Emulation of complex open quantum systems using superconducting qubits

With quantum computers being out of reach for now, quantum simulators are alternative devices for efficient and accurate simulation of problems that are challenging to tackle using conventional computers. Quantum simulators are classified into analog and digital, with the possibility of constructing “hybrid” simulators by combining both techniques. Here we focus on analog quantum simulators of open quantum systems and address the limit that they can beat classical computers. In particular, as an example, we discuss simulation of the chlorosome light-harvesting antenna from green sulfur bacteria with over 250 phonon modes coupled to each electronic state. Furthermore, we propose physical setups that can be used to reproduce the quantum dynamics of a standard and multiple-mode Holstein model. The proposed scheme is based on currently available technology of superconducting circuits consist of flux qubits and quantum oscillators.

[1]  Leonardo Silvestri,et al.  Multiple mode exciton-vibrational coupling in H-aggregates: synergistic enhancement of the quantum yield. , 2010, The Journal of chemical physics.

[2]  F. Nori,et al.  Quantum biology , 2012, Nature Physics.

[3]  Aldo H. Romero,et al.  EFFECTS OF DIMENSIONALITY AND ANISOTROPY ON THE HOLSTEIN POLARON , 1999 .

[4]  K. Schulten,et al.  Light harvesting complex II B850 excitation dynamics. , 2009, The Journal of chemical physics.

[5]  Alán Aspuru-Guzik,et al.  Memory-Assisted Exciton Diffusion in the Chlorosome Light-Harvesting Antenna of Green Sulfur Bacteria. , 2012, The journal of physical chemistry letters.

[6]  Aldo H. Romero,et al.  Polaron effective mass, band distortion, and self-trapping in the Holstein molecular-crystal model , 1999 .

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

[8]  M. Kuypers,et al.  Physiology and Phylogeny of Green Sulfur Bacteria Forming a Monospecific Phototrophic Assemblage at a Depth of 100 Meters in the Black Sea , 2005, Applied and Environmental Microbiology.

[9]  Feng Mei,et al.  Analog superconducting quantum simulator for Holstein polarons , 2013, 1307.0906.

[10]  C. Kreisbeck,et al.  High-Performance Solution of Hierarchical Equations of Motion for Studying Energy Transfer in Light-Harvesting Complexes. , 2010, Journal of chemical theory and computation.

[11]  Alán Aspuru-Guzik,et al.  Theoretical characterization of excitation energy transfer in chlorosome light-harvesting antennae from green sulfur bacteria , 2013, Photosynthesis Research.

[12]  Zoltán G. Soos,et al.  Optical absorption spectra of the Holstein molecular crystal for weak and intermediate electronic coupling , 2002 .

[13]  Alán Aspuru-Guzik,et al.  Efficiency of energy funneling in the photosystem II supercomplex of higher plants† †Electronic supplementary information (ESI) available: The ESI contains the parameters for the used spectral densities and details the convergence of HEOM. See DOI: 10.1039/c5sc04296h , 2015, Chemical science.

[14]  R. Feynman Quantum mechanical computers , 1986 .

[15]  Andrew J. Kerman,et al.  Quantum information processing using quasiclassical electromagnetic interactions between qubits and electrical resonators , 2012, 1212.3300.

[16]  Donald A. Bryant,et al.  Alternating syn-anti bacteriochlorophylls form concentric helical nanotubes in chlorosomes , 2009, Proceedings of the National Academy of Sciences.

[17]  W. Strunz,et al.  Hierarchy of stochastic pure states for open quantum system dynamics. , 2014, Physical review letters.

[18]  Tao Shi,et al.  Quantum simulation of small-polaron formation with trapped ions. , 2012, Physical review letters.

[19]  Gene H. Golub,et al.  Matrix computations , 1983 .

[20]  Osor S. Barisic Calculation of excited polaron states in the Holstein model , 2004 .

[21]  P. Kornilovitch,et al.  Effect of electron-phonon interaction range on lattice polaron dynamics: A continuous-time quantum Monte Carlo study , 2004, cond-mat/0407250.

[22]  Gene H. Golub,et al.  Matrix computations (3rd ed.) , 1996 .

[23]  Felipe Herrera,et al.  Tunable Holstein model with cold polar molecules , 2010, 1010.1782.

[24]  C. Harmans,et al.  Tuning the gap of a superconducting flux qubit. , 2008, Physical review letters.

[25]  F. Nori,et al.  Quantum Simulation , 2013, Quantum Atom Optics.

[26]  J. P. Hague,et al.  Quantum simulation of electron–phonon interactions in strongly deformable materials , 2011, 1109.1225.

[27]  Cheng Guo,et al.  Using density matrix renormalization group to study open quantum systems , 2012 .

[28]  G. Fleming,et al.  Unified treatment of quantum coherent and incoherent hopping dynamics in electronic energy transfer: reduced hierarchy equation approach. , 2009, The Journal of chemical physics.

[29]  A. Kerman,et al.  High-fidelity quantum operations on superconducting qubits in the presence of noise. , 2008, Physical review letters.

[30]  J. Bonca,et al.  The Holstein Polaron , 1998, cond-mat/9812252.

[31]  K. Berggren,et al.  Microwave-Induced Cooling of a Superconducting Qubit , 2006, Science.

[32]  Franco Nori,et al.  Interqubit coupling mediated by a high-excitation-energy quantum object , 2007, 0709.0237.

[33]  Nicolas Gisin,et al.  Open system dynamics with non-markovian quantum trajectories , 1999 .

[34]  Jarrell,et al.  Holstein model in infinite dimensions. , 1993, Physical review. B, Condensed matter.

[35]  Yu Lu,et al.  POLARONS AND BIPOLARONS , 1988 .

[36]  F. Nori,et al.  Colloquium: Stimulating uncertainty: Amplifying the quantum vacuum with superconducting circuits , 2011, 1103.0835.

[37]  Y. Tanimura Reduced hierarchy equations of motion approach with Drude plus brownian spectral distribution: probing electron transfer processes by means of two-dimensional correlation spectroscopy. , 2012, The Journal of chemical physics.

[38]  Al'an Aspuru-Guzik,et al.  Linear-algebraic bath transformation for simulating complex open quantum systems , 2014, 1408.3176.

[39]  D. DiVincenzo,et al.  Dephasing of a superconducting qubit induced by photon noise. , 2005, Physical review letters.

[40]  Marco Lanzagorta,et al.  Quantum Simulators , 2013 .

[41]  Kirk W Madison,et al.  Investigating polaron transitions with polar molecules. , 2012, Physical review letters.

[42]  J. E. Mooij,et al.  Coherent Quantum Dynamics of a Superconducting Flux Qubit , 2003, Science.

[43]  F. Nori,et al.  Atomic physics and quantum optics using superconducting circuits , 2013 .

[44]  G. Oostergetel,et al.  The chlorosome: a prototype for efficient light harvesting in photosynthesis , 2010, Photosynthesis Research.

[45]  Alán Aspuru-Guzik,et al.  Fast delocalization leads to robust long-range excitonic transfer in a large quantum chlorosome model. , 2015, Nano letters.

[46]  Alán Aspuru-Guzik,et al.  Quantum simulator of an open quantum system using superconducting qubits: exciton transport in photosynthetic complexes , 2011, New Journal of Physics.

[47]  Alán Aspuru-Guzik,et al.  Scalable High-Performance Algorithm for the Simulation of Exciton Dynamics. Application to the Light-Harvesting Complex II in the Presence of Resonant Vibrational Modes. , 2014, Journal of chemical theory and computation.

[48]  F. de Pasquale,et al.  DYNAMICAL MEAN-FIELD THEORY OF THE SMALL POLARON , 1997 .

[49]  C. Kreisbeck,et al.  Long-Lived Electronic Coherence in Dissipative Exciton Dynamics of Light-Harvesting Complexes , 2012, 1203.1485.

[50]  Aldo H. Romero,et al.  Exact weak-coupling radius of the Holstein polaron in one, two, and three dimensions , 1999 .

[51]  J. Clarke,et al.  Superconducting quantum bits , 2008, Nature.

[52]  R. Kubo,et al.  Time Evolution of a Quantum System in Contact with a Nearly Gaussian-Markoffian Noise Bath , 1989 .

[53]  J Casanova,et al.  Digital quantum simulation of the Holstein model in trapped ions. , 2012, Physical review letters.

[54]  Lin Tian,et al.  Transmon-based simulator of nonlocal electron-phonon coupling: A platform for observing sharp small-polaron transitions , 2014 .

[55]  G. Fleming,et al.  Theoretical examination of quantum coherence in a photosynthetic system at physiological temperature , 2009, Proceedings of the National Academy of Sciences.

[56]  F. Nori,et al.  Quantum Simulators , 2009, Science.

[57]  Mona Berciu Green's function of a dressed particle. , 2006, Physical review letters.

[58]  Boris Svistunov,et al.  Bold diagrammatic Monte Carlo: A generic sign-problem tolerant technique for polaron models and possibly interacting many-body problems , 2008 .

[59]  S. Lloyd,et al.  Quantum Coherent Tunable Coupling of Superconducting Qubits , 2007, Science.

[60]  Frank Stienkemeier,et al.  Vibronic line shapes of PTCDA oligomers in helium nanodroplets. , 2010, The Journal of chemical physics.

[61]  George A. Sawatzky,et al.  Greens function of the Holstein polaron , 2006 .