Southwest Quantum Information and Technology
Thirteenth Annual Meeting, February 17-20, 2011
Boulder, Colorado
Full Program | Thursday | Friday | Saturday | Sunday | All Sessions
| SESSION 8: Quantum Algorithms | Session Chair: |
| 10:45am-11:30am | David Poulin, Université de Sherbrooke | Quantum Metropolis Sampling: An algorithm to simulate thermal systems with a quantum computer | Abstract. The original motivation to build a quantum computer came from Feynman who envisaged a machine capable of simulating generic quantum mechanical systems, a task that is intractable for classical computers. Such a machine would have tremendous applications in all physical sciences, including condensed matter physics, chemistry, and high energy physics. Part of Feynman's challenge was met by Lloyd who showed how to approximately decompose the time-evolution operator of interacting quantum particles into a short sequence of elementary gates, suitable for operation on a quantum computer. However, this left open the more fundamental problem of how to simulate the equilibrium and static properties of quantum systems. This requires the preparation of ground and Gibb's states on a quantum computer. For classical systems, this problem is solved by the ubiquitous Metropolis algorithm, a method that basically acquired a monopoly for the simulation of interacting particles. In this talk, I will demonstrate that the corresponding quantum problem can be solved by a quantum Metropolis algorithm. This validates the quantum computer as a universal simulator, and proves that the so-called sign problem occurring in quantum Monte Carlo methods can be resolved with a quantum computer. |
| 11:30am-12:00pm | Bryan Eastin, Northrop Grumman Corporation | Simulating Concordant Computations | Abstract. A quantum state is called concordant if it has zero quantum discord with respect to any part. By extension, a concordant computation is one such that the state of the computer, at each time step, is concordant. In this talk, I describe a classical algorithm that, given a product state as input, permits the efficient simulation of any concordant quantum computation having a conventional form and composed of gates acting on two or fewer qubits. This shows that such a quantum computation must generate quantum discord if it is to efficiently solve a problem that requires super-polynomial time classically. While I employ the restriction to two-qubit gates sparingly, a crucial component of the simulation algorithm appears not to be extensible to gates acting on higher-dimensional systems. |
| 1:30pm-2:15pm | Jens Eisert, University of Potsdam | Relaxation, thermalization, and a quantum algorithm to prepare Gibbs states | Abstract. This talk will be concerned with recent progress on understanding how quantum many-body systems out of equilibrium eventually come to rest. The first part of the talk will highlight theoretical progress on this question - employing ideas of Lieb-Robinson bounds, quantum central limit theorems and of concentration of measure (1-4). These findings will be complemented by experimental work with ultra-cold atoms in optical lattices, constituting a dynamical "quantum simulator", allowing to probe physical questions that are presently out of reach even for state-of-the-art numerical techniques based on matrix-product states (5). The last part of the talk will sketch how based on the above ideas, a fully certifiable quantum algorithm preparing Gibbs states can be constructed, complementing quantum Metropolis algorithms (6). (Joint work with C. Gogolin, M. Mueller, T.J. Osborne, A. Flesch, C. Cramer, U. Schollwoeck, I. Bloch, S. Trotzky, Y.A. Chen, A. Riera.) (1) "Absence of thermalization in non-integrable systems", Phys. Rev. Lett., in press (2011). |