ASSESSMENT OF CURRENT RESULTS AND OUTLOOK ON FUTURE EFFORTS
4.3 QUANTUM INFORMATION SCIENCE THEORY
4.3.4 QUANTUM SIMULATIONS
Quantum simulators may become the first application of quantum computers, since with modest requirements one may be able to perform simulations which are impossible with classical computers. At the beginning of the 80's it was realized that it will be impossible to predict and describe the properties of certain quantum systems using classical computers, since the number of variables that must be stored grows exponentially with the number of particles. A quantum system in which the interactions between the particles could be engineered would be able to simulate that system in a very efficient way. This would then allow, for example, studying the microscopic properties of interesting materials permitting free variation of system parameters. Potential outcomes would be to obtain an accurate description of chemical compounds and reactions, to gain deeper understanding of high temperature superconductivity, or to find out the reason why quarks are always confined.
A quantum simulator is a quantum system whose dynamics can be engineered such that it reproduces the behaviour of another physical system which one is interested to describe. In principle, a quantum computer would be an almost perfect quantum simulator since one can program it to undergo any desired quantum dynamics. However, a quantum computer is very difficult to build in practice and has very demanding requirements. Fortunately, there are physical systems with which it is not known how to build a quantum computer, but in which one can engineer certain kind of interactions and thus simulate other systems which so far are not well understood. This is due to the fact that with classical computers it is impossible to reproduce their dynamics, given that the number of parameters required to represent the corresponding state grows exponentially with the number of particles. Examples are atoms in optical lattices or trapped ions. In those systems, one does not require to individually address the qubits, or to perform quantum gates on arbitrary pairs of qubits, but rather on all of them at the same time. Besides, one is interested in measuring physical properties (like magnetization, conductivity, etc.) which are robust with respect to the appearance of several errors (in a quantum computer without error correction, even a single error will destroy the computation). For example, to see whether a material is conducting or not one does not need to know with a high precision the corresponding conductivity.
Key references
[1] S. Lloyd, Universal Quantum Simulators, Science 273, 1073 (1996).
[2] N. Khaneja, R. Brockett, and S. J. Glaser, "Time optimal control in spin systems", Phys. Rev. A 63, 032308 (2001).
[3] E. Jané, G. Vidal, W. Dür, P. Zoller, and J. I. Cirac, Simulation of quantum dynamics with quantum optical systems, Quant. Inf. Comp. 3, 15 (2003).
[4] C. H. Bennett, J. I. Cirac, M. S. Leifer, D. W. Leung, N. Linden, S. Popescu, and G. Vidal, Optimal simulation of two-qubit Hamiltonians using general local operations, Phys. Rev. A 66, 012305 (2002).
[5] M. A. Nielsen, M. J. Bremner, J. L. Dodd, A. M. Childs, and C. M. Dawson, Universal simulation of Hamiltonian dynamics for qudits, Phys. Rev. A 66, 022317 (2002).
[6] P. Wocjan, D. Janzing, T. Beth, Simulating arbitrary pair-interactions by a given Hamiltonian: Graph-theoretical bounds on the time complexity, Quantum Information and Computation 2, 117 (2002).
