Multiqubit Decoherence in Ion-trap Quantum Computation

We will report on the realisation of high-fidelity Schroedinger- Cat states with more than six qubits in a string of $^{40}$Ca$^ {+}$ ions stored in a linear ion trap. We achieved fidelities with the target states exceeding 95\% for up to four ions and 88\% for six ions. These high fidelities allow to investigate decoherence of highly entangled quantum states in the presence of collective dephasing, the predominant source of decoherence in ion-trap based and other physical realizations of quantum computation. Assuming the noise to be Gaussian and stationary, we derive and experimentally confirm a model that predicts an exponential decay of the state fidelity that scales as $N^2$ where $N$ is the number of qubits. Such a scaling behaviour has severe effects on quantum computation and related fields, such as metrology.