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Quantum machine learning has gained attention for its potential to address computational challenges. However, whether those algorithms can effectively solve practical problems and outperform their classical counterparts, especially on current quantum hardware, remains a critical question. In this work, we propose a novel quantum machine learning method, called Quantum Support Vector Data Description (QSVDD), for practical image anomaly detection, which aims to achieve both parameter efficiency and superior accuracy compared to classical models. Emulation results indicate that QSVDD demonstrates favourable recognition capabilities compared to classical baselines, achieving an average accuracy of over 90% on benchmarks with significantly fewer trainable parameters. Theoretical analysis confirms that QSVDD has a comparable expressivity to classical counterparts while requiring only a fraction of the parameters. Furthermore, we demonstrate the first implementation of a quantum anomaly detection method for general image datasets on a superconducting quantum processor. Specifically, we achieve an accuracy of over 80% with only 16 parameters on the device, providing initial evidence of QSVDD's practical viability in the noisy intermediate-scale quantum era and highlighting its significant reduction in parameter requirements., Comment: 30 pages, 13 figures

The circulatory system, comprising the heart and blood vessels, is vital for nutrient transport, waste removal, and homeostasis. Traditional computational models often isolate individual biophysical processes, such as cardiac electromechanics and blood flow dynamics, failing to capture the system's integrated nature. This paper presents an innovative approach that couples a 3D electromechanical model of the heart with a 3D fluid mechanics model of vascular blood flow. Our file-based partitioned coupling scheme allows these models to run independently while sharing essential data through intermediate files. We validate this approach using two solvers: one for cardiac electromechanics and the other for vascular blood flow. Developed by separate research groups, these solvers emphasise different dynamical scales and utilise distinct discretisation schemes. Numerical simulations using idealised and realistic anatomies show that the implemented coupling scheme is reliable and requires minimal additional computation time relative to advancing individual time steps in the heart and blood flow models. Notably, the coupled model predicts muscle displacement differently than the standalone heart model, highlighting the influence of detailed vascular blood flow on cardiac function. This study presents a paradigm case of how to build virtual human models and digital twins by productive collaboration between teams with complementary expertise., Comment: 31 pages, 13 figures

We present an error mitigation strategy composed of Echo Verification (EV) and Clifford Data Regression (CDR), the combination of which allows one to learn the effect of the quantum noise channel to extract error mitigated estimates for the expectation value of Pauli observables. We analyse the behaviour of the method under the depolarizing channel and derive an estimator for the depolarization rate in terms of the ancilla purity and postselection probability. We also highlight the sensitivity of this probability to noise, a potential bottleneck for the technique. We subsequently consider a more general noise channel consisting of arbitrary Pauli errors, which reveals a linear relationship between the error rates and the estimation of expectation values, suggesting the learnability of noise in EV by regression techniques. Finally, we present a practical demonstration of Echo Verified Clifford Data Regression (EVCDR) on a superconducting quantum computer and observe accurate results for the time evolution of an Ising model over a spin-lattice consisting of up to 35 sites and circuit depths in excess of 1,000., Comment: 15 pages, 13 figures

This letter illustrates the opinion of the molecular dynamics (MD) community on the need to adopt a new FAIR paradigm for the use of molecular simulations. It highlights the necessity of a collaborative effort to create, establish, and sustain a database that allows findability, accessibility, interoperability, and reusability of molecular dynamics simulation data. Such a development would democratize the field and significantly improve the impact of MD simulations on life science research. This will transform our working paradigm, pushing the field to a new frontier. We invite you to support our initiative at the MDDB community (https://mddbr.eu/community/)

Data-driven approaches offer novel opportunities for improving the performance of turbulent flow simulations, which are critical to wide-ranging applications from wind farms and aerodynamic designs to weather and climate forecasting. While conventional continuum Navier-Stokes solvers have been the subject of a significant amount of work in this domain, there has hitherto been very limited effort in the same direction for the more scalable and highly performant lattice Boltzmann method (LBM), even though it has been successfully applied to a variety of turbulent flow simulations using large-eddy simulation (LES) techniques. In this work, we establish a data-driven framework for the LES-based lattice Boltzmann simulation of near-wall turbulent flow fields. We do this by training neural networks using improved delayed detached eddy simulation data. Crucially, this is done in combination with physics-based information that substantially constrains the data-driven predictions. Using data from turbulent channel flow at a friction Reynolds number at $5200$, our simulations accurately predict the behaviour of the wall model at arbitrary friction Reynolds numbers up to $1.0 \times 10^6$. In contradistinction with other models that use direct numerical simulation datasets, our physics-informed model requires data from very limited regions within the wall-bounded plane, reducing by three orders of magnitude the quantity of data needed for training. We also demonstrate that our model can handle data configurations when the near-wall grid is sparse. Our physics-informed neural network approach opens up the possibility of employing LBM in combination with highly specific and therefore much more limited quantities of macroscopic data, substantially facilitating the investigation of a wide-range of turbulent flow applications at very large scale.

In this work we present an experimental demonstration of the Contextual Subspace Variational Quantum Eigensolver on superconducting quantum hardware. In particular, we compute the potential energy curve for molecular nitrogen, where a dominance of static correlation in the dissociation limit proves challenging for many conventional quantum chemistry techniques. Our quantum simulations retain good agreement with the full configuration interaction energy in the chosen STO-3G basis, outperforming all benchmarked single-reference wavefunction techniques in capturing the bond-breaking appropriately. Moreover, our methodology is competitive with several multiconfigurational approaches, but at a considerable saving of quantum resource, meaning larger active spaces can be treated for a fixed qubit allowance. To achieve this result we deploy an error mitigation/suppression strategy comprised of dynamical decoupling, measurement-error mitigation and zero-noise extrapolation, in addition to circuit parallelization that not only provides passive averaging of noise but improves the effective shot-yield to reduce the measurement overhead. Furthermore, we introduce a modification to previous adaptive ansatz construction algorithms that incorporates hardware-awareness into our variational circuits to minimize the transpilation cost for the target qubit topology., Comment: 22 pages, 12 figures

Due to numerous limitations including restrictive qubit topologies, short coherence times and prohibitively high noise floors, few quantum chemistry experiments performed on existing noisy intermediate-scale quantum hardware have achieved the high bar of chemical precision, namely energy errors to within 1.6 mHa of full configuration interaction. To have any hope of doing so, we must layer contemporary resource reduction techniques with best-in-class error mitigation methods; in particular, we combine the techniques of qubit tapering and the contextual subspace variational quantum eigensolver with several error mitigation strategies comprised of measurement-error mitigation, symmetry verification, zero-noise extrapolation and dual-state purification. We benchmark these strategies across a suite of eight 27-qubit IBM Falcon series quantum processors, taking preparation of the HCl molecule's ground state as our testbed., Comment: 18 pages, 15 figures, 4 tables, supplementary GitHub repository: https://github.com/TimWeaving/quantum-error-mitigation

The contextual subspace variational quantum eigensolver (CS-VQE) is a hybrid quantum-classical algorithm that approximates the ground-state energy of a given qubit Hamiltonian. It achieves this by separating the Hamiltonian into contextual and noncontextual parts. The ground-state energy is approximated by classically solving the noncontextual problem, followed by solving the contextual problem using VQE, constrained by the noncontextual solution. In general, computation of the contextual correction needs fewer qubits and measurements compared with solving the full Hamiltonian via traditional VQE. We simulate CS-VQE on different tapered molecular Hamiltonians and apply the unitary partitioning measurement reduction strategy to further reduce the number of measurements required to obtain the contextual correction. Our results indicate that CS-VQE combined with measurement reduction is a promising approach to allow feasible eigenvalue computations on noisy intermediate-scale quantum devices. We also provide a modification to the CS-VQE algorithm; the CS-VQE algorithm previously could cause an exponential increase in Hamiltonian terms, but with this modification now at worst will scale quadratically., Comment: updated to match online publication

Quantum chemistry is a promising application for noisy intermediate-scale quantum (NISQ) devices. However, quantum computers have thus far not succeeded in providing solutions to problems of real scientific significance, with algorithmic advances being necessary to fully utilise even the modest NISQ machines available today. We discuss a method of ground state energy estimation predicated on a partitioning the molecular Hamiltonian into two parts: one that is noncontextual and can be solved classically, supplemented by a contextual component that yields quantum corrections obtained via a Variational Quantum Eigensolver (VQE) routine. This approach has been termed Contextual Subspace VQE (CS-VQE), but there are obstacles to overcome before it can be deployed on NISQ devices. The problem we address here is that of the ansatz - a parametrized quantum state over which we optimize during VQE. It is not initially clear how a splitting of the Hamiltonian should be reflected in our CS-VQE ans\"atze. We propose a 'noncontextual projection' approach that is illuminated by a reformulation of CS-VQE in the stabilizer formalism. This defines an ansatz restriction from the full electronic structure problem to the contextual subspace and facilitates an implementation of CS-VQE that may be deployed on NISQ devices. We validate the noncontextual projection ansatz using a quantum simulator, with results obtained herein for a suite of trial molecules., Comment: 37 pages, 3 figures; supporting information available in addition to ancillary data files for reproducibility

Owing to the computational complexity of electronic structure algorithms running on classical digital computers, the range of molecular systems amenable to simulation remains tightly circumscribed even after many decades of work. Quantum computers hold the promise of transcending such limitations although in the current era the size and noise of these devices militates against significant progress. Here we describe a new and chemically intuitive approach that permits a subdomain of the electronic structure of a molecule to be calculated accurately on a quantum device, while the rest of the molecule is described at a lower level of accuracy using density functional theory running on a classical computer. We demonstrate that our method produces improved results for molecules that cannot be simulated fully on quantum computers but which can be resolved classically at a lower level of approximation. Our algorithm is tunable, so that the size of the quantum simulation can be adjusted to run on available quantum resources. Therefore, as quantum devices become larger, our method will enable increasingly large subdomains to be studied accurately., Comment: 8 pages, 3 figures, Supplementary Information pdf available in anc folder. Updated pre-print includes changes to acknowledgements, and minor changes to the density matrix definition and orbital localization discussion

The race to meet the challenges of the global pandemic has served as a reminder that the existing drug discovery process is expensive, inefficient and slow. There is a major bottleneck screening the vast number of potential small molecules to shortlist lead compounds for antiviral drug development. New opportunities to accelerate drug discovery lie at the interface between machine learning methods, in this case developed for linear accelerators, and physics-based methods. The two in silico methods, each have their own advantages and limitations which, interestingly, complement each other. Here, we present an innovative infrastructural development that combines both approaches to accelerate drug discovery. The scale of the potential resulting workflow is such that it is dependent on supercomputing to achieve extremely high throughput. We have demonstrated the viability of this workflow for the study of inhibitors for four COVID-19 target proteins and our ability to perform the required large-scale calculations to identify lead antiviral compounds through repurposing on a variety of supercomputers.

One limitation of the variational quantum eigensolver algorithm is the large number of measurement steps required to estimate different terms in the Hamiltonian of interest. Unitary partitioning reduces this overhead by transforming the problem Hamiltonian into one containing fewer terms. We explore two different circuit constructions of the transformation required - one built by a sequence of rotations and the other a linear combination of unitaries (LCU). To assess performance, we simulated chemical Hamiltonians and studied the ground states of H2 and LiH. Both implementations are successful even in the presence of noise. The sequence of rotations realization offers the greatest benefit to calculations, whereas the probabilistic nature of LCU reduces its effectiveness. To our knowledge, this work also demonstrates the first experimental implementation of LCU on quantum hardware., Comment: Revised order of paper, and further background details about the LCU method added. A unary implementation of LCU is also explored. Results unchanged

COVID-19 has claimed more 1 million lives and resulted in over 40 million infections. There is an urgent need to identify drugs that can inhibit SARS-CoV-2. In response, the DOE recently established the Medical Therapeutics project as part of the National Virtual Biotechnology Laboratory, and tasked it with creating the computational infrastructure and methods necessary to advance therapeutics development. We discuss innovations in computational infrastructure and methods that are accelerating and advancing drug design. Specifically, we describe several methods that integrate artificial intelligence and simulation-based approaches, and the design of computational infrastructure to support these methods at scale. We discuss their implementation and characterize their performance, and highlight science advances that these capabilities have enabled.

The drug discovery process currently employed in the pharmaceutical industry typically requires about 10 years and $2-3 billion to deliver one new drug. This is both too expensive and too slow, especially in emergencies like the COVID-19 pandemic. In silicomethodologies need to be improved to better select lead compounds that can proceed to later stages of the drug discovery protocol accelerating the entire process. No single methodological approach can achieve the necessary accuracy with required efficiency. Here we describe multiple algorithmic innovations to overcome this fundamental limitation, development and deployment of computational infrastructure at scale integrates multiple artificial intelligence and simulation-based approaches. Three measures of performance are:(i) throughput, the number of ligands per unit time; (ii) scientific performance, the number of effective ligands sampled per unit time and (iii) peak performance, in flop/s. The capabilities outlined here have been used in production for several months as the workhorse of the computational infrastructure to support the capabilities of the US-DOE National Virtual Biotechnology Laboratory in combination with resources from the EU Centre of Excellence in Computational Biomedicine.

With the relentless rise of computer power, there is a widespread expectation that computers can solve the most pressing problems of science, and even more besides. We explore the limits of computational modelling and conclude that, in the domains of science and engineering that are relatively simple and firmly grounded in theory, these methods are indeed powerful. Even so, the availability of code, data and documentation, along with a range of techniques for validation, verification and uncertainty quantification, are essential for building trust in computer generated findings. When it comes to complex systems in domains of science that are less firmly grounded in theory, notably biology and medicine, to say nothing of the social sciences and humanities, computers can create the illusion of objectivity, not least because the rise of big data and machine learning pose new challenges to reproducibility, while lacking true explanatory power. We also discuss important aspects of the natural world which cannot be solved by digital means. In the long-term, renewed emphasis on analogue methods will be necessary to temper the excessive faith currently placed in digital computation., Comment: 15 pages

Molecular dynamics simulation is now a widespread approach for understanding complex systems on the atomistic scale. It finds applications from physics and chemistry to engineering, life and medical science. In the last decade, the approach has begun to advance from being a computer-based means of rationalising experimental observations, to producing apparently credible predictions for a number of real-world applications within industrial sectors such as advanced materials and drug discovery. However, key aspects concerning the reproducibility of the method have not kept pace with the speed of its uptake in the scientific community. Here, we present a discussion of uncertainty quantification for molecular dynamics simulation designed to endow the method with better error estimates that will enable the method to be used to report actionable results. The approach adopted is a standard one in the field of uncertainty quantification, namely using ensemble methods, in which a sufficiently large number of replicas are run concurrently, from which reliable statistics can be extracted. Indeed, because molecular dynamics is intrinsically chaotic, the need to use ensemble methods is fundamental and holds regardless of the duration of the simulations performed. We discuss the approach and illustrate it in a range of applications from materials science to ligand-protein binding free energy estimation., Comment: 33 pages, 3 figures

Trotter-Suzuki decompositions are frequently used in the quantum simulation of quantum chemistry. They transform the evolution operator into a form implementable on a quantum device, while incurring an error---the Trotter error. The Trotter error can be made arbitrarily small by increasing the Trotter number. However, this increases the length of the quantum circuits required, which may be impractical. It is therefore desirable to find methods of reducing the Trotter error through alternate means. The Trotter error is dependent on the order in which individual term unitaries are applied. Due to the factorial growth in the number of possible orderings with respect to the number of terms, finding an optimal strategy for ordering Trotter sequences is difficult. In this paper, we propose three ordering strategies, and assess their impact on the Trotter error incurred. Initially, we exhaustively examine the possible orderings for molecular hydrogen in a STO-3G basis. We demonstrate how the optimal ordering scheme depends on the compatibility graph of the Hamiltonian, and show how it varies with increasing bond length. We then use 44 molecular Hamiltonians to evaluate two strategies based on coloring their incompatibility graphs, while considering the properties of the obtained colorings. We find that the Trotter error for most systems involving heavy atoms, using a reference magnitude ordering, is less than 1 kcal/mol. Relative to this, the difference between ordering schemes can be substantial, being approximately on the order of millihartrees. The coloring-based ordering schemes are reasonably promising, however further work is required. Finally, we consider ordering strategies based on the norm of the Trotter error operator, including an iterative method for generating the new error operator terms added upon insertion of a term into an ordered Hamiltonian., Comment: 36 pages, 11 figures

A weakness in the wall of a cerebral artery causing a dilation or ballooning of the blood vessel is known as a cerebral aneurysm. Optimal treatment requires fast and accurate diagnosis of the aneurysm. HemeLB is a fluid dynamics solver for complex geometries developed to provide neurosurgeons with information related to the flow of blood in and around aneurysms. On a cost efficient platform, HemeLB could be employed in hospitals to provide surgeons with the simulation results in real-time. In this work, we developed an improved version of HemeLB for GPU implementation and result visualization. A visualization platform for smooth interaction with end users is also presented. Finally, a comprehensive evaluation of this implementation is reported. The results demonstrate that the proposed implementation achieves a maximum performance of 15,168,964 site updates per second, and is capable of speeding up HemeLB for deployment in hospitals and clinical investigations.

The ability to perform classically intractable electronic structure calculations is often cited as one of the principal applications of quantum computing. A great deal of theoretical algorithmic development has been performed in support of this goal. Most techniques require a scheme for mapping electronic states and operations to states of and operations upon qubits. The two most commonly used techniques for this are the Jordan-Wigner transformation and the Bravyi-Kitaev transformation. However, comparisons of these schemes have previously been limited to individual small molecules. In this paper we discuss resource implications for the use of the Bravyi-Kitaev mapping scheme, specifically with regard to the number of quantum gates required for simulation. We consider both small systems which may be simulatable on near-future quantum devices, and systems sufficiently large for classical simulation to be intractable. We use 86 molecular systems to demonstrate that the use of the Bravyi-Kitaev transformation is typically at least approximately as efficient as the canonical Jordan-Wigner transformation, and results in substantially reduced gate count estimates when performing limited circuit optimisations., Comment: 46 pages, 11 figures

We argue that the boldest claims of Big Data are in need of revision and toning-down, in view of a few basic lessons learned from the science of complex systems. We point out that, once the most extravagant claims of Big Data are properly discarded, a synergistic merging of BD with big theory offers considerable potential to spawn a new scientific paradigm capable of overcoming some of the major barriers confronted by the modern scientific method originating with Galileo. These obstacles are due to the presence of nonlinearity, nonlocality and hyperdimensions which one encounters frequently in multiscale modelling.

The efficacy of drug treatments depends on how tightly small molecules bind to their target proteins. The rapid and accurate quantification of the strength of these interactions (as measured by binding affinity) is a grand challenge of computational chemistry, surmounting which could revolutionize drug design and provide the platform for patient-specific medicine. Recent evidence suggests that molecular dynamics (MD) can achieve useful predictive accuracy (< 1 kcal/mol). For this predictive accuracy to impact clinical decision making, binding free energy computational campaigns must provide results rapidly and without loss of accuracy. This demands advances in algorithms, scalable software systems, and efficient utilization of supercomputing resources. We introduce a framework called HTBAC, designed to support accurate and scalable drug binding affinity calculations, while marshaling large simulation campaigns. We show that HTBAC supports the specification and execution of free-energy protocols at scale. This paper makes three main contributions: (1) shows the importance of adaptive execution for ensemble-based free energy protocols to improve binding affinity accuracy; (2) presents and characterizes HTBAC -- a software system that enables the scalable and adaptive execution of binding affinity protocols at scale; and (3) for a widely used free-energy protocol (TIES), shows improvements in the accuracy of simulations for a fixed amount of resource, or reduced resource consumption for a fixed accuracy as a consequence of adaptive execution.

Resistance to chemotherapy and molecularly targeted therapies is a major factor in limiting the effectiveness of cancer treatment. In many cases, resistance can be linked to genetic changes in target proteins, either pre-existing or evolutionarily selected during treatment. Key to overcoming this challenge is an understanding of the molecular determinants of drug binding. Using multi-stage pipelines of molecular simulations we can gain insights into the binding free energy and the residence time of a ligand, which can inform both stratified and personal treatment regimes and drug development. To support the scalable, adaptive and automated calculation of the binding free energy on high-performance computing resources, we introduce the High- throughput Binding Affinity Calculator (HTBAC). HTBAC uses a building block approach in order to attain both workflow flexibility and performance. We demonstrate close to perfect weak scaling to hundreds of concurrent multi-stage binding affinity calculation pipelines. This permits a rapid time-to-solution that is essentially invariant of the calculation protocol, size of candidate ligands and number of ensemble simulations. As such, HTBAC advances the state of the art of binding affinity calculations and protocols.

We expect that multiscale simulations will be one of the main high performance computing workloads in the exascale era. We propose multiscale computing patterns as a generic vehicle to realise load balanced, fault tolerant and energy aware high performance multiscale computing. Multiscale computing patterns should lead to a separation of concerns, whereby application developers can compose multiscale models and execute multiscale simulations, while pattern software realises optimized, fault tolerant and energy aware multiscale computing. We introduce three multiscale computing patterns, present an example of the extreme scaling pattern, and discuss our vision of how this may shape multiscale computing in the exascale era.

Computer simulation is finding a role in an increasing number of scientific disciplines, concomitant with the rise in available computing power. Realizing this inevitably requires access to computational power beyond the desktop, making use of clusters, supercomputers, data repositories, networks and distributed aggregations of these resources. Accessing one such resource entails a number of usability and security problems; when multiple geographically distributed resources are involved, the difficulty is compounded. This presents the user with the problem of how to gain access to suitable resources to run their workloads as they need them. In this paper we present our solutions to this problem, a resource trading platform that allows users to purchase access to resources within a distributed e-infrastructure. We present the implementation of this Resource Allocation Market Place as a distributed multi-agent system, and show how it provides a highly flexible, efficient tool to schedule workflows across high performance computing resources.

We present FabSim, a toolkit developed to simplify a range of computational tasks for researchers in diverse disciplines. FabSim is flexible, adaptable, and allows users to perform a wide range of tasks with ease. It also provides a systematic way to automate the use of resourcess, including HPC and distributed resources, and to make tasks easier to repeat by recording contextual information. To demonstrate this, we present three use cases where FabSim has enhanced our research productivity. These include simulating cerebrovascular bloodflow, modelling clay-polymer nanocomposites across multiple scales, and calculating ligand-protein binding affinities., Comment: 29 pages, 8 figures, 2 tables, submitted

Cerebrovascular diseases such as brain aneurysms are a primary cause of adult disability. The flow dynamics in brain arteries, both during periods of rest and increased activity, are known to be a major factor in the risk of aneurysm formation and rupture. The precise relation is however still an open field of investigation. We present an automated ensemble simulation method for modelling cerebrovascular blood flow under a range of flow regimes. By automatically constructing and performing an ensemble of multiscale simulations, where we unidirectionally couple a 1D solver with a 3D lattice-Boltzmann code, we are able to model the blood flow in a patient artery over a range of flow regimes. We apply the method to a model of a middle cerebral artery, and find that this approach helps us to fine-tune our modelling techniques, and opens up new ways to investigate cerebrovascular flow properties., Comment: Journal of Computational Science (in press), 10 pages, 6 figures, 2 tables