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arXiv:0709.1704 · American Journal of Physics

Quantum simulation of the single-particle Schrödinger equation

Giuliano Benenti, G. Strini

Published Jun 10, 2008• 96 citations
arXivHTMLPDF

Abstract

The nature of a quantum computer is described in the concrete context of a quantum simulator of the single-particle Schrödinger equation. We show that a register of 6–10 qubits is sufficient to realize a useful quantum simulator capable of efficiently solving standard quantum mechanical problems.
DOI
10.1119/1.2894532

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As the first useful Quantum Computers presumably will be quantum simulators, here the minimum number of qubits necessary for the solution of Schrödinger's equation in simple test problems is evaluated. From the present preliminary results it appears that it is possible to realize a useful quantum simulator with a register of only 10-15 qubits. The intrinsic sensitivity to some errors appears to be moderate without the need of error correcting methods. At present there is at least some indication that the amplitude errors are more dangerous than phase and decoherence errors. So corrections limited to amplitude errors may be very useful.
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Algorithms are described for efficiently simulating quantum mechanical systems on quantum computers. A class of algorithms for simulating the Schrodinger equation for interacting many-body systems are presented in some detail. These algorithms would make it possible to simulate nonrelativistic quantum systems on a quantum computer with an exponential speedup compared to simulations on classical computers. Issues involved in simulating relativistic systems of Dirac and gauge particles are discussed.