Linear optics with photon counting is a prominent candidate for practical quantum computing. The protocol by Knill, Laflamme, and Milburn ͓2001, Nature ͑London͒ 409, 46͔ explicitly demonstrates that efficient scalable quantum computing with single photons, linear optical elements, and projective measurements is possible. Subsequently, several improvements on this protocol have started to bridge the gap between theoretical scalability and practical implementation. The original theory and its improvements are reviewed, and a few examples of experimental two-qubit gates are given. The use of realistic components, the errors they induce in the computation, and how these errors can be corrected is discussed.

Heisenberg-limited measurement protocols can be used to gain an increase in measurement precision over classical protocols. Such measurements can be implemented using, e.g., optical Mach-Zehnder interferometers and Ramsey spectroscopes. We address the formal equivalence between the Mach-Zehnder interferometer, the Ramsey spectroscope, and a generic quantum logic circuit. Based on this equivalence we introduce the "quantum Rosetta stone", and we describe a projectivemeasurement scheme for generating the desired correlations between the interferometric input states in order to achieve Heisenberg-limited sensitivity. The Rosetta stone then tells us the same method should work in atom spectroscopy.

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.

Quantum information processing offers fundamental improvements over classical information processing, such as computing power, secure communication, and high-precision measurements. However, the best way to create practical devices is not yet known. This textbook describes the techniques that are likely to be used in implementing optical quantum information processors.After developing the fundamental concepts in quantum optics and quantum information theory, this book shows how optical systems can be used to build quantum computers according to the most recent ideas. It discusses implementations based on single photons and linear optics, optically controlled atoms and solid-state systems, atomic ensembles, and optical continuous variables.This book is ideal for graduate students beginning research in optical quantum information processing. It presents the most important techniques of the field using worked examples and over 120 exercises. Hardback Cambridge University Press has no responsibility for the persistence or accuracy of URLs for external or third-party internet websites referred to in this publication, and does not guarantee that any content on such websites is, or will remain, accurate or appropriate.

Scalable quantum technologies may be achieved by faithful conversion between matter qubits and photonic qubits in integrated circuit geometries. Within this context, quantum dots possess well-defined spin states (matter qubits), which couple efficiently to photons. By embedding them in nanophotonic waveguides, they provide a promising platform for quantum technology implementations. In this paper, we demonstrate that the naturally occurring electromagnetic field chirality that arises in nanobeam waveguides leads to unidirectional photon emission from quantum dot spin states, with resultant in-plane transfer of matter-qubit information. The chiral behaviour occurs despite the non-chiral geometry and material of the waveguides. Using dot registration techniques, we achieve a quantum emitter deterministically positioned at a chiral point and realize spin-path conversion by design. We further show that the chiral phenomena are much more tolerant to dot position than in standard photonic crystal waveguides, exhibit spin-path readout up to 95±5% and have potential to serve as the basis of spin-logic and network implementations.

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...

Large photon-number path entanglement is an important resource for enhanced precision measurements and quantum imaging. We present a general constructive protocol to create any large photon number path-entangled state based on the conditional detection of single photons. The influence of imperfect detectors is considered and an asymptotic scaling law is derived.

Publisher's Note: Linear optical quantum computing with photonic qubits ͓Rev. Mod. Phys. 79, 135 ͑2007͔͒