Quantum computation and simulation with vibrational modes of trapped ions

Vibrational degrees of freedom in trapped-ion systems have recently been gaining attention as a quantum resource, beyond the role as a mediator for entangling quantum operations on internal degrees of freedom, because of the large available Hilbert space. The vibrational modes can be represented as quantum harmonic oscillators and thus offer a Hilbert space with infinite dimensions. Here we review recent theoretical and experimental progress in the coherent manipulation of the vibrational modes, including bosonic encoding schemes in quantum information, reliable and efficient measurement techniques, and quantum operations that allow various quantum simulations and quantum computation algorithms. We describe experiments using the vibrational modes, including the preparation of non-classical states, molecular vibronic sampling, and applications in quantum thermodynamics. We finally discuss the potential prospects and challenges of trapped-ion vibrational-mode quantum information processing.

Automated summary

Vibrational degrees of freedom in trapped-ion systems are now recognized as an important quantum resource due to the large available Hilbert space. Recent progress has been made in the coherent manipulation of vibrational modes, with applications in quantum information encoding schemes, measurement techniques, and quantum operations. Experimental demonstrations have shown the preparation of non-classical states, molecular vibronic sampling, and applications in quantum thermodynamics using vibrational modes.