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Simulation of many-body interactions by conditional geometric phases

Xiaoguang Wang·Paolo Zanardi
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Abstract

It is shown how to exactly simulate many-body interactions and multi-qubit gates by coupling finite dimensional systems, e.g., qubits with a continuous variable. Cyclic evolution in the phase space of such a variable gives rise to a geometric phase, depending on a product of commuting operators. The latter allows to simulate many-body Hamiltonians and nonlinear Hamiltonians, and to implement a big variety of multi-qubit quantum gates on both qubits and encoded qubits. An application to the quantum amplitude amplification algorithm will be discussed.

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Xiaoguang Wang, Paolo Zanardi. 2001-12-03. Simulation of many-body interactions by conditional geometric phases. https://doi.org/10.1103/physreva.65.032327

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