Quantum computation with harmonic oscillators

Summary form only given. The use of continuous-variable (CV) quantum computing allows information to be encoded and processed much more compactly and efficiently than with discrete-variable (qubit) computing. That is, with CV realizations, one can perform quantum information processes using fewer coupled quantum systems: a considerable advantage for the experimental realization of quantum computing. As a result, CV quantum information theory is of interest in quantum error correction, quantum cryptography and quantum teleportation. For example, quantum teleportation has recently been tested experimentally in the CV domain. The current proposed realization of CV quantum computation employs position eigenstates as a computational basis; these states are approximated in experiment using highly squeezed states. We introduce new CV representations, where the generalized Pauli group is generated by the number and phase operators for harmonic oscillators, and the computational basis is given by either harmonic oscillator energy eigenstates or phase eigenstates.