We propose a practical, scalable, and efficient scheme for quantum computation using spatially separated matter qubits and single photon interference effects. The qubit systems can be NV-centers in diamond, Pauli-blockade quantum dots with an excess electron or trapped ions with optical transitions, which are each placed in a cavity and subsequently entangled using a double-heralded single-photon detection scheme. The fidelity of the resulting entanglement is extremely robust against the most important errors such as detector loss, spontaneous emission, and mismatch of cavity parameters. We demonstrate how this entangling operation can be used to efficiently generate cluster states of many qubits, which, together with single qubit operations and readout, can be used to implement universal quantum computation. Existing experimental parameters indicate that high fidelity clusters can be generated with a moderate constant overhead.

We describe a method to project photonic two-qubit states onto the symmetric and antisymmetric subspaces of their Hilbert space. This device utilizes an ancillary coherent state, together with a weak cross-Kerr non-linearity, generated, for example, by electromagnetically induced transparency. The symmetry analyzer is non-destructive, and works for small values of the cross-Kerr coupling. Furthermore, this device can be used to construct a non-destructive Bell state detector. 03.67.Hk, 42.50.Gy, Two-qubit measurements are an important resource in Quantum Information Processing (QIP), enabling key applications such as the teleportation of states and gate, dense coding and error correction. In particular, a measurement device that does not destroy the qubits is a very powerful tool, since it allows entanglement distillation [1] and efficient quantum computing based on measurements [2,3,4]. This is especially useful when the qubits interact weakly, and interaction-based quantum gates are hard to implement (for example, photonic qubits have negligible interaction). Furthermore, a non-destructive two-qubit measurement device can act as an deterministic source of entangled qubits.Optical QIP is of special interest, because electromagnetic fields are ideal information carriers for long distance quantum communication. Photonic quantum states generally suffer low decoherence rates compared to most massive qubit systems, but we need optical information processing devices that overcome the negligible interaction between the photons. Optical quantum computation and communication will therefore benefit greatly from non-destructive two-qubit measurements. Arguably the most important two-photon measurement is the measurement in the maximally entangled Bell basis. When the computational basis of a single-photon qubit is given by two orthogonal polarization states (H and V ), then the Bell states can be written asA non-destructive Bell measurement then projects the two photons onto one of the Bell states. This can be used in the teleportation of probabilistic gates into optical circuits [5,6], and consequently enables efficient linear optical quantum computing. In addition, a deterministic non-destructive Bell measurement would also act as a bright source of entangled photons.Braunstein and Mann presented a linear optical method to distinguish two out of the four optical Bell states [7]. In 1999, it was shown independently by Vaidman and Yoran, and Lütkenhaus et al. that the Braunstein-Mann method is optimal [8, 9]: When one is restricted to linear optics and photon counting (in-cluding feed-forward processing) at most half of the Bell states can be identified perfectly. This detection method is therefore probabilistic. Furthermore, it destroys the photons in the photon counting process, and is thus of limited use in efficient large-scale QIP.One way to improve on this scheme is to move beyond linear optics, i.e. to induce an interaction between the photons. This can be achieved using a cross-Kerr medium, i.e., a nonlinear mediu...

Many proposals for quantum information processing are subject to detectable loss errors. In this Letter, we show that topological error correcting codes, which protect against computational errors, are also extremely robust against losses. We present analytical results showing that the maximum tolerable loss rate is 50%, which is determined by the square-lattice bond percolation threshold. This saturates the bound set by the no-cloning theorem. Our numerical results support this and show a graceful trade-off between tolerable thresholds for computational and loss errors.