L. You

We present a scheme for a projective measurement of the parity operator $P_z=\prod_{i=1}^N σ_z^{(i)}$ of $N$-qubits. Our protocol uses a single ancillary qubit, or a probe qubit, and involves manipulations of the total spin of the $N$ qubits without requiring individual addressing. We illustrate our protocol in terms of an experimental implementation with atomic ions in a two-zone linear Paul trap, and further discuss its extensions to several more general cases.

We propose two protocols to encode a logical qubit into physical qubits relying on common types of qubit-qubit interactions in as simple forms as possible. We comment on its experimental implementation in several quantum computing architectures, e.g. with trapped atomic ion qubits, atomic qubits inside a high Q optical cavity, solid state Josephson junction qubits, and Bose-Einstein condensed atoms.

We propose a scheme for conditional quantum logic between two 3-state atoms that share a quantum data-bus such as a single mode optical field in cavity QED systems, or a collective vibrational state of trapped ions. Making use of quantum interference, our scheme achieves successful conditional phase evolution without any real transitions of atomic internal states or populating the quantum data-bus. In addition, it only requires common addressing of the two atoms by external laser fields.

We present a family of generalized unitary transformations that simplifies the Hamiltonian for a harmonically trapped two level atom (or ion) interacting with a plane wave laser field. Novel near resonant single as well as double vibrational phonon dynamical regimes are found. The validity condition of the often used motional rotating wave approximation (MRWA) is examined both numerically and analytically. Large errors are found within typical regimes of MRWA with respect to the motional degrees of freedom. The effects of MRWA in trapped ion systems are shown to be opposite to that of the rotating wave approximation (RWA) in the usual Jaynes-Cummings model. Our study points to a more restrictive condition on particle localization (Lamb-Dicke) parameter for the validity of MRWA in the single phonon dynamical regime. It also sheds new light on quantum information storage and processing with trapped atoms.