Quantum Computing of Poincare Recurrences and Periodic Orbits

Abstract

Quantum algorithms are built enabling to find Poincaré recurrence times and periodic orbits of classical dynamical systems. It is shown that exponential gain compared to classical algorithms can be reached for a restricted class of systems. Quadratic gain can be achieved for a larger set of dynamical systems. The simplest cases can be implemented with small number of qubits.

revtex, 5 pages, research at Quantware MIPS Center (see http://www.quantware.ups-tlse.fr); minor changes and references added

References in corpus (12)

• Quantum Mechanics helps in searching for a needle in a haystack
• Quantum Computing
• Quantum Networks for Elementary Arithmetic Operations
• Long-Time Correlations in the Stochastic Regime
• Efficient Networks for Quantum Factoring
• Simulating Ising Spin Glasses on a Quantum Computer
• Asymptotic Statistics of Poincaré Recurrences in Hamiltonian Systems with Divided Phase Space
• Efficient Quantum Computing of Complex Dynamics
• Exponential Gain in Quantum Computing of Quantum Chaos and Localization
• Factoring in a Dissipative Quantum Computer
• Quantum Computing of Classical Chaos: Smile of the Arnold-Schrodinger Cat
• Efficient quantum computation of high harmonics of the Liouville density distribution

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• Quantum Simulation
• Using Quantum Computers for Quantum Simulation
• Quantum Computation of a Complex System : the Kicked Harper Model
• Towards Large-Scale Quantum Computation
• Interference versus success probability in quantum algorithms with imperfections
• Quantum algorithm for exact Monte Carlo sampling
• Quantum computing of semiclassical formulas