arXiv subjects

Abhishek Setty

Publications and source records attributed to Abhishek Setty.

5 recordsLinked to original sources

arXiv2026

Time evolution of nonlinear dynamics on a quantum processor

From fluid flow and transport to collective dynamics, numerical simulation of nonlinear partial differential equations underpins modern scientific computing. Extending this capability to quantum computers remains a longstanding challenge because nonlinear and non-Hermitian evolution is fundamentally incompatible with conventional Hamiltonian-based quantum simulation. Here we experimentally realize the time evolution of nonlinear fluid dynamics on a quantum processor using a hybrid variational framework for the viscous and inviscid Burgers equations. Our approach directly encodes the nonlinear dynamics into a variational optimization procedure, avoiding the enlarged linear embeddings and truncation overhead associated with Carleman linearization-based quantum algorithms. We further demonstrate convection-dominated dynamics corresponding to Reynolds numbers of order $10^2$. We encode the governing evolution into parametrized quantum circuits and iteratively reconstruct the time-dependent field through quantum-classical optimization. By introducing a zero-noise extrapolation method without additional circuit-folding overhead, we accurately execute deep error-circuits with entangling-gate counts beyond those typical of Hadamard test circuits. We accurately reconstruct the time evolution across multiple timesteps despite hardware noise and finite device coherence. Our results constitute, to our knowledge, the first experimental realization of nonlinear time propagation on a quantum processor, extending quantum simulation beyond predominantly linear settings and establishing a route toward quantum computation for nonlinear continuum dynamics.

quant-ph↗

arXiv2025

A Quantum Linear Systems Pathway for Solving Differential Equations

We present a systematic pathway for solving differential equations within the quantum linear systems framework by combining block encoding with Quantum Singular Value Transformation (QSVT). The approach is demonstrated on a complex tridiagonal linear system and extended to problems in computational fluid dynamics: the heat equation with mixed boundary conditions and Carleman-linearized nonlinear Burgers' equation. Our scaling analysis of the heat equation identifies regimes where classical computation remains feasible and estimates circuit depths required to achieve potential quantum advantage. We further evaluate post-selection success probabilities for the presented examples and provide hardware resource estimates for block encoding and QSVT circuits in terms of two-qubit gate depth, evaluated on IBM superconducting processors with heavy-hex and square lattice topologies. These results highlight both the practical limitations of current hardware and key directions for depth reduction and scalable quantum linear solvers.

quant-ph↗

arXiv2025

Block Encoding of Sparse Matrices via Coherent Permutation

Block encoding of sparse matrices underpins quantum algorithms such as quantum singular value transformation, Hamiltonian simulation, and quantum linear system solvers, yet its efficient gate-level realization remains challenging, with index-mapping oracles constituting one important source of overhead. We introduce a block-encoding framework that focuses on the index-mapping component, where coherent permutation is used as the central mechanism to optimize shift, delete, and insert operations. This provides a unified treatment of index mapping and reduces local multicontrolled X control complexity through structured compression. We further connect coherent amplitude permutation to combinatorial optimization, enabling systematic assignment of control states under hardware connectivity constraints. The resulting construction supports entry-wise block encoding for general sparse matrices, with efficiency gains in structured cases. We demonstrate the approach on representative examples and provide resource analysis using IBM superconducting backends, showing significant reductions in circuit depth.

quant-ph↗

arXiv2025

Particle Trajectory Prediction in Discrete Element Simulations using a Graph-Based Interaction-Aware Model

This study explores the applicability of a graph-based interaction-aware trajectory prediction model, originally developed for the transportation domain, to forecast particle trajectories in three-dimensional discrete element simulations. The model and our enhancements are validated at two typical particle simulation use cases: (i) particle flow in a representative unit cell with periodic boundary conditions (PBCs) in combination with sinusoidal velocity profile and (ii) shear flow in a representative unit cell with Lees-Edwards boundary conditions (LEBCs). For the models to learn the particle behavior subjected to these boundary conditions requires additional data transformation and feature engineering, which we introduce. Furthermore, we introduce and compare two novel training procedures for the adapted prediction model, which we call position-centric training (PCT) and velocity-centric training (VCT). The results show that the models developed for the transportation domain can be adapted to learn the behavior of particles in discrete element simulations.

physics.comp-ph↗

arXiv2023

Self-Adaptive Physics-Informed Quantum Machine Learning for Solving Differential Equations

Chebyshev polynomials have shown significant promise as an efficient tool for both classical and quantum neural networks to solve linear and nonlinear differential equations. In this work, we adapt and generalize this framework in a quantum machine learning setting for a variety of problems, including the 2D Poisson's equation, second-order linear differential equation, system of differential equations, nonlinear Duffing and Riccati equation. In particular, we propose in the quantum setting a modified Self-Adaptive Physics-Informed Neural Network (SAPINN) approach, where self-adaptive weights are applied to problems with multi-objective loss functions. We further explore capturing correlations in our loss function using a quantum-correlated measurement, resulting in improved accuracy for initial value problems. We analyse also the use of entangling layers and their impact on the solution accuracy for second-order differential equations. The results indicate a promising approach to the near-term evaluation of differential equations on quantum devices.

quant-ph↗