The physical implementation of quantum information processing relies on individual modules—qubits—and operations that modify such modules either individually or in groups—quantum gates. Two examples of gates that entangle pairs of qubits are the controlled NOT-gate (CNOT) gate, which flips the state of one qubit depending on the state of another, and the gate that brings a two-qubit product state into a superposition involving partially swapping the qubit states. Here we show that through supramolecular chemistry a single simple module, molecular {Cr7Ni} rings, which act as the qubits, can be assembled into structures suitable for either the CNOT or gate by choice of linker, and we characterize these structures by electron spin resonance spectroscopy. We introduce two schemes for implementing such gates with these supramolecular assemblies and perform detailed simulations, based on the measured parameters including decoherence, to demonstrate how the gates would operate.

Proposals for systems embodying condensed matter spin qubits cover a very wide range of length scales, from atomic defects in semiconductors all the way to micron-sized lithographically defined structures. Intermediate scale molecular components exhibit advantages of both limits: like atomic defects, large numbers of identical components can be fabricated; as for lithographically defined structures, each component can be tailored to optimise properties such as quantum coherence. Here we demonstrate what is perhaps the most potent advantage of molecular spin qubits, the scalability of quantum information processing structures using bottom-up chemical self-assembly. Using Cr 7 Ni spin qubit building blocks, we have constructed several families of two-qubit molecular structures with a range of linking strategies. For each family, long coherence times are preserved, and we demonstrate control over the inter-qubit quantum interactions that can be used to mediate two-qubit quantum gates. INTRODUCTIONAn information processing device whose elements are capable of storing and processing quantum superposition states (a quantum computer) would support algorithms for useful tasks such as searching 1 and factoring 2 that are much more efficient than the corresponding classical algorithms, 3 and would allow efficient simulation of other quantum systems. 4 One of the key challenges in realizing a quantum computer lies in identifying a physical system that hosts quantum states sufficiently coherently, and provides appropriate interactions for implementing logic operations.5 Among the molecular spin systems that have been proposed as qubit candidates are N@C 60, 6-9 organic radicals

We study the physical implementation of an optimal tomographic reconstruction scheme for the case of determining the state of a multi-qubit system, where trapped ions are used for defining qubits. The protocol is based on the use of mutually unbiased measurements and on the physical information described in H. Häffner et. al [Nature 438, 643-646 (2005)]. We introduce the concept of physical complexity for different types of unbiased measurements and analyze their generation in terms of one and two qubit gates for trapped ions.PACS numbers: 03.67. Lx, 03.65.Wj, A main task in any experimental physical setup for implementing quantum computation is the ability to determine the output state of any given quantum algorithm [1]. The standard procedure applied for quantum state reconstruction of a density operator lying in a 2 N dimensional quantum system, in the case of N qubits, consists in projecting the density operator onto 3 N , completely factorized, bases in the corresponding Hilbert space [2]. All these measurements are obtained by applying rotations on single qubits (which are referred to as local operations) followed by projective measurements onto the logical basis. This was recently achieved for the case of eight qubits, with trapped ions [3]. The experiment was done by following the quantum computer architecture based on ions in a linear trap proposed by Cirac and Zoller [4]. Besides, the experimental implementations of several quantum protocols have also been reported by using trapped ions [5]. In all these cases the quality of the protocols is tested using standard tomography for quantum state determination. This scheme has also been used in the cases of considering optical setups [6] and NMR [7].As it was mentioned above, in the standard measurement scheme only local operations are required to generate all the necessary projections. In each basis (setup) 2 N − 1 independent measurements can be performed, so that not all the experimental outcomes obtained in different bases are linearly independent, that is, there are redundant measurements. In the case of a N -qubit system the anti-diagonal elements have the larger errors. Actually, accumulated errors are not uniform; these errors depend on the number of single logic gates used for determining given elements, so that larger errors appear when single logic gates act on all the particles. Assuming that there is an error ε in the measurement of ion populations, then the accumulated error for anti-diagonal elements is of the order of ε 2 N −1 + 2 N −2 (2 N − 1). These errors may lead to a density operator which does not satisfy the positiveness condition and so the information from the experimental data must be optimized. For this purpose the maximum likelihood estimation (MLE) method [8] has been used for the improvement of the density operators in experiments with light qubits [9] as well as in experiments with matter qubits [5].It is well known that the optimal quantum state determination is related to the concept of measurements on Mutually Unbiased Bas...

Quantum information processing (QIP) would require that the individual units involved—qubits—communicate to other qubits while retaining their identity. In many ways this resembles the way supramolecular chemistry brings together individual molecules into interlocked structures, where the assembly has one identity but where the individual components are still recognizable. Here a fully modular supramolecular strategy has been to link hybrid organic–inorganic [2]- and [3]-rotaxanes into still larger [4]-, [5]- and [7]-rotaxanes. The ring components are heterometallic octanuclear [Cr7NiF8(O2CtBu)16]– coordination cages and the thread components template the formation of the ring about the organic axle, and are further functionalized to act as a ligand, which leads to large supramolecular arrays of these heterometallic rings. As the rings have been proposed as qubits for QIP, the strategy provides a possible route towards scalable molecular electron spin devices for QIP. Double electron–electron resonance experiments demonstrate inter-qubit interactions suitable for mediating two-qubit quantum logic gates.

Supramolecular Coordination Compounds (SCCs) represent the power of Coordination Chemistry methodologies to self-assemble discrete architectures with targeted properties. SCCs are generally synthesised in solution, with isolated fully-coordinated metal atoms as structural nodes, thus severely limited as metal-based catalysts. Metal-Organic Frameworks (MOFs) show unique features to act as chemical nanoreactors for the in-situ synthesis and stabilization of otherwise not accessible functional species. Here, we present the self-assembly of Pd II SCCs within the confined space of a preformed MOF (SCCs@MOF) and its post-assembly metalation to give a Pd II -Au III supramolecular assembly, crystallography underpinned. These SCCs@MOF catalyse the coupling of boronic acids and/or alkynes, representative multisite metallic-catalysed reactions in which traditional SCCs tend to decompose, and retain its structural integrity as consequence of the synergetic hybridization between SCCs and MOF. These results open new avenues in both the synthesis of novel SCCs and their use on heterogeneous metal-based Supramolecular Catalysis.

Many protocols in atomic physics and quantum information hinge on the ability to detect the presence of neutral atoms 1-4. Up to now, two avenues have been favoured: the direct detection of spontaneously emitted photons using high-quality optics 5-7 , or the observation of changes in light transmission through cavity mirrors due to strong atom-photon coupling 8-11. Here, we present an approach that combines these two methods by detecting an atom in a driven cavity mode through the collection of spontaneous emission and forward scattering into an undriven, orthogonally polarized cavity mode. Moderate atom-cavity coupling enhances the signal, enabling the detection of multiple photons from the same atom. This real-time measurement can establish the presence of a single freely moving atom in less than 1 µs with more than 99.7% confidence, using coincidence measurements to decrease the rate of false detections. Direct detection of single atoms and molecules through the collection of resonance fluorescence requires excellent optics, very good background rejection and typical integration times of tens of milliseconds, even for trapped atoms 5-7. Faster results are possible with fluorescence burst detection 12 , which looks for above-average count rates over short time intervals 13,14 ; a recent example 15 showed detection of freely falling atoms in 60 µs using highly efficient mirrors and lenses. Alternatively, one can collect fluorescence in an optical cavity with the axis perpendicular to the driving laser, gaining the benefit of Purcell-enhanced emission into the cavity mode 9-11. Experiments based on changes in cavity transmission, which require strong atom-cavity coupling 8 , have achieved singleatom detection times of 20 µs for moving atoms 16,17 , and as low as 10 µs for trapped atoms 18,19. All of these techniques gather data (photon flux) until a targeted confidence level is reached: detection of fluorescence requires the building up of a signal against background, whereas detection through cavity transmission requires the averaging of shot noise until a change in intensity level is discernible. The resultant signalto-noise and signal-to-background ratios set the probability of obtaining a false positive for atom detection. Here, we present a new approach that achieves high-fidelity single-atom detection in a short time. We use a cavity with two modes of orthogonal linear polarization (H and V), while driving the cavity on-axis with light of only one of these polarizations (H), a technique introduced in ref. 20. With a weak magnetic field set parallel to the incident polarization, the light drives π (m = 0) transitions in 85 Rb atoms traversing the cavity mode. An excited atom can return to the ground state in one of two ways: by emitting light of the same polarization (H) through a spontaneous or stimulated emission transition that preserves

Hybrid [2]rotaxanes and pseudorotaxanes are reported where the magnetic interaction between dissimilar spins is controlled to create AB and AB2 electron spin systems, allowing independent control of weakly interacting S=${{ 1/2 }}$ centers.

A (1)H NMR analytical protocol for the detection of refined hazelnut oils in admixtures with refined olive oils is reported according to ISO format. The main purpose of this research activity is to suggest a novel analytical methodology easily usable by operators with a basic knowledge of NMR spectroscopy. The protocol, developed on 92 oil samples of different origins within the European MEDEO project, is based on (1)H NMR measurements combined with a suitable statistical analysis. It was developed using a 600 MHz instrument and was tested by two independent laboratories on 600 MHz spectrometers, allowing detection down to 10% adulteration of olive oils with refined hazelnut oils. Finally, the potential and limitations of the protocol applied on spectrometers operating at different magnetic fields, that is, at the proton frequencies of 500 and 400 MHz, were investigated.