arXiv subjects

Shah Ishmam Mohtashim

Publications and source records attributed to Shah Ishmam Mohtashim.

5 recordsLinked to original sources

arXiv2026

Continuous-time quantum-walk centrality for protein residue interaction networks

We present a quantum-dynamical framework for identifying structurally important residues in proteins based on continuous time quantum walks (CTQWs) on weighted residue interaction networks constructed from experimentally resolved structures. By mapping the weighted adjacency matrix to a Hamiltonian, residue importance emerges from the long-time averaged occupation probability, confirmed analytically through its spectral decomposition. Across a dataset of approximately 150 proteins spanning diverse structural and functional classes, CTQW centrality exhibits consistently strong agreement with classical eigenvector centrality in identifying central residues, while extending beyond it through incorporating signatures of quantum interference. Analyzing the time-averaged quantum transition matrix reveals consistently larger spectral gaps than the classical random-walk operator. Furthermore, biological relevance is confirmed through recovery of experimentally established functional residues in proteins kinase A and oxytocin. CTQW-derived centrality rankings are accessible on near-term intermediate-scale quantum hardware, as we demonstrate through a proof-of-principle implementation on IBM superconducting quantum hardware. These results establish continuous-time quantum walks as a computationally tractable framework for protein network analysis, that connects network theoretical treatments of protein structural biology to continuous-time quantum walk dynamics.

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arXiv2026

Energy Landscape Structure of Small Graph Isomorphism Under Variational Optimization

We investigate a quadratic unconstrained binary optimization (QUBO) formulation of the graph isomorphism problem using the Quantum Approximate Optimization Algorithm (QAOA) and the Variational Quantum Eigensolver (VQE). For small graph instances, we observe that isomorphic pairs exhibit consistent clustering in variational energies, indicating that the Hamiltonian successfully encodes structural features. However, we demonstrate that low variational energy alone is an unreliable certifier of isomorphism due to the high probability of converging to infeasible states that violate bijection constraints. To address this, we analyze optimization trajectories rather than final energies; consistently outperform naive energy thresholding, though absolute performance remains limited. Our results characterize the current limits of variational algorithms for graph isomorphism, positioning energy landscape analysis as a diagnostic tool rather than a scalable decision procedure in the NISQ regime.

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arXiv2025

RinQ: Towards predicting central sites in proteins on current quantum computers

We introduce RinQ, a hybrid quantum-classical framework for identifying functionally critical residues in proteins by formulating centrality detection as a Quadratic Unconstrained Binary Optimization (QUBO) problem. Protein structures are modeled as residue interaction networks (RINs), and the QUBO formulations are solved using D-Wave's simulated annealing. Applied to a diverse set of proteins, RinQ consistently identifies central residues that closely align with classical benchmarks, demonstrating both the accuracy and robustness of the approach.

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arXiv2025

A near-term quantum simulation of the transverse field Ising model hints at Glassy Dynamics

We demonstrate quantum circuit simulations of the transverse field Ising model with longitudinal fields, displaying salient features of glassy dynamics. The energy landscape and spin configurations of toy models are considered, using the Variational Quantum Eigensolver (VQE) to obtain the ground-state energies and corresponding eigenstates for a $6 \times 6$ Ising lattice using 36 qubits and a 1-dimensional Ising chain of length 25 using 25 qubits. The former showed disordered spin configurations for a specific mixture of values of the two fields. These insights mirror catalytic processes, where disorder within a catalyst can lead to inefficient reaction mechanisms. Results obtained from our proof-of-principle implementation make the case for kick-starting more concentrated efforts in harnessing existing quantum computational tools for computationally probing complex dynamical behaviour arising in quantum matter. Our aim is to leverage tools from quantum information processing to bring about a more nuanced understanding of the dynamics and structure of glassy systems, ultimately informing the development of novel materials and technology.

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arXiv2021

Qurzon: A Prototype for a Divide and Conquer Based Quantum Compiler

When working with algorithms on quantum devices, quantum memory becomes a crucial bottleneck due to low qubit count in NISQ-era devices. In this context, the concept of `divide and compute', wherein a quantum circuit is broken into several subcircuits and executed separately, while stitching the results of the circuits via classical post-processing, becomes a viable option, especially in NISQ-era devices. This paper introduces \textbf{Qurzon}, a proposed novel quantum compiler that incorporates the marriage of techniques of divide and compute with the state-of-the-art algorithms of optimal qubit placement for executing on real quantum devices. A scheduling algorithm is also introduced within the compiler that can explore the power of distributed quantum computing while paving the way for quantum parallelism for large algorithms. Several benchmark circuits have been executed using the compiler, thereby demonstrating the power of the divide and compute when working with real NISQ-era quantum devices.

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