Linear optics with photon counting is a prominent candidate for practical quantum computing. The protocol by Knill, Laflamme, and Milburn [2001, Nature (London) 409, 46] 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.

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Linear optical quantum computing with photonic qubits

Quantum mechanics---the theory describing the fundamental workings of nature---is famously counterintuitive: it predicts that a particle can be in two places at the same time, and that two remote particles can be inextricably and instantaneously linked These predictions have been the topic of intense metaphysical debate ever since the theory's inception early last century However, supreme predictive power combined with direct experimental observation of some of these unusual phenomena leave little doubt as to its fundamental correctness In fact, without quantum mechanics we could not explain the workings of a laser, nor indeed how a fridge magnet operates Over the last several decades quantum information science has emerged to seek answers to the question: can we gain some advantage by storing, transmitting and processing information encoded in systems that exhibit these unique quantum properties? Today it is understood that the answer is yes Many research groups around the world are working towards one of the most ambitious goals humankind has ever embarked upon: a quantum computer that promises to exponentially improve computational power for particular tasks A number of physical systems, spanning much of modern physics, are being developed for this task---ranging from single particles of light to superconducting circuits---and it is not yet clear which, if any, will ultimately prove successful Here we describe the latest developments for each of the leading approaches and explain what the major challenges are for the future

Quantum Computing

"Quantum sensing" describes the use of a quantum system, quantum properties or quantum phenomena to perform a measurement of a physical quantity Historical examples of quantum sensors include magnetometers based on superconducting quantum interference devices and atomic vapors, or atomic clocks More recently, quantum sensing has become a distinct and rapidly growing branch of research within the area of quantum science and technology, with the most common platforms being spin qubits, trapped ions and flux qubits The field is expected to provide new opportunities - especially with regard to high sensitivity and precision - in applied physics and other areas of science In this review, we provide an introduction to the basic principles, methods and concepts of quantum sensing from the viewpoint of the interested experimentalist

Quantum sensing

Magnetic resonance imaging and optical microscopy are key technologies in the life sciences. For microbiological studies, especially of the inner workings of single cells, optical microscopy is normally used because it easily achieves resolution close to the optical wavelength. But in conventional microscopy, diffraction limits the resolution to about half the wavelength. Recently, it was shown that this limit can be partly overcome by nonlinear imaging techniques, but there is still a barrier to reaching the molecular scale. In contrast, in magnetic resonance imaging the spatial resolution is not determined by diffraction; rather, it is limited by magnetic field sensitivity, and so can in principle go well below the optical wavelength. The sensitivity of magnetic resonance imaging has recently been improved enough to image single cells, and magnetic resonance force microscopy has succeeded in detecting single electrons and small nuclear spin ensembles. However, this technique currently requires cryogenic temperatures, which limit most potential biological applications. Alternatively, single-electron spin states can be detected optically, even at room temperature in some systems. Here we show how magneto-optical spin detection can be used to determine the location of a spin associated with a single nitrogen-vacancy centre in diamond with nanometre resolution under ambient conditions. By placing these nitrogen-vacancy spins in functionalized diamond nanocrystals, biologically specific magnetofluorescent spin markers can be produced. Significantly, we show that this nanometre-scale resolution can be achieved without any probes located closer than typical cell dimensions. Furthermore, we demonstrate the use of a single diamond spin as a scanning probe magnetometer to map nanoscale magnetic field variations. The potential impact of single-spin imaging at room temperature is far-reaching. It could lead to the capability to probe biologically relevant spins in living cells.

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Nanoscale imaging magnetometry with diamond spins under ambient conditions

The nitrogen-vacancy (NV) colour centre in diamond is an important physical system for emergent quantum technologies, including quantum metrology, information processing and communications, as well as for various nanotechnologies, such as biological and sub-diffraction limit imaging, and for tests of entanglement in quantum mechanics. Given this array of existing and potential applications and the almost 50 years of NV research, one would expect that the physics of the centre is well understood, however, the study of the NV centre has proved challenging, with many early assertions now believed false and many remaining issues yet to be resolved. This review represents the first time that the key empirical and ab initio results have been extracted from the extensive NV literature and assembled into one consistent picture of the current understanding of the centre. As a result, the key unresolved issues concerning the NV centre are identified and the possible avenues for their resolution are examined.

The nitrogen-vacancy colour centre in diamond

The fluorescence of individual nitrogen-vacancy defect centers in diamond was observed with room-temperature scanning confocal optical microscopy. The centers were photostable, showing no detectable change in their fluorescence emission spectrum as a function of time. Magnetic resonance on single centers at room temperature was shown to be feasible. The magnetic resonance spectra revealed marked changes in zero-field splitting parameters among different centers. These changes were attributed to strain-induced differences in the symmetry of the centers.

http://science.sciencemag.org/content/sci/276/5321/2012.full.pdf

Scanning confocal optical microscopy and magnetic resonance on single defect centers

Individual paramagnetic defect centers in diamond nanocrystals have been investigated by low-temperature high-resolution optical spectroscopy. Narrow fluorescence excitation spectral lines have been found, indicating transitions between individual spin sublevels. Spectral diffusion is explained by cross relaxation among spin sublevels and by the presence of excited electrons in the conduction band of diamond. The relaxation times are in the millisecond range. The system may be useful for quantum information processing with individual electron spins.

Single spin states in a defect center resolved by optical spectroscopy

In this paper we present a detailed comparison of experimentally observed modifications of the emission behavior of dye molecules embedded in colloidal photonic crystals with corresponding theoretical calculations of the optical mode density. For this purpose, angle-resolved measurements of emission spectra and time-resolved measurements were performed with a high spatial resolution using a confocal microscopy setup. The spectra reveal a strongly modified radiation pattern, including a highly directional fourfold intensity enhancement at the high frequency edge of the photonic stop band, while the radiative lifetime is only slightly affected. For the first time these experimental results are quantitatively compared to theoretical predictions based on calculations of the angle-dependent local density of optical states. It is demonstrated that the observed modifications can be explained by a spectral and angular redistribution of the optical mode density inside the photonic crystal, suggesting an altered radiation probability of the dye molecules for certain frequencies and directions. Furthermore, our calculations reveal a strong dependence of these modifications on the exact location of the dye molecules within the photonic crystal.

Spectral and angular redistribution of photoluminescence near a photonic stop band

Performing fluorescence wide-field microscopy we have imaged single semiconductor quantum dots deep inside a 3-dimensional photonic crystal prepared from colloidal polymer beads. Exploring the emission diffraction patterns in defocused images of quantum dots we demonstrate that the direction-dependent photonic stop band imprints an anisotropy to the angular emission of a single quantum dot. Hence a single, quasi-point-like emitter is manipulated to radiate its photons only to certain well-defined directions by means of the anisotropic light propagation in photonic crystals. The experiments thus provide new routes to evaluate local, frequency selective optical properties in 3-dimensional photonic crystals employing single emitters.

A. Gruber

Papers

Scanning confocal optical microscopy and magnetic resonance on single defect centers

Single spin states in a defect center resolved by optical spectroscopy

Spectral and angular redistribution of photoluminescence near a photonic stop band

Imaging single quantum dots in three-dimensional photonic crystals.

Magnetic resonance on single nuclei