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The nitrogen-vacancy (NV) centre in diamond has emerged as a candidate to non-invasively hyperpolarise nuclear spins in molecular systems to improve the sensitivity of nuclear magnetic resonance (NMR) experiments. Several promising proof of principle experiments have demonstrated small-scale polarisation transfer from single NVs to hydrogen spins outside the diamond. However, the scaling up of these results to the use of a dense NV ensemble, which is a necessary prerequisite for achieving realistic NMR sensitivity enhancement, has not yet been demonstrated. In this work, we present evidence for a polarising interaction between a shallow NV ensemble and external nuclear targets over a micrometre scale, and characterise the challenges in achieving useful polarisation enhancement. In the most favourable example of the interaction with hydrogen in a solid state target, a maximum polarisation transfer rate of $\approx 7500$ spins per second per NV is measured, averaged over an area containing order $10^6$ NVs. Reduced levels of polarisation efficiency are found for liquid state targets, where molecular diffusion limits the transfer. Through analysis via a theoretical model, we find that our results suggest implementation of this technique for NMR sensitivity enhancement is feasible following realistic diamond material improvements.

There are two important, and potentially interconnecting, avenues to the realisation of large-scale quantum algorithms: improvement of the hardware, and reduction of resource requirements demanded by algorithm components. In focusing on the latter, one crucial subroutine to many sought-after applications is the quantum adder. A variety of different implementations exist with idiosyncratic pros and cons. One of these, the Draper quantum Fourier adder, offers the lowest qubit count of any adder, but requires a substantial number of gates as well as extremely fine rotations. In this work, we present a modification of the Draper adder which eliminates small-angle rotations to highly coarse levels, matched with some strategic corrections. This reduces hardware requirements without sacrificing the qubit saving. We show that the inherited loss of fidelity is directly given by the rate of carry and borrow bits in the computation. We derive formulae to predict this, complemented by complete gate-level matrix product state simulations of the circuit. Moreover, we analytically describe the effects of possible stochastic control error. We present an in-depth analysis of this approach in the context of Shor's algorithm, focusing on the factoring of RSA-2048. Surprisingly, we find that each of the $7\times 10^7$ quantum Fourier transforms may be truncated down to $\pi/64$, with additive rotations left only slightly finer. This result is much more efficient than previously realised. We quantify savings both in terms of logical resources and raw magic states, demonstrating that phase adders can be competitive with Toffoli-based constructions., Comment: Main text 18 pages, 8 figures. SI 11 pages, 7 figures

Dynamic nuclear polarisation (DNP) refers to a class of techniques used to increase the signal in nuclear magnetic resonance measurements by transferring spin polarisation from ensembles of highly polarised electrons to target nuclear analytes. These techniques, however, require the application of strong magnetic fields to maximise electron spin polarisation, limiting pathways for electron-nuclear (hyperfine) spin coupling and transfer. In this work we show that, for systems of electronic spin $S\geq1$ possessing an intrinsic zero-field splitting, a separate class of stronger hyperfine interactions based on lab-frame cross relaxation may be utilised to improve DNP efficiency and yield, whilst operating at moderate fields. We analytically review existing methods, and determine that this approach increases the rate of polarisation transfer to the nuclear ensemble by up to an order of magnitude over existing techniques. This result is demonstrated experimentally at room temperature using the optically polarisable $S=1$ electron spin system of the nitrogen vacancy (NV) defect in diamond as the source of electron spin polarisation. Finally we assess the utility of these NV-based approaches for the polarisation of macroscopic quantities of molecular spins external to the diamond for NMR and MRI applications., 18 pages, 7 figures

We demonstrate locally coherent heteroepitaxial growth of silicon carbide (SiC) on diamond, a result contrary to current understanding of heterojunctions as the lattice mismatch exceeds $20\%$. High-resolution transmission electron microscopy (HRTEM) confirms the quality and atomic structure near the interface. Guided by molecular dynamics simulations, a theoretical model is proposed for the interface wherein the large lattice strain is alleviated via point dislocations in a two-dimensional plane without forming extended defects in three dimensions. The possibility of realising heterojunctions of technologically important materials such as SiC with diamond offers promising pathways for thermal management of high power electronics. At a fundamental level, the study redefines our understanding of heterostructure formation with large lattice mismatch., 16 pages, 4 figures

Quantum sensors based on optically active defects in diamond such as the nitrogen vacancy (NV) centre represent a promising platform for nanoscale sensing and imaging of magnetic, electric, temperature and strain fields. Enhancing the optical interface to such defects is key to improving the measurement sensitivity of these systems. Photonic nanostructures are often employed in the single emitter regime for this purpose, but their applicability to widefield sensing with NV ensembles remains largely unexplored. Here we fabricate and characterize closely-packed arrays of diamond nanopillars, each hosting its own dense, near-surface ensemble of NV centres. We explore the optimal geometry for diamond nanopillars hosting NV ensembles and realise enhanced spin and photoluminescence properties which lead to increased measurement sensitivities (greater than a factor of 3) when compared to unpatterned surfaces. Utilising the increased measurement sensitivity, we image the mechanical stress tensor in each nanopillar across the arrays and show the fabrication process has negligible impact on in-built stress compared to the unpatterned surface. Our results demonstrate that photonic nanostructuring of the diamond surface is a viable strategy for increasing the sensitivity of ensemble-based widefield sensing and imaging., 7 pages, 4 figures

The precise measurement of mechanical stress at the nanoscale is of fundamental and technological importance. In principle, all six independent variables of the stress tensor, which describe the direction and magnitude of compression/tension and shear stress in a solid, can be exploited to tune or enhance the properties of materials and devices. However, existing techniques to probe the local stress are generally incapable of measuring the entire stress tensor. Here, we make use of an ensemble of atomic-sized in-situ strain sensors in diamond (nitrogen-vacancy defects) to achieve spatial mapping of the full stress tensor, with a sub-micrometer spatial resolution and a sensitivity of the order of 1 MPa (corresponding to a strain of less than $10^{-6}$). To illustrate the effectiveness and versatility of the technique, we apply it to a broad range of experimental situations, including mapping the elastic stress induced by localized implantation damage, nano-indents and scratches. In addition, we observe surprisingly large stress contributions from functional electronic devices fabricated on the diamond, and also demonstrate sensitivity to deformations of materials in contact with the diamond. Our technique could enable in-situ measurements of the mechanical response of diamond nanostructures under various stimuli, with potential applications in strain engineering for diamond-based quantum technologies and in nanomechanical sensing for on-chip mass spectroscopy., Comment: 20 pages including SI

Ultra-scaled FinFET transistors bear unique fingerprint-like device-to-device differences attributed to random single impurities. This paper describes how, through correlation of experimental data with multimillion atom tight-binding simulations using the NEMO 3-D code, it is possible to identify the impurity's chemical species and determine their concentration, local electric field and depth below the Si/SiO$_{\mathrm{2}}$ interface. The ability to model the excited states rather than just the ground state is the critical component of the analysis and allows the demonstration of a new approach to atomistic impurity metrology., 6 pages, 3 figures

The ground state spin of the negatively charged nitrogen-vacancy center in diamond has been the platform for the recent rapid expansion of new frontiers in quantum metrology and solid state quantum information processing. In ambient conditions, the spin has been demonstrated to be a high precision magnetic and electric field sensor as well as a solid state qubit capable of coupling with nearby nuclear and electronic spins. However, in spite of its many outstanding demonstrations, the theory of the spin has not yet been fully developed and there does not currently exist thorough explanations for many of its properties, such as the anisotropy of the electron g-factor and the existence of Stark effects and strain splittings. In this work, the theory of the ground state spin is fully developed for the first time using the molecular orbital theory of the center in order to provide detailed explanations for the spin's fine and hyperfine structures and its interactions with electric, magnetic and strain fields., 12 pages, 3 figures, 3 tables

Recent work on fault-tolerant quantum computation making use of topological error correction shows great potential, with the 2d surface code possessing a threshold error rate approaching 1% (NJoP 9:199, 2007), (arXiv:0905.0531). However, the 2d surface code requires the use of a complex state distillation procedure to achieve universal quantum computation. The colour code of (PRL 97:180501, 2006) is a related scheme partially solving the problem, providing a means to perform all Clifford group gates transversally. We review the colour code and its error correcting methodology, discussing one approximate technique based on graph matching. We derive an analytic lower bound to the threshold error rate of 6.25% under error-free syndrome extraction, while numerical simulations indicate it may be as high as 13.3%. Inclusion of faulty syndrome extraction circuits drops the threshold to approximately 0.1%., 20 pages, 19 figures

We describe how the effect of charge noise on a pair of spins coupled via the exchange interaction can be calculated by modelling charge fluctuations as a random telegraph noise process using probability density functions. We develop analytic expressions for the time dependent superoperator of a pair of spins as a function of fluctuation amplitude and rate. We show that the theory can be extended to include multiple fluctuators, in particular, spectral distributions of fluctuators. These superoperators can be included in time dependent analyses of the state of spin systems designed for spintronics or quantum information processing to determine the decohering effects of exchange fluctuations., 7 pages, 2 figures

The surface code scheme for quantum computation features a 2d array of nearest-neighbor coupled qubits yet claims a threshold error rate approaching 1% (NJoP 9:199, 2007). This result was obtained for the toric code, from which the surface code is derived, and surpasses all other known codes restricted to 2d nearest-neighbor architectures by several orders of magnitude. We describe in detail an error correction procedure for the toric and surface codes, which is based on polynomial-time graph matching techniques and is efficiently implementable as the classical feed-forward processing step in a real quantum computer. By direct simulation of this error correction scheme, we determine the threshold error rates for the two codes (differing only in their boundary conditions) for both ideal and non-ideal syndrome extraction scenarios. We verify that the toric code has an asymptotic threshold of p = 15.5% under ideal syndrome extraction, and p = 7.8 10^-3 for the non-ideal case, in agreement with prior work. Simulations of the surface code indicate that the threshold is close to that of the toric code., Comment: 14 pages, 11 figures

Electromagnetically induced transparency (EIT) has been often proposed for generating nonlinear optical effects at the single photon level; in particular, as a means to effect a quantum non-demolition measurement of a single photon field. Previous treatments have usually considered homogeneously broadened samples, but realisations in any medium will have to contend with inhomogeneous broadening. Here we reappraise an earlier scheme [Munro \textit{et al.} Phys. Rev. A \textbf{71}, 033819 (2005)] with respect to inhomogeneities and show an alternative mode of operation that is preferred in an inhomogeneous environment. We further show the implications of these results on a potential implementation in diamond containing nitrogen-vacancy colour centres. Our modelling shows that single mode waveguide structures of length $200 \mu\mathrm{m}$ in single-crystal diamond containing a dilute ensemble of NV$^-$ of only 200 centres are sufficient for quantum non-demolition measurements using EIT-based weak nonlinear interactions., Comment: 21 pages, 9 figures (some in colour) at low resolution for arXiv purposes

We demonstrate how using two-qubit composite rotations a high fidelity controlled-NOT (CNOT) gate can be constructed, even when the strength of the interaction between qubits is not accurately known. We focus on the exchange interaction oscillation in silicon based solid-state architectures with a Heisenberg Hamiltonian. This method easily applies to a general two-qubit Hamiltonian. We show how the robust CNOT gate can achieve a very high fidelity when a single application of the composite rotations is combined with a modest level of Hamiltonian characterisation. Operating the robust CNOT gate in a suitably characterised system means concatenation of the composite pulse is unnecessary, hence reducing operation time, and ensuring the gate operates below the threshold required for fault-tolerant quantum computation., Comment: 9 pages, 8 figures

By taking into account the physical nature of quantum errors it is possible to improve the efficiency of quantum error correction. Here we consider an optimisation to conventional quantum error correction which involves exploiting asymmetries in the rates of X and Z errors by reducing the rate of X correction. As an example, we apply this optimisation to the [[7,1,3]] code and make a comparison with conventional quantum error correction. After two levels of concatenated error correction we demonstrate a circuit depth reduction of at least 43% and reduction in failure rate of at least 67%. This improvement requires no additional resources and the required error asymmetry is likely to be present in most physical quantum computer architectures., Comment: 8 pages, 4 figures

Classically it is impossible to have transport without transit, i.e., if the points one, two and three lie sequentially along a path then an object moving from one to three must, at some point in time, be located at two. However, for a quantum particle in a three-well system it is possible to transport the particle between wells one and three such that the probability of finding it at any time in the classically accessible state in well two is negligible. We consider theoretically the analogous scenario for a Bose-Einstein condensate confined within a three well system. In particular, we predict the adiabatic transportation of an interacting Bose-Einstein condensate of 2000 Li atoms from well one to well three without transiting the allowed intermediate region. To an observer of this macroscopic quantum effect it would appear that, over a timescale of the order of one second, the condensate had transported, but not transited, a macroscopic distance of 20 microns between wells one and three., Comment: 6 pages, 4 figures

Quantum error correction and fault-tolerant quantum computation are two fundamental concepts which make quantum computing feasible. While providing a theoretical means with which to ensure the arbitrary accuracy of any quantum circuit, fault-tolerant error correction is predicated upon the robust preparation of logical states. An optimal direct circuit and a more complex fault-tolerant circuit for the preparation of the [[7,1,3]] Steane logical-zero are simulated in the presence of discrete quantum errors to quantify the regime within which fault-tolerant preparation of logical states is preferred., Comment: 8 pages, 2 figures

We present a theoretical analysis of a microwave spectroscopy experiment on a charge qubit defined by a P$_2^+$ donor pair in silicon, for which we calculate Hamiltonian parameters using the effective-mass theory of shallow donors. We solve the master equation of the driven system in a dissipative environment to predict experimental outcomes. We describe how to calculate physical parameters of the system from such experimental results, including the dephasing time, $T_2$, and the ratio of the resonant Rabi frequency to the relaxation rate. Finally we calculate probability distributions for experimentally relevant system parameters for a particular fabrication regime.

Through the introduction of a new electron spin transport mechanism, a 2D donor electron spin quantum computer architecture is proposed. This design addresses major technical issues in the original Kane design, including spatial oscillations in the exchange coupling strength and cross-talk in gate control. It is also expected that the introduction of a degree of non-locality in qubit gates will significantly improve the scaling fault-tolerant threshold over the nearest-neighbour linear array., 4 pages, 5 figures, v2 reference added

We report a nanofabrication, control and measurement scheme for charge-based silicon quantum computing which utilises a new technique of controlled single ion implantation. Each qubit consists of two phosphorus dopant atoms ~50 nm apart, one of which is singly ionized. The lowest two energy states of the remaining electron form the logical states. Surface electrodes control the qubit using voltage pulses and dual single electron transistors operating near the quantum limit provide fast readout with spurious signal rejection. A low energy (keV) ion beam is used to implant the phosphorus atoms in high-purity Si. Single atom control during the implantation is achieved by monitoring on-chip detector electrodes, integrated within the device structure, while positional accuracy is provided by a nanomachined resist mask. We describe a construction process for implanted single atom and atom cluster devices with all components registered to better than 20 nm, together with electrical characterisation of the readout circuitry. We also discuss universal one- and two-qubit gate operations for this architecture, providing a possible path towards quantum computing in silicon., 9 pages, 5 figures

We examine a stochastic noise process that has a decohering effect on the average evolution of qubits in the quantum register of the solid state quantum computer proposed by Kane. We consider the effects of this process on the single qubit operations necessary to perform quantum logical gates and derive an expression for the fidelity of these gates in this system. We then calculate an upper bound on the level of this stochastic noise tolerable in a workable quantum computer.

We develop the formalism for calculating arbitrary expectation values for any extensive lattice Hamiltonian system using a new analytic Lanczos expansion, or plaquette expansion, and a recently proved exact theorem for ground state energies. The ground state energy, staggered magnetisation and the excited state gap of the 2D anisotropic antiferromagnetic Heisenberg Model are then calculated using this expansion for a range of anisotropy parameters and compared to other moment based techniques, such as the "t"-expansion, and spin-wave theory and series expansion methods. We find that far from the isotropic point all moment methods give essentially very similar results, but near the isotropic point the plaquette expansion is generally better than the others., 15 pages, Latex + RevTex, to appear in Phys. Rev. B