Jonas Haferkamp

A quantum repeater segment is a basic building block of a quantum repeater, generating buffered entanglement of quantum memories to connect quantum repeater cells. It also enables the connection between quantum computers. In the implementation we present here, photons emitted from two co-trapped free-space coupled $^{40}$Ca$^+$ ions are converted to the telecom-C band and interfered after transmission over 440$\,$m of optical fiber (220$\,$m per arm), where a photonic Bell measurement is performed to create entanglement between the memories. With this scheme we generate an entangled $\left|Ψ^+\right\rangle$ Bell state with $\ge 68(8)\,$% fidelity, highlighting trapped $^{40}$Ca$^+$ ions as a promising quantum repeater hardware platform.

The dynamical structure factor is one of the experimental quantities crucial in scrutinizing the validity of the microscopic description of strongly correlated systems. However, despite its long-standing importance, it is exceedingly difficult in generic cases to numerically calculate it, ensuring that the necessary approximations involved yield a correct result. Acknowledging this practical difficulty, we discuss in what way results on the hardness of classically tracking time evolution under local Hamiltonians are precisely inherited by dynamical structure factors; and hence offer in the same way the potential computational capabilities that dynamical quantum simulators do: We argue that practically accessible variants of the dynamical structure factors are BQP-hard for general local Hamiltonians. Complementing these conceptual insights, we improve upon a novel, readily available, measurement setup allowing for the determination of the dynamical structure factor in different architectures, including arrays of ultra-cold atoms, trapped ions, Rydberg atoms, and superconducting qubits. Our results suggest that quantum simulations employing near-term noisy intermediate scale quantum devices should allow for the observation of features of dynamical structure factors of correlated quantum matter in the presence of experimental imperfections, for larger system sizes than what is achievable by classical simulation.