arXiv subjects

Lloyd C. L. Hollenberg

Publications and source records attributed to Lloyd C. L. Hollenberg.

At least 55 records · Page 3Linked to original sources

arXiv2021

Cost-optimal single-qubit gate synthesis in the Clifford hierarchy

For universal quantum computation, a major challenge to overcome for practical implementation is the large amount of resources required for fault-tolerant quantum information processing. An important aspect is implementing arbitrary unitary operators built from logical gates within the quantum error correction code. A synthesis algorithm can be used to approximate any unitary gate up to arbitrary precision by assembling sequences of logical gates chosen from a small set of universal gates that are fault-tolerantly performable while encoded in a quantum error-correction code. However, current procedures do not yet support individual assignment of base gate costs and many do not support extended sets of universal base gates. We analysed cost-optimal sequences using an exhaustive search based on Dijkstra's pathfinding algorithm for the canonical Clifford+$T$ set of base gates and compared them to when additionally including $Z$-rotations from higher orders of the Clifford hierarchy. Two approaches of assigning base gate costs were used. First, costs were reduced to $T$-counts by recursively applying a $Z$-rotation catalyst circuit. Second, costs were assigned as the average numbers of raw (i.e. physical level) magic states required to directly distil and implement the gates fault-tolerantly. We found that the average sequence cost decreases by up to $54\pm 3\%$ when using the $Z$-rotation catalyst circuit approach and by up to $33\pm 2 \%$ when using the magic state distillation approach. In addition, we investigated observed limitations of certain assignments of base gate costs by developing an analytic model to estimate the proportion of sets of $Z$-rotation gates from higher orders of the Clifford hierarchy that are found within sequences approximating random target gates.

quant-ph↗

arXiv2021

Performance optimization for drift-robust fidelity improvement of two-qubit gates

Quantum system characterization techniques represent the front line in the identification and mitigation of noise in quantum computing, but can be expensive in terms of quantum resources and time to repeatedly employ. Another challenging aspect is that parameters governing the performance of various operations tend to drift over time, and monitoring these is hence a difficult task. One of the most promising characterization techniques, gate set tomography (GST), provides a self-consistent estimate of the completely positive, trace-preserving (CPTP) maps for a complete set of gates, as well as preparation and measurement operators. We develop a method for performance optimization seeded by tomography (POST), which couples the power of GST with a classical optimization routine to achieve a consistent gate improvement in just a short number of steps within a given calibration cycle. By construction, the POST procedure finds the best available gate operation given the hardware, and is therefore robust to the effects of drift. Further, in comparison to other quantum error mitigation techniques, it builds upon a one-time application of GST. To demonstrate the performance of this method on a real quantum computer, we map out the operations of six qubit pairs on the superconducting \emph{ibmq\_poughkeepsie} quantum device. Under the restriction of logical-only control, we monitor the performance of the POST approach on a chosen CNOT gate over a period of six weeks. In this time, we achieve a consistent improvement in gate fidelity, averaging a fidelity increase of 21.1\% as measured by randomized benchmarking. The POST approach should find wide applicability as it is hardware agnostic, and can be applied at the upper logical level or at a deeper pulse control level.

quant-ph↗

arXiv2021

Entanglement in a 20-Qubit Superconducting Quantum Computer

Towards realising larger scale quantum algorithms, the ability to prepare sizeable multi-qubit entangled states with full qubit control is used as a benchmark for quantum technologies. 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 Poughkeepsie 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.

quant-ph↗

arXiv2020

Demonstration of non-Markovian process characterisation and control on a quantum processor

In the scale-up of quantum computers, the framework underpinning fault-tolerance generally relies on the strong assumption that environmental noise affecting qubit logic is uncorrelated (Markovian). However, as physical devices progress well into the complex multi-qubit regime, attention is turning to understanding the appearance and mitigation of correlated -- or non-Markovian -- noise, which poses a serious challenge to the progression of quantum technology. This error type has previously remained elusive to characterisation techniques. Here, we develop a framework for characterising non-Markovian dynamics in quantum systems and experimentally test it on multi-qubit superconducting quantum devices. Where noisy processes cannot be accounted for using standard Markovian techniques, our reconstruction predicts the behaviour of the devices with an infidelity of $10^{-3}$. Our results show this characterisation technique leads to superior quantum control and extension of coherence time by effective decoupling from the non-Markovian environment. This framework, validated by our results, is applicable to any controlled quantum device and offers a significant step towards optimal device operation and noise reduction.

quant-ph↗

arXiv2020

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 (STM) and spectroscopy (STS), non-contact atomic force microscopy (ncAFM) and density functional theory (DFT). Single, isolated MgPc's exhibit a flat, four-fold 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 two-fold 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.

cond-mat.mtrl-sci↗

arXiv2020

Imaging domain reversal in an ultrathin van der Waals ferromagnet

The recent isolation of two-dimensional van der Waals magnetic materials has uncovered rich physics that often differs from the magnetic behaviour 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 we employ a widefield nitrogen-vacancy (NV) microscope to directly image these processes in few-layer flakes of magnetic semiconductor vanadium triiodide (VI$_3$). We observe complete and abrupt switching of most flakes at fields $H_c\approx0.5-1$ T (at 5 K) independent of thickness down to two atomic layers, with no intermediate partially-reversed state. The coercive field decreases as the temperature approaches the Curie temperature ($T_c\approx50$ K), however, the switching remains abrupt. We then image the initial magnetization process, which reveals thickness-dependent domain wall depinning fields well below $H_c$. These results point to ultrathin VI$_3$ 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 could be used to elucidate the origin of the hard ferromagnetic properties of other materials and explore field- and current-driven domain wall dynamics.

cond-mat.mes-hall↗

arXiv2019

Laser modulation of superconductivity in a cryogenic widefield nitrogen-vacancy microscope

Microscopic imaging based on nitrogen-vacancy (NV) centres in diamond, a tool increasingly used for room-temperature studies of condensed matter systems, has recently been extended to cryogenic conditions. However, it remains unclear whether the technique is viable for imaging temperature-sensitive phenomena below 10 K given the inherent laser illumination requirements, especially in a widefield configuration. Here we realise a widefield NV microscope with a field of view of 100 $μ$m and a base temperature of 4 K, 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 that laser powers as low as 1 mW (4 orders of magnitude below the NV saturation) are sufficient to locally quench the superconductivity of the film ($T_c = 9$ K). This significant local heating is confirmed by resistance measurements, which reveal the presence of large temperature gradients (several K) 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, widefield NV microscopy enables imaging over mesoscopic scales down to 4 K with a submicrometer spatial resolution, providing a new platform for real-space investigations of a range of systems from topological insulators to van der Waals ferromagnets.

cond-mat.supr-con↗

arXiv2019

Mapping NP-Hard Problems to Restricted Adiabatic Quantum Architectures

We introduce a framework for mapping NP-Hard problems to adiabatic quantum computing (AQC) architectures that are heavily restricted in both connectivity and dynamic range of couplings, for which minor-embedding -- the standard problem mapping method -- cannot be directly applied. Separating the mapping into two distinct stages, we introduce problem-specific reductions for both quadratic unconstrained binary optimisation (QUBO) and satisfiability (SAT) and develop the subdivision-embedding method that is suitable for directly embedding onto these heavily restricted architectures. The theory underpinning this framework provides tools to aid in the manipulation of Ising Hamiltonians for the purposes of Ising energy minimisation, and could be used to assist in developing and optimising further problem mapping techniques. For each of the problem mapping methods presented, we examine how the physical qubit count scales with problem size on architectures of varying connectivity.

quant-ph↗

arXiv2019

Observation of a quantum phase from classical rotation of a single spin

The theory of angular momentum connects physical rotations and quantum spins together at a fundamental level. Physical rotation of a quantum system will therefore affect fundamental quantum operations, such as spin rotations in projective Hilbert space, but these effects are subtle and experimentally challenging to observe due to the fragility of quantum coherence. Here we report a measurement of a single-electron-spin phase shift arising directly from physical rotation, without transduction through magnetic fields or ancillary spins. This phase shift is observed by measuring the phase difference between a microwave driving field and a rotating two-level electron spin system, and can accumulate nonlinearly in time. We detect the nonlinear phase using spin-echo interferometry of a single nitrogen-vacancy qubit in a diamond rotating at 200,000rpm. Our measurements demonstrate the fundamental connections between spin, physical rotation and quantum phase, and will be applicable in schemes where the rotational degree of freedom of a quantum system is not fixed, such as spin-based rotation sensors and trapped nanoparticles containing spins.

quant-ph↗

arXiv2019

Imaging graphene field-effect transistors on diamond using nitrogen-vacancy microscopy

The application of imaging techniques based on ensembles of nitrogen-vacancy (NV) sensors in diamond to characterise electrical devices has been proposed, but the compatibility of NV sensing with operational gated devices remains largely unexplored. Here we fabricate graphene field-effect transistors (GFETs) directly on the diamond surface and characterise them via NV microscopy. The current density within the gated graphene is reconstructed from NV magnetometry under both mostly p- and n-type doping, but the exact doping level is found to be affected by the measurements. Additionally, we observe a surprisingly large modulation of the electric field at the diamond surface under an applied gate potential, seen in NV photoluminescence and NV electrometry measurements, suggesting a complex electrostatic response of the oxide-graphene-diamond structure. Possible solutions to mitigate these effects are discussed.

cond-mat.mes-hall↗

arXiv2019

Atomic-level Characterisation of Quantum Computer Arrays by Machine Learning

Atomic level qubits in silicon are attractive candidates for large-scale quantum computing, however, their quantum properties and controllability are sensitive to details such as the number of donor atoms comprising a qubit and their precise location. This work combines machine learning techniques with million-atom simulations of scanning-tunnelling-microscope (STM) images of dopants to formulate a theoretical framework capable of determining the number of dopants at a particular qubit location and their positions with exact lattice-site precision. A convolutional neural network was trained on 100,000 simulated STM images, acquiring a characterisation fidelity (number and absolute donor positions) of above 98\% over a set of 17,600 test images including planar and blurring noise. The method established here will enable a high-precision post-fabrication characterisation of dopant qubits in silicon, with high-throughput potentially alleviating the requirements on the level of resource required for quantum-based characterisation, which may be otherwise a challenge in the context of large qubit arrays for universal quantum computing.

cond-mat.mes-hall↗

arXiv2019

Quantum magnetic imaging of iron biomineralisation in teeth of the chiton Acanthopleura hirtosa

Iron biomineralisation is critical for life. Nature capitalises on the physical attributes of iron biominerals for a variety of functional, structural and sensory applications. Although magnetism is an integral property of iron biominerals, the role it plays in their nano-assembly remains a fundamental, unanswered question. This is well exemplified by the magnetite-bearing radula of chitons. Chitons, a class of marine mollusc, create the hardest biomineral of any animal in their abrasion-resistant, self-sharpening teeth4. Despite this system being subjected to a range of high resolution imaging studies, the mechanisms that drive mineral assembly remain unresolved. However, the advent of quantum imaging technology provides a new avenue to probe magnetic structures directly. Here we use quantum magnetic microscopy, based on nitrogen-vacancy centres in diamond, to attain the first subcellular magnetic profiling of a eukaryotic system. Using complementary magnetic imaging protocols, we spatially map the principal mineral phases (ferrihydrite and magnetite) in the developing teeth of Acanthopleura hirtosa with submicron resolution. The images reveal previously undiscovered long-range magnetic order, established at the onset of magnetite mineralisation. This is in contrast to electron microscopy studies that show no strong common crystallographic orientation. The quantum-based magnetic profiling techniques presented in this work have broad application in biology, earth science, chemistry and materials engineering and can be applied across the range of systems for which iron is vital.

physics.bio-ph↗

arXiv2019

Optimising Matrix Product State Simulations of Shor's Algorithm

We detail techniques to optimise high-level classical simulations of Shor's quantum factoring algorithm. Chief among these is to examine the entangling properties of the circuit and to effectively map it across the one-dimensional structure of a matrix product state. Compared to previous approaches whose space requirements depend on $r$, the solution to the underlying order-finding problem of Shor's algorithm, our approach depends on its factors. We performed a matrix product state simulation of a 60-qubit instance of Shor's algorithm that would otherwise be infeasible to complete without an optimised entanglement mapping.

quant-ph↗

arXiv2018

Evidence for Primal sp2 Defects at the Diamond Surface: Candidates for Electron Trapping and Noise Sources

Diamond materials are central to an increasing range of advanced technological demonstrations, from high power electronics, to nano-scale quantum bio-imaging with unprecedented sensitivity. However, the full exploitation of diamond for these applications is often limited by the uncontrolled nature of the diamond material surface, which suffers from Fermi-level pinning and hosts a significant density of electro-magnetic noise sources. These issues occur despite the oxide-free and air-stable nature of the diamond crystal surface, which should be an ideal candidate for functionalization and chemical-engineering. In this work we reveal a family of previously unidentified and near-ubiquitous primal surface defects which we assign to differently reconstructed surface vacancies. The density of these defects is quantified with X-ray absorption spectroscopy, their energy structures are elucidated by ab initio calculations, and their effect on near-surface quantum probes is measured directly. Subsequent ab-initio calculation of band-bending from these defects suggest they are the source of Fermi-level pinning at most diamond surfaces. Finally, an investigation is conducted on a broad range of post-growth surface treatments and concludes that none of them can reproducibly reduce this defect density below the Fermi-pinning threshold, making this defect a prime candidate as the source for decoherence-limiting noise in near-surface quantum probes.

cond-mat.mes-hall↗

arXiv2018

Non-neurotoxic Nanodiamond Probes for Intraneuronal Temperature Mapping

Optical bio-markers 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 NV centre in nanodiamond has emerged as a promising candidate for bio-imaging and bio-sensing with low cytotoxicity and stable photoluminescence. Here we study the electrophysiological effects of this quantum probe in primary cortical neurons. Multi-electrode array (MEA) 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 hr. 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 multi-functional intraneuronal sensors with nanoscale resolution, that may ultimately be used to detect magnetic and electrical activity at the membrane level in excitable cellular systems.

physics.bio-ph↗

arXiv2018

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. Realising a single qubit that can be measured and controlled during physical rotation is experimentally challenging. In this work, we demonstrate quantum control of a single nitrogen-vacancy (NV) centre within a diamond rotated at 200,000rpm, a rotational period comparable to the NV spin coherence time $T_2$. We stroboscopically image individual NV centres 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 realisation of single-qubit diamond-based rotation sensors.

quant-ph↗

arXiv2017

High precision single qubit tuning via thermo-magnetic field control

Precise control of the resonant frequency of a spin qubit is of fundamental importance to quantum sensing protocols. We demonstrate a control technique on a single nitrogen-vacancy (NV) centre in diamond where the applied magnetic field is modified by fine-tuning a permanent magnet's magnetisation via temperature control. Through this control mechanism, nanoscale cross-relaxation spectroscopy of both electron and nuclear spins in the vicinity of the NV centre are performed. We then show that through maintaining the magnet at a constant temperature an order of magnitude improvement in the stability of the NV qubit frequency can be achieved. This improved stability is tested in the polarisation of a small ensemble of nearby $^{13}$C spins via resonant cross-relaxation and the lifetime of this polarisation explored. The effectiveness and relative simplicity of this technique may find use in the realisation of portable spectroscopy and/or hyperpolarisation systems.

quant-ph↗

arXiv2017

Quantum probe hyperpolarisation of molecular nuclear spins

The hyperpolarisation of nuclear spins within target molecules is a critical and complex challenge in magnetic resonance imaging (MRI) and nuclear magnetic resonance (NMR) spectroscopy. Hyperpolarisation offers enormous gains in signal and spatial resolution which may ultimately lead to the development of molecular MRI and NMR. At present, techniques used to polarise nuclear spins generally require low temperatures and/or high magnetic fields, radio-frequency control fields, or the introduction of catalysts or free-radical mediators. The emergence of room temperature solid-state spin qubits has opened exciting new pathways to circumvent these requirements to achieve direct nuclear spin hyperpolarisation using quantum control. Employing a novel cross-relaxation induced polarisation (CRIP) protocol using a single nitrogen-vacancy (NV) centre in diamond, we demonstrate the first external nuclear spin hyperpolarisation achieved by a quantum probe, in this case of $^1$H molecular spins in poly(methyl methacrylate). In doing so, we show that a single qubit is capable of increasing the thermal polarisation of $\sim 10^6$ nuclear spins by six orders of magnitude, equivalent to an applied magnetic field of $10^5$\,T. The technique can also be tuned to multiple spin species, which we demonstrate using both \C{13} and $^1$H nuclear spin ensembles. Our results are analysed and interpreted via a detailed theoretical treatment, which is also used to describe how the system can be scaled up to a universal quantum hyperpolarisation platform for the production of macroscopic quantities of contrast agents at high polarisation levels for clinical applications. These results represent a new paradigm for nuclear spin hyperpolarisation for molecular imaging and spectroscopy, and beyond into areas such as materials science and quantum information processing.

quant-ph↗