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Quantum Information

Over the last decade remarkable progress has been made in understanding the links between physics and information. Uniting two of the most exciting intellectual developments of the early twentieth century, quantum mechanics and the theory of computation, the field of quantum information has seen explosive growth since Peter Shor showed that the problem of factoring integers, long thought to be intractable on classical computers, could be solved "easily" on a quantum computer.

An exciting area of potential applications of quantum computation and quantum information theory is in understanding the difficulty of simulating quantum systems. For certain cases, it appears that quantum computers would be exponentially better than classical machines at, e.g. computing the ground state energies of molecules. On the other hand, insights from quantum information theory improve our understanding of quantum systems, sometimes enabling efficient classical calculations of quantum properties.

Selected Papers

  • Constructive Quantum Shannon Decomposition from Cartan Involutions, Byron Drury, Peter J. Love,  J. Phys. A. Math. Theor., 41 (2008) 395305,
  • Realizable Hamiltonians for Universal Adiabatic Quantum Computers, Jacob D. Biamonte, Peter J. Love, Phys. Rev. A, 78, 012352 (2008), 
  • Simulated Quantum Computation of Molecular Energies, Alan Aspuru-Guzik, Anthony Dutoi, Peter J. Love, Martin Head-Gordon, Science, 309, 5741, (2005) quant-ph/0604193
  • A characterization of global entanglement, Peter J. Love, Alec Maassen van den Brink, A.Yu. Smirnov, M.H.S. Amin, M. Grajcar, E. Il'ichev, A. Izmalkov, A.M. Zagoskin, quant-ph/0602143
  • Quaternionic Madelung transformation and non-Abelian fluid dynamics , Peter J. Love, Bruce M. Boghosian Physica A 332 47-59 (2004) hep-th/0210242

Lattice gases and nonequilibrium dynamics

My D. Phil work used a very simple model for amphiphilic fluids to explore the huge range of phenomenology which complex fluid mixtures can display. In subsequent work I showed that this heuristically motivated model could be obtained from an underlying picture of interparticle interactions. Lattice gases provide a simple set of models whose macroscopic behaviour can be analysed, yielding many of the equations of interest in nonequilibrium physics.

Current work investigates a lattice gas model with dynamical geometry - particles moving on a lattice may create and delete sites. In one-dimension, the macroscopic dynamics is simply the time evolution of the size of the lattice. The underlying model is time reversible, and so the size of the lattice may either grow without bound or oscillate. Numerical and theoretical work shows that the average behaviour is that the lattice grows as the square root of time. Reformulating the model in terms of the gaps between particles enables exact characterization of the orbits for special cases.

This work is currently supported by a Cottrell College Science Award from Research Corporation

Selected Papers

  • Lattice-gas simulations of dynamical geometry in one-dimension , Peter J. Love, Bruce M. Boghosian, David A. Meyer, Philosophical Transactions of the Royal Society, 362 1667-1675 (2004)
  • On the dependence of the Navier Stokes equations on the distribution of molecular velocities , Peter J. Love, Bruce M. Boghosian Physica D, 193 182-194 (2004)
  • Simulations of amphiphilic fluids using mesoscale lattice-Boltzmann and lattice-gas methods , Peter J. Love, M. Nekovee, J. Chin, N. Gonzalez-Segredo, P.V. Coveney, Computer Physics Communications 153 (3) 340-358 2003.
  • Toward the simplest hydrodynamic lattice gas model Bruce M. Boghosian, Peter J. Love, David A. Meyer, Philosophical Transactions of the Royal Society A 360 (1792): 333-344 March 15 2002
  • A particulate basis for a lattice-gas model of amphiphilic fluids , Peter J. Love, Philosophical Transactions of the Royal Society A 360 (1792): 345-355 March 15 2002