we extend the concept of Hong-Ou-Mandel interference from individual particles to many-body states to directly quantify entanglement entropy. We perform collective measurements on two copies of a quantum state and detect entanglement entropy through many-body interference. We measure the second order Rényi entropy in small Bose-Hubbard systems and detect the buildup of spatial entanglement across the superfluid-insulator transition.\n\nOur experiments open new opportunities for the single-particle-resolved preparation and characterization of many-body quantum states.
Boson sampling is the task of producing samples from the number-basis distribution of many bosons traveling through a passive linear optical network. It is believed to be extremely difficult to accomplish classically, and has been the motivation for many "quantum advantage" demonstrations. Here we discuss the characterization tools that were developed to interpret the results of a boson sampling experiment performed at JILA, using atoms instead of photons. We measured the indistinguishability of the atoms using a Hong-Ou-Mandel style measurement, and found that it was 99.5−1.6+0.5%99.5^{+0.5}_{-1.6}\%99.5−1.6+0.5​%. We then showed that the indistinguishability of the atoms was a good predictor of the multiparticle bunching features, which in turn was a measure of multiparticle indistinguishability itself. To make this latter connection explicit, we introduce the weak generalized bunching conjecture and show it is equivalent to an existing mathematical conjecture. For the purpose of characterizing the dynamics that were present in the experiment, we discuss how to optimize the experimental design for inferring the single-particle unitary from Fock basis measurements. We showed that having very cold atoms was necessary to perform the inference of the dynamics in a reasonable amount of time. We then partially characterized the single particle unitary via direct measurements using one and two atoms, and compared our measurements to a separate characterization using a new statistic that describes the deviation between the two characterization methods while being insensitive to uninferable parameters.
Fermionic atoms in optical lattices provide a native implementation of Fermi-Hubbard (FH) models that can be used as analog quantum simulators of many-body fermionic systems. Recent experimental advances include the time-dependent local control of chemical potentials and tunnelings, and thus enable us to operate this platform digitally as a programmable quantum simulator. Here, we explore these opportunities and develop ground-state preparation algorithms for different fermionic models, based on the ability to implement both single-particle and many-body high-fidelity fermionic gates, as provided by the native FH Hamiltonian. In particular, we first design variational precompiled quantum circuits to prepare the ground state of the natively implemented FH model, with significant speedups relative to competing adiabatic protocols. Besides, the versatility of this variational approach enables us to target extended FH models, i.e., including terms that are not natively realized on the platform. As an illustration, we include next-nearest-neighbor tunnelings at finite dopings, relevant in the context of d -wave superconductivity. Furthermore, we discuss how to approximate the imaginary-time evolution using variational fermionic circuits, both as an alternative state-preparation strategy and as a subroutine for the quantum Lanczos algorithm to further improve the energy estimation. We benchmark our protocols for ladder geometries, though they can be readily applied to two-dimensional experimental setups to address regimes beyond the capabilities of current classical methods. These results pave the way for more efficient and comprehensive explorations of relevant many-body phases with existing programmable fermionic quantum simulators.
Progress in the reliable preparation, coherent propagation and efficient detection of many-body states has recently brought collective quantum phenomena of many identical particles into the spotlight. This tutorial introduces the physics of many-boson and many-fermion interference required for the description of current experiments and for the understanding of novel approaches to quantum computing. The field is motivated via the two-particle case, for which the uncorrelated, classical dynamics of distinguishable particles is compared to the quantum behaviour of identical bosons and fermions. Bunching of bosons is opposed to anti-bunching of fermions, while both species constitute equivalent sources of bipartite two-level entanglement. The realms of indistinguishable and distinguishable particles are connected by a monotonic transition, on a scale defined by the coherence length of the interfering particles. As we move to larger systems, any attempt to understand many particles via the two-particle paradigm fails: In contrast to two-particle bunching and anti-bunching, the very same signatures can be exhibited by bosons and fermions, and coherent effects dominate over statistical behaviour. The simulation of many-boson interference, termed Boson-Sampling, entails a qualitatively superior computational complexity when compared to fermions. The hierarchy between bosons and fermions also characterises multipartite entanglement generation, for which bosons again clearly outmatch fermions. Finally, the quantum-to-classical transition between many indistinguishable and many distinguishable particles features non-monotonic structures. While the same physical principles govern small and large systems, the deployment of the intrinsic complexity of collective many-body interference makes more particles behave differently.