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Quantum Algorithms for Fermionic Simulations

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arxiv cond-mat/0012334 v1 pith:RUTRM6KJ submitted 2000-12-18 cond-mat hep-thquant-ph

classification cond-mathep-thquant-ph
keywords quantumproblemcomplexitycomputerfermionicsimulationssystemsalgebraic
verification ladder T0 review T1 audit T2 compute T3 formal
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We investigate the simulation of fermionic systems on a quantum computer. We show in detail how quantum computers avoid the dynamical sign problem present in classical simulations of these systems, therefore reducing a problem believed to be of exponential complexity into one of polynomial complexity. The key to our demonstration is the spin-particle connection (or generalized Jordan-Wigner transformation) that allows exact algebraic invertible mappings of operators with different statistical properties. We give an explicit implementation of a simple problem using a quantum computer based on standard qubits.

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