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Quantum algorithms will likely play a key role in future high-performance-computing (HPC) environments. These algorithms are typically expressed as quantum circuits composed of arbitrary gates or as unitary matrices. Executing these on physical devices, however, requires translation to device-compatible circuits, in a process called quantum compilation or circuit synthesis, since these devices support a limited number of native gates. Moreover, these devices typically have specific qubit topologies, which constrain how and where gates can be applied. Consequently, logical qubits in input circuits and unitaries may need to be mapped to and routed between physical qubits. Furthermore, current Noisy Intermediate-Scale Quantum (NISQ) devices present additional constraints. They are vulnerable to errors during gate application and their short decoherence times lead to qubits rapidly succumbing to accumulated noise and possibly corrupting computations. Therefore, circuits synthesized for NISQ devices need to minimize gates and execution times. The problem of synthesizing device-compatible circuits, while optimizing for low gate count and short execution times, can be shown to be computationally intractable using analytical methods. Therefore, interest has grown towards heuristics-based synthesis techniques, which are able to produce approximations of the desired algorithm, while optimizing depth and gate-count. In this work, we investigate using genetic algorithms (GA)—a proven gradient-free optimization technique based on natural selection—for circuit synthesis. In particular, we formulate the quantum synthesis problem as a multi-objective optimization (MOO) problem, with the objectives of minimizing the approximation error, number of multi-qubit gates, and circuit depth. We also employ fuzzy logic for runtime parameter adaptation of GA to enhance search efficiency and solution quality in our proposed method. 

Quantum computing has the potential to solve certain compute-intensive problems faster than classical computing by leveraging the quantum mechanical properties of superposition and entanglement. This capability can be particularly useful for solving Partial Differential Equations (PDEs), which are challenging to solve even for High-Performance Computing (HPC) systems, especially for multidimensional PDEs. This led researchers to investigate the usage of Quantum-Centric High-Performance Computing (QC-HPC) to solve multidimensional PDEs for various applications. However, the current quantum computing-based PDE-solvers, especially those based on Variational Quantum Algorithms (VQAs) suffer from limitations, such as low accuracy, long execution times, and limited scalability. In this work, we propose an innovative algorithm to solve multidimensional PDEs with two variants. The first variant uses Finite Difference Method (FDM), Classical-to-Quantum (C2Q) encoding, and numerical instantiation, whereas the second variant utilizes FDM, C2Q encoding, and Column-by-Column Decomposition (CCD). We evaluated the proposed algorithm using the Poisson equation as a case study and validated it through experiments conducted on noise-free and noisy simulators, as well as hardware emulators and real quantum hardware from IBM. Our results show higher accuracy, improved scalability, and faster execution times in comparison to variational-based PDE-solvers, demonstrating the advantage of our approach for solving multidimensional PDEs. 

The cytotoxic self-aggregation of β-amyloid (Aβ) peptide and islet amyloid polypeptide (IAPP) is implicated in the pathogenesis of Alzheimer’s disease (AD) and Type 2 diabetes (T2D), respectively. Increasing evidence, particularly the co-deposition of Aβ and IAPP in both brain and pancreatic tissues, suggests that Aβ and IAPP cross-interaction may be responsible for a pathological link between AD and T2D. Here, we examined the nature of IAPP-Aβ40 co-aggregation and its inhibition by small molecules. In specific, we characterized the kinetic profiles, morphologies, secondary structures and toxicities of IAPP-Aβ40 hetero-assemblies and compared them to those formed by their homo-assemblies. We demonstrated that monomeric IAPP and Aβ40 form stable hetero-dimers and hetero-assemblies that further aggregate into β-sheet-rich hetero-aggregates that are toxic (cell viability <50%) to both PC-12 cells, a neuronal cell model, and RIN-m5F cells, a pancreatic cell model for β-cells. We then selected polyphenolic candidates to inhibit IAPP or Aβ40 self-aggregation and examined the inhibitory effect of the most potent candidate on IAPP-Aβ40 co-aggregation. We demonstrated that epigallocatechin gallate (EGCG) form inter-molecular hydrogen bonds with each of IAPP and Aβ40. We also showed that EGCG reduced hetero-aggregate formation and resulted in lower β-sheets content and higher unordered structures in IAPP-Aβ40-EGCG samples. Importantly, we showed that EGCG is highly effective in reducing the toxicity of IAPP-Aβ40 hetero-aggregates on both cell models, specifically at concentrations that are equivalent to or are 2.5-fold higher than the mixed peptide concentrations. To the best of our knowledge, this is the first study to report the inhibition of IAPP-Aβ40 co-aggregation by small molecules. We conclude that EGCG is a promising candidate to prevent co-aggregation and cytotoxicity of IAPP-Aβ40, which in turn, contribute to the pathological link between AD and T2D.