Scalable Implementation of Boson Sampling with Trapped Ions

Boson sampling solves a classically intractable problem by sampling from a probability distribution given by matrix permanents. We propose a scalable implementation of boson sampling using local transverse phonon modes of trapped ions to encode the bosons. The proposed scheme allows deterministic preparation and high-efficiency readout of the bosons in the Fock states and universal mode mixing. With the state-of-the-art trapped ion technology, it is feasible to realize boson sampling with tens of bosons by this scheme, which would outperform the most powerful classical computers and constitute an effective disproof of the famous extended Church-Turing thesis.

Figure 1

Control of the tunneling Hamiltonian through the dynamical decoupling. The negative signs in (a) and (b) denote the set of ions to be applied to a $\pi$-phase shift at half of the evolution time, while the positive signs denote the ions left intact. (a) The $\pi$-phase pattern to turn off other tunneling terms in $H_{\mathrm{NN}}$ except for a neighboring pair $j$, $j+1$. (b) The $\pi$-phase pattern to shrink the tunneling range of the Hamiltonian from $k$ to $k-1$.

Figure 2

A consecutive measurement scheme to perform projective detection of the phonon mode in the Fock basis. (a) The initial state configuration right before the measurement. (b)–(d) The state configuration after the blue sideband transition, the carrier transition, and the quantum jump detection. These three steps are repeated until one finally registers the bright state (see the text for details).