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Quantum Algorithms for Fermionic Simulations

G. Ortiz·J. E. Gubernatis·E. Knill·R. Laflamme
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Abstract

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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G. Ortiz, J. E. Gubernatis, E. Knill, R. Laflamme. 2000-12-18. Quantum Algorithms for Fermionic Simulations. https://doi.org/10.1103/physreva.64.022319

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