GASP: a genetic algorithm for state preparation on quantum computers.

The efficient preparation of quantum states is an important step in the execution of many quantum algorithms. In the noisy intermediate-scale quantum (NISQ) computing era, this is a significant challenge given quantum resources are scarce and typically only low-depth quantum circuits can be implemented on physical devices. We present a genetic algorithm for state preparation (GASP) which generates relatively low-depth quantum circuits for initialising a quantum computer in a specified quantum state. The method uses a basis set of [Formula: see text], [Formula: see text], [Formula: see text], and CNOT gates and a genetic algorithm to systematically generate circuits to synthesize the target state to the required fidelity. GASP can produce more efficient circuits of a given accuracy with lower depth and gate counts than other methods. This variability of the required accuracy facilitates overall higher accuracy on implementation, as error accumulation in high-depth circuits can be avoided. We directly compare the method to the state initialisation technique based on an exact synthesis technique by implemented in IBM Qiskit simulated with noise and implemented on physical IBM Quantum devices. Results achieved by GASP outperform Qiskit's exact general circuit synthesis method on a variety of states such as Gaussian states and W-states, and consistently show the method reduces the number of gates required for the quantum circuits to generate these quantum states to the required accuracy.

Quantum computing: a new paradigm for ecology.

A global technology arms race is underway to build evermore powerful and precise quantum computers. Quantum computers have the potential to tackle certain quantitative problems quicker than classical computers. The current focus of quantum computing is on pushing the boundaries of fundamental quantum information and commercial applications in industrial sectors, financial services, and other profit-led sectors, particularly where improvements in optimisation and sampling can improve increased economic return. We believe that ecologists could exploit the computational power of quantum computers because the statistical approaches commonly used in ecology already have proven pathways on quantum computers. Moreover, quantum computing could ultimately leapfrog our understanding of complex ecological systems, if the hardware, opportunity, and creativity of quantitative ecologists all align.

Nonmonotonic Superparamagnetic Behavior of the Ferritin Iron Core Revealed via Quantum Spin Relaxometry.

Ferritin is the primary storage protein in our body and is of significant interest in biochemistry, nanotechnology, and condensed matter physics. More specifically within this sphere of interest are the magnetic properties of the iron core of ferritin, which have been utilized as a contrast agent in applications such as magnetic resonance imaging. This magnetism depends on both the number of iron atoms present, L, and the nature of the magnetic ordering of their electron spins. In this work, we create a series of ferritin samples containing homogeneous iron loads and apply diamond-based quantum spin relaxometry to systematically study their room temperature magnetic properties. We observe anomalous magnetic behavior that can be explained using a theoretical model detailing a morphological change to the iron core occurring at relatively low iron loads. This model provides an L0.35±0.06 scaling of the uncompensated Fe spins, in agreement with previous theoretical predictions. The necessary inclusion of this morphological change within the model is also supported by electron microscopy studies of ferritin with low iron content. This provides evidence for a magnetic consequence of this morphological change and positions diamond-based quantum spin relaxometry as an effective, noninvasive tool for probing the magnetic properties of metalloproteins. The low detection limit (ferritin 2% loaded at a concentration of 7.5 ± 0.4 µg/mL) also makes this a promising method for precision applications where low analyte concentrations are unavoidable, such as in biological research or even clinical analysis.

Varied Magnetic Phases in a van der Waals Easy-Plane Antiferromagnet Revealed by Nitrogen-Vacancy Center Microscopy.

Interest in van der Waals materials often stems from a desire to miniaturize existing technologies by exploiting their intrinsic layered structures to create near-atomically thin components that do not suffer from surface defects. One appealing property is an easily switchable yet robust magnetic order, which is only sparsely demonstrated in the case of in-plane anisotropy. In this work, we use widefield nitrogen-vacancy (NV) center magnetic imaging to measure the properties of individual flakes of CuCrP2S6, a multiferroic van der Waals magnet known to exhibit weak easy-plane anisotropy in the bulk. We chart the crossover between the in-plane ferromagnetism in thin flakes down to the trilayer and the bulk behavior dominated by a low-field spin-flop transition. Further, by exploiting the directional dependence of NV center magnetometry, we are able to observe an instance of a predominantly out-of-plane ferromagetic phase near zero field, in contrast with our expectation and previous experiments on the bulk material. We attribute this to the presence of surface anisotropies caused by the sample preparation process or exposure to the ambient environment, which is expected to have more general implications for a broader class of weakly anisotropic van der Waals magnets.

Chemistry beyond the Hartree-Fock energy via quantum computed moments.

Quantum computers hold promise to circumvent the limitations of conventional computing for difficult molecular problems. However, the accumulation of quantum logic errors on real devices represents a major challenge, particularly in the pursuit of chemical accuracy requiring the inclusion of electronic correlation effects. In this work we implement the quantum computed moments (QCM) approach for hydrogen chain molecular systems up to H[Formula: see text]. On a superconducting quantum processor, Hamiltonian moments, [Formula: see text] are computed with respect to the Hartree-Fock state, which are then employed in Lanczos expansion theory to determine an estimate for the ground-state energy which incorporates electronic correlations and manifestly improves on the direct energy measurement. Post-processing purification of the raw QCM data takes the estimate below the Hartree-Fock energy to within 99.9% of the exact electronic ground-state energy for the largest system studied, H[Formula: see text]. Calculated dissociation curves indicate precision at about 10mH for this system and as low as 0.1mH for molecular hydrogen, H[Formula: see text], over a range of bond lengths. In the context of stringent precision requirements for chemical problems, these results provide strong evidence for the error suppression capability of the QCM method, particularly when coupled with post-processing error mitigation. While calculations based on the Hartree-Fock state are tractable to classical computation, these results represent a first step towards implementing the QCM method in a quantum chemical trial circuit. Greater emphasis on more efficient representations of the Hamiltonian and classical preprocessing steps may enable the solution of larger systems on near-term quantum processors.

Quantum magnetic imaging of iron organelles within the pigeon cochlea.

The ability of pigeons to sense geomagnetic fields has been conclusively established despite a notable lack of determination of the underlying biophysical mechanisms. Quasi-spherical iron organelles previously termed "cuticulosomes" in the cochlea of pigeons have potential relevance to magnetoreception due to their location and iron composition; however, data regarding the magnetic susceptibility of these structures are currently limited. Here quantum magnetic imaging techniques are applied to characterize the magnetic properties of individual iron cuticulosomes in situ. The stray magnetic fields emanating from cuticulosomes are mapped and compared to a detailed analytical model to provide an estimate of the magnetic susceptibility of the individual particles. The images reveal the presence of superparamagnetic and ferrimagnetic domains within individual cuticulosomes and magnetic susceptibilities within the range 0.029 to 0.22. These results provide insights into the elusive physiological roles of cuticulosomes. The susceptibilities measured are not consistent with a torque-based model of magnetoreception, placing iron storage and stereocilia stabilization as the two leading putative cuticulosome functions. This work establishes quantum magnetic imaging as an important tool to complement the existing array of techniques used to screen for potential magnetic particle-based magnetoreceptor candidates.

Long-Range Surface-Assisted Molecule-Molecule Hybridization.

Metalated phthalocyanines (Pc's) are robust and versatile molecular complexes, whose properties can be tuned by changing their functional groups and central metal atom. The electronic structure of magnesium Pc (MgPc)-structurally and electronically similar to chlorophyll-adsorbed on the Ag(100) surface is investigated by low-temperature scanning tunneling microscopy and spectroscopy, non-contact atomic force microscopy, and density functional theory. Single, isolated MgPc's exhibit a flat, fourfold rotationally symmetric morphology, with doubly degenerate, partially populated (due to surface-to-molecule electron transfer) lowest unoccupied molecular orbitals (LUMOs). In contrast, MgPc's with neighbouring molecules in proximity undergo a lift of LUMOs degeneracy, with a near-Fermi local density of states with reduced twofold rotational symmetry, indicative of a long-range attractive intermolecular interaction. The latter is assigned to a surface-mediated two-step electronic hybridization process. First, LUMOs interact with Ag(100) conduction electrons, forming hybrid molecule-surface orbitals with enhanced spatial extension. Then, these delocalized molecule-surface states further hybridize with those of neighbouring molecules. This work highlights how the electronic structure of molecular adsorbates-including orbital degeneracies and symmetries-can be significantly altered via surface-mediated intermolecular hybridization, over extended distances (beyond 3 nm), having important implications for prospects of molecule-based solid-state technologies.

Imaging Domain Reversal in an Ultrathin Van der Waals Ferromagnet.

The recent isolation of 2D van der Waals magnetic materials has uncovered rich physics that often differs from the magnetic behavior of their bulk counterparts. However, the microscopic details of fundamental processes such as the initial magnetization or domain reversal, which govern the magnetic hysteresis, remain largely unknown in the ultrathin limit. Here a widefield nitrogen-vacancy (NV) microscope is employed to directly image these processes in few-layer flakes of the magnetic semiconductor vanadium triiodide (VI3 ). Complete and abrupt switching of most flakes is observed at fields Hc  ≈ 0.5-1 T (at 5 K) independent of thickness. The coercive field decreases as the temperature approaches the Curie temperature (Tc  ≈ 50 K); however, the switching remains abrupt. The initial magnetization process is then imaged, which reveals thickness-dependent domain wall depinning fields well below Hc . These results point to ultrathin VI3 being a nucleation-type hard ferromagnet, where the coercive field is set by the anisotropy-limited domain wall nucleation field. This work illustrates the power of widefield NV microscopy to investigate magnetization processes in van der Waals ferromagnets, which can be used to elucidate the origin of the hard ferromagnetic properties of other materials and explore field- and current-driven domain wall dynamics.

Enhanced Widefield Quantum Sensing with Nitrogen-Vacancy Ensembles Using Diamond Nanopillar Arrays.

Surface micro- and nano-patterning techniques are often employed to enhance the optical interface to single photoluminescent emitters in diamond, but the utility of such surface structuring in applications requiring ensembles of emitters is still open to investigation. Here, we demonstrate scalable and fault-tolerant fabrication of closely packed arrays of fluorescent diamond nanopillars, each hosting its own dense, uniformly bright ensemble of near-surface nitrogen-vacancy centers. We explore the optimal sizes for these structures and realize enhanced spin and photoluminescence properties resulting in a 4.5 times increase in optically detected magnetic resonance sensitivity when compared to unpatterned surfaces. Utilizing the increased measurement sensitivity, we image the mechanical stress tensor in each diamond pillar across the arrays and show that the fabrication process has a negligible impact on in-built stress compared to the unpatterned surface. Our results represent a valuable pathway toward future multimodal and vector-resolved imaging studies, for instance in biological contexts.

Laser Modulation of Superconductivity in a Cryogenic Wide-field Nitrogen-Vacancy Microscope.

We realize a cryogenic wide-field nitrogen-vacancy microscope and use it to image Abrikosov vortices and transport currents in a superconducting Nb film. We observe the disappearance of vortices upon increase of laser power and their clustering about hot spots upon decrease, indicating local quenching of superconductivity by the laser. Resistance measurements confirm the presence of large temperature gradients across the film. We then investigate the effect of such gradients on transport currents where the current path is seen to correlate with the temperature profile even in the fully superconducting phase. In addition to highlighting the role of temperature inhomogeneities in superconductivity phenomena, this work establishes that under sufficiently low laser power conditions wide-field nitrogen-vacancy microscopy enables imaging over mesoscopic scales down to 4 K with submicrometer spatial resolution, providing a new platform for spatially resolved investigations of a range of systems from topological insulators to van der Waals ferromagnets.

Entanglement in a 20-Qubit Superconducting Quantum Computer.

The ability to prepare sizeable multi-qubit entangled states with full qubit control is a critical milestone for physical platforms upon which quantum computers are built. We investigate the extent to which entanglement is found within a prepared graph state on the 20-qubit superconducting quantum computer IBM Q Poughkeepsie. We prepared a graph state along a path consisting of all twenty qubits within the device and performed full quantum state tomography on all groups of four connected qubits along this path. We determined that each pair of connected qubits was inseparable and hence the prepared state was entangled. Additionally, a genuine multipartite entanglement witness was measured on all qubit subpaths of the graph state and we found genuine multipartite entanglement on chains of up to three qubits. These results represent a demonstration of entanglement in one of the largest solid-state qubit arrays to date and indicate the positive direction of progress towards the goal of implementing complex quantum algorithms relying on such effects.

Rapid, High-Resolution Magnetic Microscopy of Single Magnetic Microbeads.

Magnetic microparticles or "beads" are used in a variety of research applications from cell sorting through to optical force traction microscopy. The magnetic properties of such particles can be tailored for specific applications with the uniformity of individual beads critical to their function. However, the majority of magnetic characterization techniques quantify the magnetic properties from large bead ensembles. Developing new magnetic imaging techniques to evaluate and visualize the magnetic fields from single beads will allow detailed insight into the magnetic uniformity, anisotropy, and alignment of magnetic domains. Here, diamond-based magnetic microscopy is applied to image and characterize individual magnetic beads with varying magnetic and structural properties: ferromagnetic and superparamagnetic/paramagnetic, shell (coated with magnetic material), and solid (magnetic material dispersed in matrix). The single-bead magnetic images identify irregularities in the magnetic profiles from individual bead populations. Magnetic simulations account for the varying magnetic profiles and allow to infer the magnetization of individual beads. Additionally, this work shows that the imaging technique can be adapted to achieve illumination-free tracking of magnetic beads, opening the possibility of tracking cell movements and mechanics in photosensitive contexts.

Quantum measurement of a rapidly rotating spin qubit in diamond.

A controlled qubit in a rotating frame opens new opportunities to probe fundamental quantum physics, such as geometric phases in physically rotating frames, and can potentially enhance detection of magnetic fields. Realizing a single qubit that can be measured and controlled during physical rotation is experimentally challenging. We demonstrate quantum control of a single nitrogen-vacancy (NV) center within a diamond rotated at 200,000 rpm, a rotational period comparable to the NV spin coherence time T2. We stroboscopically image individual NV centers that execute rapid circular motion in addition to rotation and demonstrate preparation, control, and readout of the qubit quantum state with lasers and microwaves. Using spin-echo interferometry of the rotating qubit, we are able to detect modulation of the NV Zeeman shift arising from the rotating NV axis and an external DC magnetic field. Our work establishes single NV qubits in diamond as quantum sensors in the physically rotating frame and paves the way for the realization of single-qubit diamond-based rotation sensors.

Proximity-Induced Artefacts in Magnetic Imaging with Nitrogen-Vacancy Ensembles in Diamond.

Magnetic imaging with ensembles of nitrogen-vacancy (NV) centres in diamond is a recently developed technique that allows for quantitative vector field mapping. Here we uncover a source of artefacts in the measured magnetic field in situations where the magnetic sample is placed in close proximity (a few tens of nm) to the NV sensing layer. Using magnetic nanoparticles as a test sample, we find that the measured field deviates significantly from the calculated field, in shape, amplitude and even in sign. By modelling the full measurement process, we show that these discrepancies are caused by the limited measurement range of NV sensors combined with the finite spatial resolution of the optical readout. We numerically investigate the role of the stand-off distance to identify an artefact-free regime, and discuss an application to ultrathin materials. This work provides a guide to predict and mitigate proximity-induced artefacts that can arise in NV-based wide-field magnetic imaging, and also demonstrates that the sensitivity of these artefacts to the sample can make them a useful tool for magnetic characterisation.

Quantum probe hyperpolarisation of molecular nuclear spins.

Hyperpolarisation of nuclear spins is important in overcoming sensitivity and resolution limitations of magnetic resonance imaging and nuclear magnetic resonance spectroscopy. Current hyperpolarisation techniques require high magnetic fields, low temperatures, or catalysts. Alternatively, the emergence of room temperature spin qubits has opened new pathways to achieve direct nuclear spin hyperpolarisation. Employing a microwave-free cross-relaxation induced polarisation protocol applied to a nitrogen vacancy qubit, we demonstrate quantum probe hyperpolarisation of external molecular nuclear spins to ~50% under ambient conditions, showing a single qubit increasing the polarisation of ~106 nuclear spins by six orders of magnitude over the thermal background. Results are verified against a detailed theoretical treatment, which also describes how the system can be scaled up to a universal quantum hyperpolarisation platform for macroscopic samples. Our results demonstrate the prospects for this approach to nuclear spin hyperpolarisation for molecular imaging and spectroscopy and its potential to extend beyond into other scientific areas.

Impact of Surface Functionalization on the Quantum Coherence of Nitrogen-Vacancy Centers in Nanodiamonds.

Nanoscale quantum probes such as the nitrogen-vacancy (NV) center in diamonds have demonstrated remarkable sensing capabilities over the past decade as control over fabrication and manipulation of these systems has evolved. The biocompatibility and rich surface chemistry of diamonds has added to the utility of these probes but, as the size of these nanoscale systems is reduced, the surface chemistry of diamond begins to impact the quantum properties of the NV center. In this work, we systematically study the effect of the diamond surface chemistry on the quantum coherence of the NV center in nanodiamonds (NDs) 50 nm in size. Our results show that a borane-reduced diamond surface can on average double the spin relaxation time of individual NV centers in nanodiamonds when compared to thermally oxidized surfaces. Using a combination of infrared and X-ray absorption spectroscopy techniques, we correlate the changes in quantum relaxation rates with the conversion of sp2 carbon to C-O and C-H bonds on the diamond surface. These findings implicate double-bonded carbon species as a dominant source of spin noise for near surface NV centers. The link between the surface chemistry and quantum coherence indicates that through tailored engineering of the surface, the quantum properties and magnetic sensitivity of these nanoscale systems may approach that observed in bulk diamond.

Non-Neurotoxic Nanodiamond Probes for Intraneuronal Temperature Mapping.

Optical biomarkers have been used extensively for intracellular imaging with high spatial and temporal resolution. Extending the modality of these probes is a key driver in cell biology. In recent years, the nitrogen-vacancy (NV) center in nanodiamond has emerged as a promising candidate for bioimaging and biosensing with low cytotoxicity and stable photoluminescence. Here we study the electrophysiological effects of this quantum probe in primary cortical neurons. Multielectrode array recordings across five replicate studies showed no statistically significant difference in 25 network parameters when nanodiamonds are added at varying concentrations over various time periods, 12-36 h. The physiological validation motivates the second part of the study, which demonstrates how the quantum properties of these biomarkers can be used to report intracellular information beyond their location and movement. Using the optically detected magnetic resonance from the nitrogen-vacancy defects within the nanodiamonds we demonstrate enhanced signal-to-noise imaging and temperature mapping from thousands of nanodiamond probes simultaneously. This work establishes nanodiamonds as viable multifunctional intraneuronal sensors with nanoscale resolution, which may ultimately be used to detect magnetic and electrical activity at the membrane level in excitable cellular systems.

Fan-out Estimation in Spin-based Quantum Computer Scale-up.

Solid-state spin-based qubits offer good prospects for scaling based on their long coherence times and nexus to large-scale electronic scale-up technologies. However, high-threshold quantum error correction requires a two-dimensional qubit array operating in parallel, posing significant challenges in fabrication and control. While architectures incorporating distributed quantum control meet this challenge head-on, most designs rely on individual control and readout of all qubits with high gate densities. We analysed the fan-out routing overhead of a dedicated control line architecture, basing the analysis on a generalised solid-state spin qubit platform parameterised to encompass Coulomb confined (e.g. donor based spin qubits) or electrostatically confined (e.g. quantum dot based spin qubits) implementations. The spatial scalability under this model is estimated using standard electronic routing methods and present-day fabrication constraints. Based on reasonable assumptions for qubit control and readout we estimate 102-105 physical qubits, depending on the quantum interconnect implementation, can be integrated and fanned-out independently. Assuming relatively long control-free interconnects the scalability can be extended. Ultimately, the universal quantum computation may necessitate a much higher number of integrated qubits, indicating that higher dimensional electronics fabrication and/or multiplexed distributed control and readout schemes may be the preferredstrategy for large-scale implementation.

Towards visualisation of central-cell-effects in scanning tunnelling microscope images of subsurface dopant qubits in silicon.

Atomic-scale understanding of phosphorus donor wave functions underpins the design and optimisation of silicon based quantum devices. The accuracy of large-scale theoretical methods to compute donor wave functions is dependent on descriptions of central-cell corrections, which are empirically fitted to match experimental binding energies, or other quantities associated with the global properties of the wave function. Direct approaches to understanding such effects in donor wave functions are of great interest. Here, we apply a comprehensive atomistic theoretical framework to compute scanning tunnelling microscopy (STM) images of subsurface donor wave functions with two central-cell correction formalisms previously employed in the literature. The comparison between central-cell models based on real-space image features and the Fourier transform profiles indicates that the central-cell effects are visible in the simulated STM images up to ten monolayers below the silicon surface. Our study motivates a future experimental investigation of the central-cell effects via the STM imaging technique with potential of fine tuning theoretical models, which could play a vital role in the design of donor-based quantum systems in scalable quantum computer architectures.

Electron paramagnetic resonance microscopy using spins in diamond under ambient conditions.

Magnetic resonance spectroscopy is one of the most important tools in chemical and bio-medical research. However, sensitivity limitations typically restrict imaging resolution to ~ 10 µm. Here we bring quantum control to the detection of chemical systems to demonstrate high-resolution electron spin imaging using the quantum properties of an array of nitrogen-vacancy centres in diamond. Our electron paramagnetic resonance microscope selectively images electronic spin species by precisely tuning a magnetic field to bring the quantum probes into resonance with the external target spins. This provides diffraction limited spatial resolution of the target spin species over a field of view of 50 × 50 µm2 with a spin sensitivity of 104 spins per voxel or ∼100 zmol. The ability to perform spectroscopy and dynamically monitor spin-dependent redox reactions at these scales enables the development of electron spin resonance and zepto-chemistry in the physical and life sciences.Electron paramagnetic resonance spectroscopy has important scientific and medical uses but improving the resolution of conventional methods requires cryogenic, vacuum environments. Simpson et al. show nitrogen vacancy centres can be used for sub-micronmetre imaging with improved sensitivity in ambient conditions.