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.

We describe in detail the theory underpinning the measurement of density matrices of a pair of quantum two-level systems ͑''qubits''͒. Our particular emphasis is on qubits realized by the two polarization degrees of freedom of a pair of entangled photons generated in a down-conversion experiment; however, the discussion applies in general, regardless of the actual physical realization. Two techniques are discussed, namely, a tomographic reconstruction ͑in which the density matrix is linearly related to a set of measured quantities͒ and a maximum likelihood technique which requires numerical optimization ͑but has the advantage of producing density matrices that are always non-negative definite͒. In addition, a detailed error analysis is presented, allowing errors in quantities derived from the density matrix, such as the entropy or entanglement of formation, to be estimated. Examples based on down-conversion experiments are used to illustrate our results.

We show how to construct a near deterministic CNOT using several single photons sources, linear optics, photon number resolving quantum non-demolition detectors and feed-forward. This gate does not require the use of massively entangled states common to other implementations and is very efficient on resources with only one ancilla photon required. The key element of this gate are non-demolition detectors that use a weak cross-Kerr nonlinearity effect to conditionally generate a phase shift on a coherent probe, if a photon is present in the signal mode. These potential phase shifts can then be measured using highly efficient homodyne detection.PACS numbers: 03.67. Lx, 03.67.Mn, In the past few years we have seen the emergence of single photon optics with polarisation states as a realistic path for achieving universal quantum computation. This started with the pioneering work of Knill, Laflamme and Milburn [KLM][1] who showed that with only single photon sources and detectors and linear elements such as beam-splitters, a near deterministic CNOT gate could be created, through with the use of significant but polynomial resources. With this architecture for the CNOT gate and trivial single qubit rotations a universal set of gates is hence possible and a route forward for creating large devices can be seen. Since this original work there has been significant progress both theoretically [2,3,4,5,6] and experimentally [7,8,9], with a number of CNOT gates actually demonstrated.Much of the theoretical effort has focused on determining more efficient ways to perform the controlled logic. The standard model for linear logic uses only[1]:• Single photon sources, • Linear optical elements including feed-forward, • Photon number resolving single photon detectors, and it has been shown by Knill[4] that the maximum probability for achieving the CNOT gate is 3/4. While these upper bounds are not thought to be tight, with the best success probabilities for the CNOT gate being 2/27[10], it does indicate that near deterministic gates are not possible using only the above resources and strategy. These gates can be made efficient using the "standard" optical teleportation tricks which require the use of massively entangled resources. Are there other natural ways to increase the efficient of these gate operations? Franson et al. [2] showed that if you can increase your allowed physical resources to include maximally entangled two photon states, then the CNOT gate can have its probability of success boosted to 1/4, though this is still far below the 3/4 maximum. Alternatively it is possible to use single photons for the cluster state method of one way quantum computation [5,6]. This can dramatically decrease the number of single photons sources required to perform a CNOT gate (from up to 10000 for KLM logic to 45 for the cluster approaches). The overhead here in single photon sources is large (but polynomial and hence still efficient in a sense). Can we however build near deterministic (or deterministic) linear optics gates with a low ...

We show that quantum computation circuits using coherent states as the logical qubits can be constructed from simple linear networks, conditional photon measurements and "small" coherent superposition resource states.

We describe a quantum repeater protocol for long-distance quantum communication. In this scheme, entanglement is created between qubits at intermediate stations of the channel by using a weak dispersive light-matter interaction and distributing the outgoing bright coherent light pulses among the stations. Noisy entangled pairs of electronic spin are then prepared with high success probability via homodyne detection and postselection. The local gates for entanglement purification and swapping are deterministic and measurement-free, based upon the same coherent-light resources and weak interactions as for the initial entanglement distribution. Finally, the entanglement is stored in a nuclear-spin-based quantum memory. With our system, qubit-communication rates approaching 100 Hz over 1280 km with fidelities near 99% are possible for reasonable local gate errors.PACS numbers: 03.67. Hk, 03.67.Mn, 42.50.Pq In a quantum repeater, long-distance entanglement is created by distributing entangled states over sufficiently short segments of a channel such that the noisy entangled states in each segment can be purified and connected via entanglement swapping [1,2]. The resulting entanglement between the qubits at distant stations can then be used, for example, to teleport quantum information [3] or transmit secret classical information [4]. Existing approaches to quantum repeaters generate entanglement using postselection with single-photon detection [5,6,7]. In these schemes, high-fidelity entanglement is created and the subsequent entanglement purification is needed primarily to compensate the degrading effect of connecting the imperfect entangled pairs via swapping. However, due to their rather low success probabilities in the initial entanglement distribution, these protocols feature very low communication rates.More efficient schemes, compatible with existing classical optical communication networks, would involve bright multi-photon signals. In this Letter, we propose such a scheme that operates in a regime of modest initial fidelities, but creates entangled states at high speed. The high rate in the generation of entangled pairs is mainly due to the near-unit efficiencies for the homodyne detection of bright signals, as opposed to the low efficiencies of single-photon detectors. In our scheme, the resulting entangled pairs will be discrete atomic qubit states, but the probe system we use is a bright light pulse described and measured via a continuous phase observable; hence, our quantum repeater is "hybrid" not only because it employs matter signals and light probes (as in other schemes), but more distinctly, by utilizing both discrete and continuous quantum variables.In general, in order to realize universal quantum computation or, more relevant to us here, long-distance quantum communication, a nonlinear element is needed for the implementation. Optically, this nonlinear element may be introduced in at least two possible ways. The first method uses only linear transformations, but a measurement-induced nonlinear...

During the past decade, research into superconducting quantum bits (qubits) based on Josephson junctions has made rapid progress. Many foundational experiments have been performed, and superconducting qubits are now considered one of the most promising systems for quantum information processing. However, the experimentally reported coherence times are likely to be insufficient for future large-scale quantum computation. A natural solution to this problem is a dedicated engineered quantum memory based on atomic and molecular systems. The question of whether coherent quantum coupling is possible between such natural systems and a single macroscopic artificial atom has attracted considerable attention since the first demonstration of macroscopic quantum coherence in Josephson junction circuits. Here we report evidence of coherent strong coupling between a single macroscopic superconducting artificial atom (a flux qubit) and an ensemble of electron spins in the form of nitrogen-vacancy colour centres in diamond. Furthermore, we have observed coherent exchange of a single quantum of energy between a flux qubit and a macroscopic ensemble consisting of about 3 × 10(7) such colour centres. This provides a foundation for future quantum memories and hybrid devices coupling microwave and optical systems.

We propose a quantum non-demolition method -giant Faraday rotation -to detect a single electron spin in a quantum dot inside a microcavity where negatively-charged exciton strongly couples to the cavity mode. Left-and right-circularly polarized light reflected from the cavity feels different phase shifts due to cavity quantum electrodynamics and the optical spin selection rule. This yields giant and tunable Faraday rotation which can be easily detected experimentally. Based on this spin-detection technique, a scalable scheme to create an arbitrary amount of entanglement between two or more remote spins via a single photon is proposed.PACS numbers: 78.67. Hc, 03.67.Mn, 42.50.Pq, 78.20.Ek Photons and spins hold great potential in quantum information science, especially for quantum communications, quantum information processing and quantum networks [1]. Photons are ideal candidates to transmit quantum information with little decoherence, whereas spins can be used to store and process quantum information due to their long coherence times. Therefore investigations of spin manipulation, spin detection, remote spin entanglement mediated by photons, and quantum state transfer between photons and spins are of great importance [2,3,4,5,6,7].Spin manipulation is well developed using pulsed magnetic resonance techniques, whereas single spin detection remains a challenging task. Electrical detection of single spin has been reported in a gate-defined quantum box [8,9] and in a silicon field-effect transistor [10]. The optically detected magnetic resonance technique (ODMR) proves to be an effective way to detect a single spin either in a single molecule [11,12] or a single N-V center in diamond [13]. However, the ODMR technique is based on the spin dependent fluorescence such that the spin is destroyed after detection. Recently, a non-demolition method to detect a single electron spin has been experimentally reported by Berezovsky et al [14] and Atatüre et al [15]. Both groups detect the tiny Faraday rotation angle induced by a single electron spin in a quantum dot (QD), so the measured signals (even enhanced by a cavity) are rather weak and noisy.It is widely accepted that entanglement is a useful resource in quantum information science. Recently remote entanglement between photons, trapped ions and atom ensembles have been demonstrated [16,17,18], however, all current experimental proposals for entangling two atoms are restricted to one entanglement bit rather than an arbitrary amount of entanglement [19,20]. To our knowledge, entanglement between remote single spins has not yet been achieved due to the lack of realizable proposals [21,22,23].In this Letter, we propose a quantum non-demolition method -giant Faraday rotation -to detect a single electron spin in a single QD inside a microcavity. The different phase shifts for the left and right circularly polarized light reflected from the QD-cavity system yields giant Faraday rotation which can be easily detected experimentally. This giant Faraday rotation induced by a sin...

Quantum error correction (QEC) and fault-tolerant quantum computation represent one of the most vital theoretical aspect of quantum information processing. It was well known from the early developments of this exciting field that the fragility of coherent quantum systems would be a catastrophic obstacle to the development of large scale quantum computers. The introduction of quantum error correction in 1995 showed that active techniques could be employed to mitigate this fatal problem. However, quantum error correction and fault-tolerant computation is now a much larger field and many new codes, techniques, and methodologies have been developed to implement error correction for large scale quantum algorithms. In response, we have attempted to summarize the basic aspects of quantum error correction and fault-tolerance, not as a detailed guide, but rather as a basic introduction. This development in this area has been so pronounced that many in the field of quantum information, specifically researchers who are new to quantum information or people focused on the many other important issues in quantum computation, have found it difficult to keep up with the general formalisms and methodologies employed in this area. Rather than introducing these concepts from a rigorous mathematical and computer science framework, we instead examine error correction and fault-tolerance largely through detailed examples, which are more relevant to experimentalists today and in the near future.