Towards Continuous Variables Quantum Computing with Trapped Ions

The usually employed methods of using spin states of atomic-like systems for quantum information encoding [1,2] suffer from scalability issues. For example, it becomes very challenging to control a large number of trapped atomic ions each representing a physical qubit. The alternative approach would be to exploit the large Hilbert space provided by a near-harmonic trapping potential and encode the information in the oscillator states [3,4]. We use sideband-resolved addressing of motional states in a single trapped
¹⁷¹
Yb
⁺
ion to demonstrate a conditional beam splitter gate. The conditional beam splitter (CBS) Hamiltonian |e〉〈e|(a
^†
b + ab
^†
) swaps the quantum states of two motional modes of a trapped ion, conditioned on the ion's internal state. It thus can be viewed as a SWAP gate and we uilize it to demonstrate SWAP tests, implement single shot parity measurements, and generate maximally entangled NOON states of motion (see Figure 1).