Quantum simulations based on measurements and feedback control

We propose a scheme for performing quantum simulations with atoms in cavities based on a photon detection feedback loop that requires only linear optical elements. Atoms can be stored individually without the need of directly interacting with one another. The scheme is able to simulate any time evolution that can be written as a sum of two-qubit Hamiltonians, e.g., any nearest-neighbor interaction on a lattice. It can also be made robust against photon losses.

Figure 1

The atom stores a qubit in two ground states. In addition several excited levels are used to create photons in the cavity. The double arrays indicate photon modes supported by the cavity, whereas the single arrows stand for external laser pulses to excite the atoms. In (a) only one photon mode is supported by the cavity. The photon qubit is encoded in the presence or absence of a photon. In (b) two different photon modes are supported.

Figure 2

Two distant atoms are effectively coupled by sending photons coming out of the cavity to a beam splitter. Dependent on the measurement outcome, we apply a feedback loop on the atoms until the desired evolution has been done.

Figure 3

To simulate a nearest-neighbor Hamiltonian, we can do $m/2$ of the rotations in parallel. We need a basic setup such that each cavity sends a photon on a beam splitter together with either its right or its left neighbor.

Figure 4

(a) To fight photon losses the atom needs to store a second qubit to carry a security copy of the photon. (b) In the first attempt we try to establish an evolution by sending the photons on a beam splitter. In case of success we erase the security copy; in case of failure we can reuse the copy by measuring in different bases.