arXiv subjects

Nahid Binandeh Dehaghani

Publications and source records attributed to Nahid Binandeh Dehaghani.

At least 19 recordsLinked to original sources

arXiv2026

On Embedding Design in Quantum Physics-Informed Neural Networks

Quantum physics-informed neural networks (QPINNs) solve partial differential equations (PDEs) by training parameterized quantum circuits against physics-based residuals, yet the role of the embedding that maps coordinates into quantum states remains insufficiently understood. In this research, we introduce a unified embedding framework that formulates embedding as a functional transformation shaping the feature representation available to the variational circuit, and we propose two embeddings within it. The Linear Quantum Neural Network Trainable Embedding QPINN (LQNN-TE-QPINN) generates data-dependent features with an auxiliary quantum circuit and adds them to the input coordinates, instead of multiplying them as in our previous formulation. The adaptive-frequency QPINN (AdaFreq-QPINN) promotes the frequency-scaling factors of an arccos-Chebyshev encoding to trainable parameters. We evaluate both against direct and fixed analytical frequency encodings and alternative hybrid architectures on one- and two-dimensional Burgers equations. In one dimension, LQNN-TE-QPINN achieves a relative $L_2$ error of 0.0916 with 720 trainable parameters, compared with 0.4501 for direct-encoding QPINN and 0.1233 for a locally adaptive classical physics-informed neural network with approximately eleven times more parameters, while AdaFreq-QPINN attains the lowest error among the analytical embeddings with only four additional parameters. In two dimensions, LQNN-TE-QPINN attains the lowest training objective, although its solution error is not clearly separated from that of a data re-uploading QPINN. Under simulated hardware noise, LQNN-TE-QPINN retains the lowest absolute derivative error while degrading most relative to its noiseless baseline. These results demonstrate that embedding design substantially influences the approximation and optimization behavior of QPINNs.

quant-ph↗

arXiv2026

Rank-Dependent Error Bounds and Near-Optimality in Quantum Control via Hierarchical Tucker Surrogates

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-accuracy condition, we establish exponentially decaying trajectory, cost, and value-function errors and near-optimality of surrogate-generated controls. We further derive a logarithmic rank--performance relation, an a posteriori cost certificate from realized truncation perturbations, and guarantees for inexact surrogate optimization and control convergence under additional regularity conditions. Numerical experiments on controlled XXZ spin chains provide finite-sample evidence consistent with the truncation condition and illustrate the trade-off between HT rank, representation size, surrogate accuracy, and control performance.

math.OC↗

arXiv2026

A Variational Surrogate Approach to Finite-Horizon Quantum Control via Hardware-Efficient Ansatz

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 state to a desired target state over a fixed time horizon by minimizing a terminal cost defined in terms of state fidelity. Instead of explicitly synthesizing time-dependent control fields or enforcing Hamiltonian reachability constraints, the proposed method reformulates the control objective as a variational optimization problem in which a hardware-efficient parameterized quantum circuit provides a surrogate parameterization of the terminal evolution. The circuit consists of alternating layers of single-qubit rotations and entangling gates, whose parameters are optimized using classical routines to minimize the terminal infidelity. This formulation avoids reliance on problem-specific or physics-inspired ansätze, providing a flexible and implementation-friendly approach compatible with near-term quantum devices. Numerical experiments on multi-qubit state-transfer benchmarks demonstrate high-fidelity state transfer while highlighting the trade-off between ansatz expressivity, optimization complexity, and scalability with respect to system size and circuit depth.

quant-ph↗

arXiv2026

Tensor Network Methods for Advection-Diffusion-Reaction Systems Using Quantum-Inspired Representations

We present a quantum-inspired tensor-network framework for solving advection-diffusion-reaction (ADR) partial differential equations. Discretized solution fields are encoded as matrix product states (MPS), while differential operators are represented as matrix product operators (MPOs). Time integration is performed entirely in tensor-network form using explicit Euler updates with controlled truncation. The method is evaluated on one- and two-dimensional ADR problems and compared with high-accuracy Runge-Kutta reference solutions. Numerical results show that the proposed representation remains compact, stable, and accurate across a range of dynamical regimes. The solver captures both local solution profiles and global observables while maintaining small bond dimensions throughout the simulation. These results highlight the potential of tensor networks as efficient structure-preserving tools for PDE simulation in multiple spatial dimensions.

math.NA↗

arXiv2026

A QPINN Framework with Quantum Trainable Embeddings for the Lid-Driven Cavity Problem

The steady incompressible Navier--Stokes equations pose significant computational challenges due to their nonlinear convective terms and pressure--velocity coupling. Physics-informed neural networks (PINNs) provide a mesh-free framework for approximating such systems, but classical PINNs can experience optimization difficulties in nonlinear flow regimes. In this work, we propose a quantum physics-informed neural network (QPINN) framework with a quantum neural network (QNN)-based trainable embedding for the lid-driven cavity problem. The proposed approach uses a QNN to learn data-adaptive quantum feature maps that encode spatial coordinates before they are processed by a variational quantum circuit within a physics-informed loss formulation. Numerical experiments show that the proposed QNN-TE-QPINN exhibits stable training behavior and competitive solution accuracy compared with classical PINNs and hybrid quantum models using classical embeddings, while requiring significantly fewer trainable parameters. Rather than claiming computational speedup, these results highlight the potential of trainable quantum embeddings for parameter-efficient physics-informed learning. The findings suggest that embedding design plays an important role in quantum-assisted PDE solvers and support further investigation of QNN-based trainable embeddings for nonlinear fluid dynamics benchmarks.

quant-ph↗

arXiv2026

Certified Quantum Schrödinger Control via Hierarchical Tucker Models

High-dimensional Schrödinger systems arising from tensor-product discretizations suffer from exponential state growth, making direct controller synthesis and real-time closed-loop simulation computationally challenging. Hierarchical Tucker (HT) tensor representations offer scalable low-rank surrogates, but the impact of fixed-rank truncation on closed-loop stability is not well understood. This paper develops a local robustness framework for sampled-data feedback control implemented with fixed-rank HT projections. By viewing each truncation as a bounded, rank-dependent perturbation of the nominal closed loop, and assuming a local phase-invariant contraction certificate together with trajectory-level hierarchical spectral decay, we show that the HT-projected dynamics are practically exponentially stable: trajectories converge to a dimension-independent tube whose radius decreases with the prescribed rank. We further obtain an explicit logarithmic rank-accuracy relation and establish conditions under which controllers designed on the HT-truncated surrogate model retain practical exponential tracking guarantees when deployed on the full system, together with an explicit bound quantifying the resulting surrogate-to-plant mismatch. A compact lattice example demonstrates the applicability of the framework.

quant-ph↗

arXiv2026

Quantum-Assisted Trainable-Embedding Physics-Informed Neural Networks for Parabolic PDEs

Physics-informed neural networks (PINNs) have emerged as a powerful framework for solving partial differential equations (PDEs) by embedding governing physical laws directly into the training objective. Recent advances in quantum machine learning have motivated hybrid quantum-classical extensions aimed at enhancing representational capacity while remaining compatible with near-term quantum hardware. In this work, we investigate trainable embedding strategies within quantum-assisted PINNs for solving parabolic PDEs, using one- and two-dimensional heat equations as canonical benchmarks. We introduce two quantum-assisted architectures that differ in their embedding components. In the first approach, a classical feed-forward neural network generates trainable feature maps for quantum data encoding (FNN-TE-QPINN). In the second, the embedding stage is realized entirely by a parameterized quantum circuit (QNN-TE-QPINN), yielding a fully quantum feature map. Our findings emphasize the critical role of embedding design and support hybrid quantum-classical approaches for parabolic PDE modeling in the NISQ era.

quant-ph↗

arXiv2026

Quantum-Inspired Tensor Networks for Approximating PDE Flow Maps

We investigate quantum-inspired tensor networks (QTNs) for approximating flow maps of hydrodynamic partial differential equations (PDEs). Motivated by the effective low-rank structure that emerges after tensorization of discretized transport and diffusion dynamics, we encode PDE states as matrix product states (MPS) and represent the evolution operator as a structured low-rank matrix product operator (MPO) in tensor-train form (e.g., arising from finite-difference discretizations assembled in MPO form). The MPO is applied directly in MPS form, and rank growth is controlled via canonicalization and SVD-based truncation after each step. We provide theoretical context through standard matrix product properties, including exact MPS representability bounds, local optimality of SVD truncation, and a Lipschitz-type multi-step error propagation estimate. Experiments on one- and two-dimensional linear advection-diffusion and nonlinear viscous Burgers equations demonstrate accurate short-horizon prediction, favorable scaling in smooth diffusive regimes, and error growth in nonlinear multi-step predictions.

math.NA↗

arXiv2026

A Trainable-Embedding Quantum Physics-Informed Framework for Multi-Species Reaction-Diffusion Systems

Physics-informed neural networks (PINNs) and hybrid quantum-classical extensions provide a promising framework for solving partial differential equations (PDEs) by embedding physical laws directly into the learning process. In this work, we study embedding strategies for trainable embedding quantum physics-informed neural networks (TE-QPINNs) in the context of nonlinear reaction-diffusion (RD) systems. We introduce an extended TE-QPINN (x-TE-QPINN) architecture that supports both classical and fully quantum embeddings, enabling a controlled comparison between feedforward neural network-based feature maps and parameterized quantum circuit embeddings. The first architecture is the classical embedding feed-forward neural network-based TE-QPINN (FNN-TE-QPINN), while the latter variant is a purely quantum one, referred to as quantum embedding neural network-based TE-QPINN (QNN-TE-QPINN). The proposed framework employs hardware-efficient variational quantum circuits and species-specific readout operators to approximate coupled multi-field dynamics while enforcing governing equations, boundary conditions, and initial conditions through a physics-informed loss function. By isolating the embedding mechanism while keeping the variational ansatz, loss formulation, and optimization procedure fixed, we analyze the impact of embedding design on gradient structure, parameter scaling, and quantum resource requirements. Numerical experiments on one- and two-dimensional RD equations demonstrate that quantum embeddings can replace classical embeddings without degradation in solution accuracy and, in certain regimes, exhibit improved optimization behavior compared to classical PINNs and hybrid quantum models with fixed embeddings. These results provide architectural insight into hybrid quantum PDE solvers and inform the design of resource-efficient quantum physics-informed learning methods.

quant-ph↗

arXiv2025

Trotterized Variational Quantum Control for Spin-Chain State Transfer

We present a hybrid variational framework for quantum optimal control aimed at high-fidelity state transfer in spin chains. The system dynamics are discretized and compiled into a parameterized circuit, where deterministic two-qubit blocks implement the drift interactions, while trainable on-site RZ rotations encode the control inputs. We study two parameterizations: a compact global scheme with a small number of shared parameters per slice, and a local scheme with site-wise angles. Using a Sequential Least Squares Quadratic Programming (SLSQP) optimization to minimize infidelity, simulations on XXZ spin chains show that both parameterizations can achieve near-unit fidelities in the noiseless regime. Under depolarizing noise, the global scheme provides improved robustness for comparable circuit depth and iteration budgets. The results make explicit an expressivity-stability trade-off and suggest a scalable route to Noisy Intermediate-Scale Quantum (NISQ) compatible control synthesis.

quant-ph↗

arXiv2025

Quantum-Assisted Barrier Sequential Quadratic Programming for Nonlinear Optimal Control

We propose a quantum-assisted framework for solving constrained finite-horizon nonlinear optimal control problems using a barrier Sequential Quadratic Programming (SQP) approach. Within this framework, a quantum subroutine is incorporated to efficiently solve the Schur complement step using block-encoding and Quantum Singular Value Transformation (QSVT) techniques. We formally analyze the time complexity and convergence behavior under the cumulative effect of quantum errors, establishing local input-to-state stability and convergence to a neighborhood of the stationary point, with explicit error bounds in terms of the barrier parameter and quantum solver accuracy. The proposed framework enables computational complexity to scale polylogarithmically with the system dimension demonstrating the potential of quantum algorithms to enhance classical optimization routines in nonlinear control applications.

quant-ph↗

arXiv2025

Quantum-Assisted Learning of Time-Dependent Parabolic PDEs

We present a hybrid quantum-classical framework for solving general time-dependent parabolic partial differential equations (PDEs) using quantum variational circuits. Building on the QPINN approach, this method applies broadly to parabolic PDEs. To demonstrate its effectiveness, we focus on the 1D and 2D heat equations as representative examples and analyze its performance under constrained quantum resources. Our results show that the framework can accurately capture spatiotemporal dynamics, offering a promising direction for quantum-assisted scientific computing.

quant-ph↗

arXiv2025

Quantum Solution Framework for Finite-Horizon LQG Control via Block Encodings and QSVT

We present a quantum algorithm for solving the finite-horizon discrete-time Linear Quadratic Gaussian (LQG) control problem, which integrates optimal control and state estimation in the presence of stochastic disturbances and noise. Classical approaches to LQG require solving a backward Riccati recursion and a forward Kalman filter, both requiring computationally expensive matrix operations with overall time complexity $\mathcal{O}(T n^3)$, where $n$ is the system dimension and $T$ is the time horizon. While efficient classical solvers exist, especially for small to medium-sized systems, their computational complexity grows rapidly with system dimension. To address this, we reformulate the full LQG pipeline using quantum linear algebra primitives, including block-encoded matrix representations and quantum singular value transformation (QSVT) techniques for matrix inversion and multiplication. We formally analyze the time complexity of each algorithmic component. Under standard assumptions on matrix condition numbers and encoding precision, the total runtime of the quantum LQG algorithm scales polylogarithmically with the system dimension $n$ and linearly with the time horizon $T$, offering an asymptotic quantum speedup over classical methods.

quant-ph↗

arXiv2025

Robust Entanglement Generation in Bipartite Quantum Systems Using Optimal Control

Quantum entanglement is a key resource for quantum technologies, yet its efficient and high-fidelity generation remains a challenge due to the complexity of quantum dynamics. This paper presents a quantum optimal control framework to maximize bipartite entanglement within a fixed time horizon, under bounded control inputs. By leveraging Pontryagin's Minimum Principle, we derive a set of necessary conditions that guide the design of time-dependent control fields to steer a two-qubit system toward maximally entangled Bell states. The entanglement is quantified using concurrence, and the control objective is formulated as maximizing this measure at the terminal time. Our approach is validated through numerical simulations of Liouville-von Neumann dynamics. The results demonstrate the effectiveness of switching-based control strategies in achieving robust entanglement, offering insights into practical implementations of quantum control for entanglement generation in quantum networks.

quant-ph↗

arXiv2025

Optimizing Maximally Entangled State Generation via Pontryagin's Principle

We propose an optimal control strategy to generate maximally entangled states in bipartite quantum systems. Leveraging the Pontryagin Principle, we derive time-dependent control fields that maximize the entanglement measure, specifically concurrence, within minimal time while adhering to input constraints. Our formulation addresses the Liouville-von Neumann dynamics of the reduced density matrix under unitary evolution. The strategy is numerically validated through simulations, demonstrating its ability to drive the system from an initial perturbed separable state to a maximally entangled target state. The results showcase the effectiveness of switching control fields in optimizing entanglement, with potential applications in quantum technologies, including communication, computation, and sensing.

quant-ph↗

arXiv2024

State-Constrained Optimal Control for Coherence Preservation in Multi-Level Open Quantum Systems

This paper addresses the optimal control of quantum coherence in multi-level systems, modeled by the Lindblad master equation, which captures both unitary evolution and environmental dissipation. We develop an energy minimization framework to control the evolution of a qutrit (three-level) quantum system while preserving coherence between states. The control problem is formulated using Pontryagin's Minimum Principle in the form of Gamkrelidze, incorporating state constraints to ensure coherence remains within desired bounds. Our approach accounts for Markovian decoherence, demonstrating that the Lindblad operator is non-unital, which reflects the irreversible decay processes inherent in the system. The results provide insights into effectively maintaining quantum coherence in the presence of dissipation.

quant-ph↗

arXiv2024

State Estimation and Control for Stochastic Quantum Dynamics with Homodyne Measurement: Stabilizing Qubits under Uncertainty

This paper introduces a Lyapunov-based control approach with homodyne measurement. We study two filtering approaches: (i) the traditional quantum filtering and (ii) a modified version of the extended Kalman filtering. We examine both methods in order to directly estimate the evolution of the coherence vector elements, using sequential homodyne current measurements. The latter case explicitly addresses the dynamics of a stochastic master equation with correlated noise, transformed into a state-space representation, ensuring by construction the quantum properties of the estimated state variable. In addition, we consider the case where the quantum-mechanical Hamiltonian is unknown, and the system experiences uncertainties. In this case, we show as expected that both filters lose performance, exhibiting large expected estimation errors. To address this problem, we propose a simple multiple model estimation scheme that can be directly applied to any of the studied filters. We then reconstruct the estimated density operator $ \hatρ $, describing the full state of the system, and subject it to a control scheme. The proposed switching-based Lyapunov control scheme, which is fed with $ \hatρ $, guarantees noise-to-state practically stable in probability of the desired stationary target set with respect to the estimation error variance. We demonstrate our approach's efficacy in stabilizing a qubit coupled to a leaky cavity under homodyne detection in the presence of uncertainty in resonance frequency.

quant-ph↗

arXiv2024

A Hybrid Quantum-Classical Physics-Informed Neural Network Architecture for Solving Quantum Optimal Control Problems

This paper proposes an integrated quantum-classical approach that merges quantum computational dynamics with classical computing methodologies tailored to address control problems based on Pontryagin's minimum principle within a Physics-Informed Neural Network (PINN) framework. By leveraging a dynamic quantum circuit that combines Gaussian and non-Gaussian gates, the study showcases an innovative approach to optimizing quantum state manipulations. The proposed hybrid model effectively applies machine learning techniques to solve optimal control problems. This is illustrated through the design and implementation of a hybrid PINN network to solve a quantum state transition problem in a two and three-level system, highlighting its potential across various quantum computing applications.

quant-ph↗