Simulation of many-body interactions by conditional geometric phases

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.

8 pages, no figures, some references are added and the revised version submitted to PRA

References in corpus (7)

• Geometric Manipulation of Trapped Ions for Quantum Computation
• Non-adiabatic conditional geometric phase shift with NMR
• Multi-bit gates for quantum computing
• Complete controllability of finite-level quantum systems
• Suppression of arbitrary internal coupling in a quantum register
• Quantum phase gate with a selective interaction
• A More General Quantum Searching Algorithm And the Precise Formula of the Amplitude and the Non-symmetric Effects of Different Rotating Angles

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