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On Embedding Design in Quantum Physics-Informed Neural Networks
Ban Q. Tran, Nahid Binandeh Dehaghani, Susan Mengel +2
Quantum physics-informed neural networks (QPINNs) solve partial differential equations (PDEs) by training parameterized quantum circuits against physics-based residuals, yet the ro…
Rank-Dependent Error Bounds and Near-Optimality in Quantum Control via Hierarchical Tucker Surrogates
Nahid Binandeh Dehaghani, Rafal Wisniewski, Julian Berberich +1
We develop a certified finite-horizon quantum optimal-control framework based on fixed-rank Hierarchical Tucker (HT) surrogates. Under a uniform rank-dependent HT truncation-accura…
Tensor Network Methods for Advection-Diffusion-Reaction Systems Using Quantum-Inspired Representations
Nahid Binandeh Dehaghani, Rafal Wisniewski, A. Pedro Aguiar
We present a quantum-inspired tensor-network framework for solving advection-diffusion-reaction (ADR) partial differential equations. Discretized solution fields are encoded as mat…
A Variational Surrogate Approach to Finite-Horizon Quantum Control via Hardware-Efficient Ansatz
Nahid Binandeh Dehaghani, Rafal Wisniewski, A. Pedro Aguiar
We present a variational quantum framework for finite-horizon quantum control based on hardware-efficient ansätze. The objective is to steer a quantum system from a given initial s…
A QPINN Framework with Quantum Trainable Embeddings for the Lid-Driven Cavity Problem
Nahid Binandeh Dehaghani, Ban Q. Tran, Susan Mengel +2
The steady incompressible Navier--Stokes equations pose significant computational challenges due to their nonlinear convective terms and pressure--velocity coupling. Physics-inform…
Quantum-Inspired Tensor Networks for Approximating PDE Flow Maps
Nahid Binandeh Dehaghani, Ban Q. Tran, Rafal Wisniewski +2
We investigate quantum-inspired tensor networks (QTNs) for approximating flow maps of hydrodynamic partial differential equations (PDEs). Motivated by the effective low-rank struct…
Quantum-Assisted Trainable-Embedding Physics-Informed Neural Networks for Parabolic PDEs
Ban Q. Tran, Nahid Binandeh Dehaghani, Rafal Wisniewski +2
Physics-informed neural networks (PINNs) have emerged as a powerful framework for solving partial differential equations (PDEs) by embedding governing physical laws directly into t…