Signatures of a sampling quantum advantage in driven quantum many-body systems

A crucial milestone in the field of quantum simulation and computation is to demonstrate that a quantum device can perform a computation task that is classically intractable. A key question is to identify setups that can achieve such goal within current technologies. In this work, we provide formal evidence that sampling bit-strings from a periodic evolution of a unitary drawn from the circular orthogonal ensemble (COE) cannot be efficiently simulated with classical computers. As the statistical properties of COE coincide with a large class of driven analog quantum systems thanks to the Floquet eigenstate thermalization hypothesis, our results indicate the possibility that those driven systems could constitute practical candidates for a sampling quantum advantage. To further support this, we give numerical examples of driven disordered Ising chains and 1D driven Bose–Hubbard model.

[1]  Y. Liu,et al.  Efficiently Extracting Multi-Point Correlations of a Floquet Thermalized System , 2022, 2210.08556.

[2]  J. Eisert,et al.  Computational advantage of quantum random sampling , 2022, Reviews of Modern Physics.

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

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

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

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

[7]  J. Tangpanitanon,et al.  Expressibility and trainability of parametrized analog quantum systems for machine learning applications , 2020, Physical Review Research.

[8]  Immanuel Bloch,et al.  Floquet Prethermalization in a Bose-Hubbard System , 2020, Physical Review X.

[9]  C. Monroe,et al.  Programmable quantum simulations of spin systems with trapped ions , 2019, Reviews of Modern Physics.

[10]  Leonardo Novo,et al.  Quantum advantage from energy measurements of many-body quantum systems , 2019, Quantum.

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

[12]  Jian-Wei Pan,et al.  Boson Sampling with 20 Input Photons and a 60-Mode Interferometer in a 10^{14}-Dimensional Hilbert Space. , 2019, Physical review letters.

[13]  J. Eisert,et al.  Quantum certification and benchmarking , 2019, Nature Reviews Physics.

[14]  U. Vazirani,et al.  On the complexity and verification of quantum random circuit sampling , 2018, Nature Physics.

[15]  Shankari V. Rajagopal,et al.  Quantifying and Controlling Prethermal Nonergodicity in Interacting Floquet Matter , 2018, Physical Review X.

[16]  N. Goldman,et al.  Parametric Instabilities of Interacting Bosons in Periodically Driven 1D Optical Lattices , 2018, Physical Review X.

[17]  Immanuel Bloch,et al.  Colloquium : Many-body localization, thermalization, and entanglement , 2018, Reviews of Modern Physics.

[18]  John Preskill,et al.  Quantum Computing in the NISQ era and beyond , 2018, Quantum.

[19]  Tatsuhiko N. Ikeda,et al.  Thermalization and prethermalization in isolated quantum systems: a theoretical overview , 2017, 1712.08790.

[20]  H Neven,et al.  A blueprint for demonstrating quantum supremacy with superconducting qubits , 2017, Science.

[21]  Aram W. Harrow,et al.  Quantum computational supremacy , 2017, Nature.

[22]  L. A. Goldberg,et al.  The Complexity of Approximating complex-valued Ising and Tutte partition functions , 2017, computational complexity.

[23]  Martin Schwarz,et al.  Anticoncentration theorems for schemes showing a quantum speedup , 2017, 1706.03786.

[24]  J. Eisert,et al.  Architectures for quantum simulation showing a quantum speedup , 2017, 1703.00466.

[25]  Michael J. Bremner,et al.  Quantum sampling problems, BosonSampling and quantum supremacy , 2017, npj Quantum Information.

[26]  Daniel A. Roberts,et al.  Chaos and complexity by design , 2016, 1610.04903.

[27]  H. Neven,et al.  Characterizing quantum supremacy in near-term devices , 2016, Nature Physics.

[28]  Immanuel Bloch,et al.  Periodically driving a many-body localized quantum system , 2016, Nature Physics.

[29]  L. Duan,et al.  Quantum Supremacy for Simulating a Translation-Invariant Ising Spin Model. , 2016, Physical review letters.

[30]  A. Eckardt,et al.  Colloquium: Atomic quantum gases in periodically driven optical lattices , 2016, 1606.08041.

[31]  Jae-yoon Choi,et al.  Exploring the many-body localization transition in two dimensions , 2016, Science.

[32]  M. Rigol,et al.  From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics , 2015, 1509.06411.

[33]  Tomotaka Kuwahara,et al.  Rigorous Bound on Energy Absorption and Generic Relaxation in Periodically Driven Quantum Systems. , 2015, Physical review letters.

[34]  Ashley Montanaro,et al.  Average-case complexity versus approximate simulation of commuting quantum computations , 2015, Physical review letters.

[35]  Leslie Ann Goldberg,et al.  The Complexity of Approximating complex-valued Ising and Tutte partition functions , 2014, computational complexity.

[36]  J. Eisert,et al.  Quantum many-body systems out of equilibrium , 2014, Nature Physics.

[37]  Tatsuhiko N. Ikeda,et al.  Testing whether all eigenstates obey the eigenstate thermalization hypothesis. , 2014, Physical review. E, Statistical, nonlinear, and soft matter physics.

[38]  D. Jaksch,et al.  What is a quantum simulator? , 2014, 1405.2831.

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

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

[42]  Andrew G. White,et al.  Photonic Boson Sampling in a Tunable Circuit , 2012, Science.

[43]  J. Cirac,et al.  Goals and opportunities in quantum simulation , 2012, Nature Physics.

[44]  M. Lewenstein,et al.  Can one trust quantum simulators? , 2011, Reports on progress in physics. Physical Society.

[45]  Scott Aaronson,et al.  A linear-optical proof that the permanent is #P-hard , 2011, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[46]  Scott Aaronson,et al.  The computational complexity of linear optics , 2010, STOC '11.

[47]  R. Jozsa,et al.  Classical simulation of commuting quantum computations implies collapse of the polynomial hierarchy , 2010, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[48]  A. Harrow,et al.  Random Quantum Circuits are Approximate 2-designs , 2008, 0802.1919.

[49]  Vijay V. Vazirani,et al.  Approximation Algorithms , 2001, Springer Berlin Heidelberg.

[50]  Larry J. Stockmeyer,et al.  On Approximation Algorithms for #P , 1985, SIAM J. Comput..

[51]  Nicholas Hunter-Jones.  Chaos and Randomness in Strongly-Interacting Quantum Systems , 2018 .

[52]  Marvin Simon,et al.  Probability Distributions Involving Gaussian Random Variables , 2002 .