Thresholds for Linear Optics Quantum Computation

We previously established that in principle, it is possible to quantum compute using passive linear optics with photo-detectors (quant-ph/0006088). Here we describe techniques based on error detection and correction that greatly improve the resource and device reliability requirements needed for scalability. The resource requirements are analyzed for ideal linear optics quantum computation (LOQC). The coding methods can be integrated both with loss detection and phase error-correction to deal with the primary relaxation processes in non-ideal optics, including detector inefficiencies. The main conclusion of our work is that the resource requirements for implementing quantum communication or computation with LOQC are reasonable. Furthermore, this work clearly demonstrates how special knowledge of the error behavior can be exploited for greatly improving the fault tolerance and overheads of a physical quantum computer.