Efficiently Extracting Multi-Point Correlations of a Floquet Thermalized System

Nonequilibrium dynamics of many-body systems is challenging for classical computing, providing opportunities for demonstrating practical quantum computational advantage with analogue quantum simulators. It is proposed to be classically intractable to sample driven thermalized many-body states of Bose-Hubbard systems, and further extract multi-point correlations for characterizing quantum phases. Here, leveraging dedicated precise manipulations and number-resolved detection through a quantum gas microscope, we implement and sample a 32-site driven Hubbard chain in the thermalized phase. Multi-point correlations of up to 14th-order extracted from experimental samples offer clear distinctions between the thermalized and many-body-localized phases. In terms of estimated computational powers, the quantum simulator is comparable to the fastest supercomputer with currently known best algorithms. Our work paves the way towards practical quantum advantage in simulating Floquet dynamics of many-body systems.

[1]  Y. Liu,et al.  Robust site-resolved addressing via dynamically tracking the phase of optical lattices , 2022, Optics Letters.

[2]  P. Zoller,et al.  Practical quantum advantage in quantum simulation , 2022, Nature.

[3]  Zhen-Sheng Yuan,et al.  A compact gain-enhanced microwave helical antenna for 87Rb atomic experiments. , 2022, The Review of scientific instruments.

[4]  Trevor Vincent,et al.  Quantum computational advantage with a programmable photonic processor , 2022, Nature.

[5]  M. Lukin,et al.  Peer Review File Manuscript Title: A quantum processor based on coherent transport of entangled atom arrays Reviewer Comments & Author Rebuttals , 2022 .

[6]  Haibin Zhang,et al.  Quantum computational advantage via 60-qubit 24-cycle random circuit sampling. , 2021, Science bulletin.

[7]  Hao Li,et al.  Phase-Programmable Gaussian Boson Sampling Using Stimulated Squeezed Light. , 2021, Physical review letters.

[8]  Haibin Zhang,et al.  Strong Quantum Computational Advantage Using a Superconducting Quantum Processor. , 2021, Physical review letters.

[9]  Julian F. Wienand,et al.  Programmable interactions and emergent geometry in an array of atom clouds , 2021, Nature.

[10]  Jian-Wei Pan,et al.  High-powered optical superlattice with robust phase stability for quantum gas microscopy. , 2021, Optics express.

[11]  M. Lukin,et al.  Controlling quantum many-body dynamics in driven Rydberg atom arrays , 2021, Science.

[12]  J. Tangpanitanon,et al.  Quantum supremacy and quantum phase transitions , 2020, 2012.06459.

[13]  Jian-Wei Pan,et al.  Quantum computational advantage using photons , 2020, Science.

[14]  E. Demler,et al.  Microscopic evolution of doped Mott insulators from polaronic metal to Fermi liquid , 2020, Science.

[15]  Zhen-Sheng Yuan,et al.  Generating two-dimensional quantum gases with high stability , 2020 .

[16]  J. Tangpanitanon,et al.  Quantum supremacy in driven quantum many-body systems. , 2020, 2002.11946.

[17]  T. Hsieh,et al.  Hamiltonian Tomography via Quantum Quench. , 2019, Physical review letters.

[18]  Alicia J. Kollár,et al.  Quantum Simulators: Architectures and Opportunities , 2019, 1912.06938.

[19]  John C. Platt,et al.  Quantum supremacy using a programmable superconducting processor , 2019, Nature.

[20]  Joel Nothman,et al.  SciPy 1.0-Fundamental Algorithms for Scientific Computing in Python , 2019, ArXiv.

[21]  Jian-Wei Pan,et al.  Cooling and entangling ultracold atoms in optical lattices , 2019, Science.

[22]  M. Rispoli,et al.  Quantum critical behaviour at the many-body localization transition , 2018, Nature.

[23]  Jian-Wei Pan,et al.  12-Photon Entanglement and Scalable Scattershot Boson Sampling with Optimal Entangled-Photon Pairs from Parametric Down-Conversion. , 2018, Physical review letters.

[24]  Eyal Bairey,et al.  Learning a Local Hamiltonian from Local Measurements. , 2018, Physical review letters.

[25]  Frank Pollmann,et al.  Efficient numerical simulations with Tensor Networks: Tensor Network Python (TeNPy) , 2018, SciPost Physics Lecture Notes.

[26]  M. Bukov,et al.  QuSpin: a Python package for dynamics and exact diagonalisation of quantum many body systems. Part II: bosons, fermions and higher spins , 2018, SciPost Physics.

[27]  Björn Dahlgren,et al.  pyodesys: Straightforward numerical integration of ODE systems from Python , 2018, J. Open Source Softw..

[28]  Jian-Wei Pan,et al.  Spin-dependent optical superlattice , 2017, 1708.07406.

[29]  J. Schmiedmayer,et al.  Experimental characterization of a quantum many-body system via higher-order correlations , 2015, Nature.

[30]  Christian Schneider,et al.  High-efficiency multiphoton boson sampling , 2017, Nature Photonics.

[31]  J. Rarity,et al.  Experimental quantum Hamiltonian learning , 2017, Nature Physics.

[32]  Hengyun Zhou,et al.  Observation of discrete time-crystalline order in a disordered dipolar many-body system , 2016, Nature.

[33]  P. W. Hess,et al.  Observation of a discrete time crystal , 2016, Nature.

[34]  Matthew Rispoli,et al.  Quantum thermalization through entanglement in an isolated many-body system , 2016, Science.

[35]  M. Rispoli,et al.  Measuring entanglement entropy in a quantum many-body system , 2015, Nature.

[36]  Ivan Oseledets,et al.  Unifying time evolution and optimization with matrix product states , 2014, 1408.5056.

[37]  Jakub Zakrzewski,et al.  Non-standard Hubbard models in optical lattices: a review , 2014, Reports on progress in physics. Physical Society.

[38]  A. Chandran,et al.  Periodically driven ergodic and many-body localized quantum systems , 2014, 1403.6480.

[39]  Roderich Moessner,et al.  Equilibrium states of generic quantum systems subject to periodic driving. , 2014, Physical review. E, Statistical, nonlinear, and soft matter physics.

[40]  J. O'Brien,et al.  On the experimental verification of quantum complexity in linear optics , 2013, Nature Photonics.

[41]  A. Crespi,et al.  Integrated multimode interferometers with arbitrary designs for photonic boson sampling , 2013, Nature Photonics.

[42]  S. Hodgman,et al.  Ideal n-body correlations with massive particles , 2013, Nature Physics.

[43]  B. Terhal.  Quantum error correction for quantum memories , 2013, 1302.3428.

[44]  B. J. Metcalf,et al.  Boson Sampling on a Photonic Chip , 2012, Science.

[45]  Philip Walther,et al.  Experimental boson sampling , 2012, Nature Photonics.

[46]  P. Zoller,et al.  Measuring entanglement growth in quench dynamics of bosons in an optical lattice. , 2012, Physical review letters.

[47]  John Preskill,et al.  Quantum computing and the entanglement frontier , 2012, 1203.5813.

[48]  S. Hodgman,et al.  Direct Measurement of Long-Range Third-Order Coherence in Bose-Einstein Condensates , 2011, Science.

[49]  Norbert Schuch,et al.  Entropy scaling and simulability by matrix product states. , 2007, Physical review letters.

[50]  R. Feynman.  Simulating physics with computers , 1999 .

[51]  D. Weiss,et al.  Unity Occupation of Sites in a 3D Optical Lattice , 1999 .

[52]  S. Stringari,et al.  Collective Excitations of a Trapped Bose-Condensed Gas. , 1996, Physical review letters.

[53]  W. Magnus.  On the exponential solution of differential equations for a linear operator , 1954 .