Wisniewski group
Aalborg University, Aalborg, Denmark
- Tracked papers
- 17 (2023–2026)
Topics
The most frequent field-map topics among the PI' tracked papers.
Recent papers
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Rank-Dependent Error Bounds and Near-Optimality in Quantum Control via Hierarchical Tucker Surrogates
Abstract
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.
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A Variational Surrogate Approach to Finite-Horizon Quantum Control via Hardware-Efficient Ansatz
Abstract
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.
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Certified Quantum Schrödinger Control via Hierarchical Tucker Models
Abstract
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.
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Trotterized Variational Quantum Control for Spin-Chain State Transfer
Abstract
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.
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Quantum-Assisted Barrier Sequential Quadratic Programming for Nonlinear Optimal Control
Abstract
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.
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Robust Entanglement Generation in Bipartite Quantum Systems Using Optimal Control
Abstract
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.
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Quantum Solution Framework for Finite-Horizon LQG Control via Block Encodings and QSVT
Abstract
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.
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Feedback-Based Quantum Strategies for Constrained Combinatorial Optimization Problems
Abstract
Feedback-based quantum algorithms have recently emerged as potential methods for approximating the ground states of Hamiltonians. One such algorithm, the feedback-based algorithm for quantum optimization (FALQON), is specifically designed to solve quadratic unconstrained binary optimization problems. Its extension, the feedback-based algorithm for quantum optimization with constraints (FALQON-C), was introduced to handle constrained optimization problems with equality and inequality constraints. In this work, we extend the feedback-based quantum algorithms framework to address a broader class of constraints known as invalid configuration (IC) constraints, which explicitly prohibit specific configurations of decision variables. We first present a transformation technique that converts the constrained optimization problem with invalid configuration constraints into an equivalent unconstrained problem by incorporating a penalizing term into the cost function. Then, leaning upon control theory, we propose an alternative method tailored for feedback-based quantum algorithms that directly tackles IC constraints without requiring slack variables. Our approach introduces a new operator that encodes the optimal feasible solution of the constrained optimization problem as its ground state. Then, a controlled quantum system based on the Lyapunov control technique is designed to ensure convergence to the ground state of this operator. Two approaches are introduced in the design of this operator to address IC constraints: the folded spectrum approach and the deflation approach. These methods eliminate the need for slack variables, significantly reducing the quantum circuit depth and the number of qubits required. We show the effectiveness of our proposed algorithms through numerical simulations.
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State-Constrained Optimal Control for Coherence Preservation in Multi-Level Open Quantum Systems
Abstract
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.
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Feedback-Based Quantum Algorithm for Constrained Optimization Problems
Abstract
The feedback-based algorithm for quantum optimization (FALQON) has recently been proposed to solve quadratic unconstrained binary optimization problems. This paper efficiently generalizes FALQON to tackle quadratic constrained binary optimization (QCBO) problems. For this purpose, we introduce a new operator that encodes the problem's solution as its ground state. Using Lyapunov control theory, we design a quantum control system such that the state converges to the ground state of this operator. When applied to the QCBO problem, we show that our proposed algorithm saves computational resources by reducing the depth of the quantum circuit and can perform better than FALQON. The effectiveness of our proposed algorithm is further illustrated through numerical simulations.