Quantum control papers on arXiv, selected and classified automatically by QOC. https://llorebaga.github.io/QOC/topics/lyapunov-control/ 2026-07-21T00:00:00Z QOC https://arxiv.org/abs/2607.19154 2026-07-21T00:00:00Z 2026-07-21T00:00:00Z Mykhaylo KhomaValeriia BilokonElvira BilokonDenys I. Bondar

Sublinear optical response, in which the emitted field scales as a fractional power of the driving field, lies beyond the conventional perturbative hierarchy of nonlinear optics. Here, we show that such a response can be engineered in a hydrogen atom using tracking control. Rather than prescribing the driving waveform, the field is determined self-consistently from the evolving quantum state to enforce a chosen relation between the optical response and the applied field. We demonstrate accurate tracking for multiple exponents and scaling strengths, establishing that a single atomic system can be driven to realize a family of distinct sublinear responses. The calculations are enabled by a compact wave-packet continuum discretization that treats bound and continuum states on equal footing and is applied here, to the best of our knowledge, for the first time to strong-field optics and quantum control. These results establish tracking control as a general route to engineering optical responses beyond conventional polynomial nonlinearities.

https://arxiv.org/abs/2604.10255 2026-04-11T00:00:00Z 2026-04-11T00:00:00Z Robert Vrabel

We develop a model-free framework for stabilizing quantum states using only empirical finite-difference evaluations of a measurement-derived Lyapunov observable. The controller requires no knowledge of the Hamiltonian, dissipative structure, or generator of the dynamics, and relies solely on discrete measurement data. The approach combines three key elements: sign-based Lyapunov descent, adaptive gain amplification, and a finite-difference analogue of LaSalle's invariance principle. We provide rigorous conditions under which these mechanisms guarantee asymptotic stabilization along the sampling instants in the drift-free case and practical input-to-state stability (ISS) in the presence of unknown drift and noise. The resulting feedback law is simple, derivative-free, and experimentally feasible. A qubit example illustrates the complete closed-loop scheme and the predicted ISS-type behavior. Although demonstrated on a single qubit, the theory applies to arbitrary finite-dimensional quantum systems and offers a foundation for further developments in stochastic, subspace, and multi-qudit model-free quantum control.

https://arxiv.org/abs/2604.06574 2026-04-08T00:00:00Z 2026-04-08T00:00:00Z Guofeng ZhangIan R. Petersen

The purpose of this paper is to investigate the coherent feedback $H^\infty$ control problem for linear quantum systems. A key contribution is a simplified design methodology that guarantees closed-loop stability and a prescribed level of disturbance attenuation. It is shown that for general linear quantum systems, a physically realizable quantum controller can be obtained by solving at most four Lyapunov equations. In the passive case, a necessary and sufficient condition is provided in terms of two uncoupled pairs of Lyapunov equations. These results represent a significant simplification over the standard approach, which requires solving two coupled algebraic Riccati equations. The effectiveness of the proposed method is demonstrated through two typical quantum optical devices: an empty optical cavity and a degenerate parametric amplifier. These results provide a computationally efficient procedure for the robust and optimal control of quantum optical and optomechanical systems.

https://arxiv.org/abs/2603.05417 2026-03-05T00:00:00Z 2026-03-05T00:00:00Z Valeriia BilokonElvira BilokonDenys I. Bondar

Quantum tracking control encodes the desired dynamics into a tailored driving field; here, we let the system find its own way there. We propose a real-time feedback control framework in which a proportional controller continuously corrects a simple transform-limited field based on the instantaneous mismatch between two systems' responses - producing the required control on the fly, without prior waveform design. The framework is demonstrated on two distinct examples: a single-active-electron atom, where hydrogen is driven to mimic argon's strong-field optical emission, and a Fermi-Hubbard chain, where a weakly interacting lattice reproduces the transport dynamics of a Mott-insulating reference. By shifting the control paradigm from predesigned inputs to adaptive response tracking, this approach establishes closed-loop feedback as a broadly applicable route to programmable quantum dynamics.

https://arxiv.org/abs/2602.21080 2026-02-24T00:00:00Z 2026-02-24T00:00:00Z Pedro M. PradoLucas A. M. RattighieriRafael Simões do CarmoGiovanni S. FrancoGuilherme E. L. PexeAlexandre DrinkoErick G. DorlassTatiana F. de AlmeidaFelipe F. Fanchini

Reconstructing DNA sequences without a reference, known as de novo assembly, is a complex computational task involving the alignment of overlapping fragments. To address this problem, a usual strategy is to map the assembly to a Quadratic Unconstrained Binary Optimization (QUBO) formulation, which can be solved by different quantum algorithms. In this work, we focus on three versions of the Feedback-based Algorithm, a protocol that eliminates classical optimization loops via measurement feedback. We analyze long-read DNA fragments from SARS-CoV-2 and human mitochondrial DNA using standard FALQON, second-order FALQON (SO-FALQON), and time-rescaled FALQON (TR-FALQON). Numerical results show that both variants improve convergence to the ground state and increase success probabilities at reduced circuit depths. These findings indicate that enhanced feedback-driven dynamics are effective for solving combinatorial problems on near-term quantum hardware.

https://arxiv.org/abs/2602.12387 2026-02-12T00:00:00Z 2026-02-12T00:00:00Z Masih MozakkaMohsen Heidari

Feedback-based methods have gained significant attention as an alternative training paradigm for the Quantum Approximate Optimization Algorithm (QAOA) in solving combinatorial optimization problems such as MAX-CUT. In particular, Quantum Lyapunov Control (QLC) employs feedback-driven control laws that guarantee monotonic non-decreasing objective values, can substantially reduce the training overhead of QAOA, and mitigate barren plateaus. However, these methods might require long control sequences, leading to sub-optimal convergence rates. In this work, we propose a hybrid method that incorporates per-layer gradient estimation to accelerate the convergence of QLC while preserving its low training overhead and stability guarantees. By leveraging layer-wise gradient information, the proposed approach selects near-optimal control parameters, resulting in significantly faster convergence and improved robustness. We validate the effectiveness of the method through extensive numerical experiments across a range of problem instances and optimization settings.

https://arxiv.org/abs/2602.08881 2026-02-09T00:00:00Z 2026-02-09T00:00:00Z Leonardo Colombo

We propose a geometric model predictive control framework for quantum systems subject to smoothness and state constraints. By formulating quantum state evolution intrinsically on the projective Hilbert space, we penalize covariant accelerations to generate smooth trajectories in the form of Riemannian cubics, while incorporating state-dependent constraints through potential functions. A structure-preserving variational discretization enables receding-horizon implementation, and a Lyapunov-type stability result is established for the closed-loop system. The approach is illustrated on the Bloch sphere for a two-level quantum system, providing a viable pathway toward predictive feedback control of constrained quantum dynamics.

https://arxiv.org/abs/2602.05595 2026-02-05T00:00:00Z 2026-02-05T00:00:00Z Langyu LiRuoyu WuYong WangGuofeng ZhangJinhu LüQing GaoYu Pan

As a quantum-inspired, non-traditional analog solver architecture, the analog Ising machine (AIM) has emerged as a distinctive computational paradigm to address the rapidly growing demand for computational power. However, the mathematical understanding of its principles, as well as the optimization of its solution speed and accuracy, remain unclear. In this work, we for the first time systematically discuss multiple implementations of AIM and establish a unified mathematical formulation. On this basis, by treating the binarization constraint of AIM (such as injection locking) as a Lagrange multiplier in optimization theory and combining it with a Lyapunov analysis from dynamical systems theory, an analytical framework for evaluating solution speed and accuracy is constructed, and further demonstrate that conventional AIMs possess a theoretical performance upper bound. Subsequently, by elevating the binarization constraint to a control variable, we propose the controllable analog Ising machine (CAIM), which integrates control Lyapunov functions and momentum-based optimization algorithms to realize adaptive sampling-feedback control, thereby surpassing the performance limits of conventional AIMs. In a proof-of-concept CAIM demonstration implemented using an FPGA-controlled LC-oscillator Ising machine, CAIM achieves a twofold speedup and a 7\% improvement in accuracy over AIM on a 50-node all-to-all weighted MaxCut problem, validating both the effectiveness and interpretability of the proposed theoretical framework.

https://arxiv.org/abs/2601.18082 2026-01-26T00:00:00Z 2026-01-26T00:00:00Z Mai Nguyen Phuong NhiLan Nguyen TranLe Bin Ho

Drug-drug interactions (DDIs) strongly affect the safety and efficacy of combination therapies. Despite the availability of large DDI databases, selecting optimal multi-drug combinations that balance safety, therapeutic benefit, and regimen size remains a challenging combinatorial optimization problem. Here, we present a quantum-control-based framework for DDI-aware drug combination optimization, in which known harmful and synergistic interactions are encoded into Ising Hamiltonians as penalties and rewards, respectively. The optimization is performed using the feedback-based quantum algorithm FALQON, a gradient-free variational approach. We study two clinically motivated tasks: the Maximum Safe Subset problem and the Synergy-Constrained Optimization problem. Numerical simulations using interaction data from Drugs.com and SYNERGxDB demonstrate efficient convergence and high-quality solutions for clinically relevant drug sets, including COVID-19 case studies.

https://arxiv.org/abs/2512.13044 2025-12-15T00:00:00Z 2025-12-15T00:00:00Z Thanh Nguyen Van LongLan Nguyen TranLe Bin Ho

Preparing ground states of strongly correlated quantum systems is a central goal in quantum simulation and optimization. The feedback-based quantum algorithm (FALQON) provides an attractive alternative to variational methods with a fully quantum feedback rule, but it fails in the presence of spectral degeneracies, where the feedback signal collapses and the evolution cannot reach the ground state. Using the Fermi-Hubbard model on lattices up to 3x3, we show that this breakdown appears at half-filling on the 2x2 lattice and extends to both half-filled and doped configurations on the 3x3 lattice. We then introduce an imaginary-time-enhanced FALQON (ITE-FALQON) scheme, which inserts short imaginary-time evolution steps into the feedback loop. The hybrid method suppresses excited-state components, escapes degenerate subspaces, and restores monotonic energy descent. The ITE-FALQON achieves a reliable ground-state convergence across all fillings, providing a practical route to scalable ground-state preparation in strongly correlated quantum systems.

https://arxiv.org/abs/2511.05916 2025-11-08T00:00:00Z 2025-12-03T00:00:00Z Yunyan LeeIan R. PetersenDaoyi Dong

Model predictive control has shown potential to enhance the robustness of quantum control systems. In this work, we propose a tractable Stochastic Model Predictive Control (SMPC) framework for finite-dimensional quantum systems under continuous-time measurement and quantum filtering. Using the almost-sure eigenstate reduction of quantum trajectories, we prove that the infinite-horizon stochastic objective collapses to a fidelity term that is computable in closed form from the one-step averaged state. Consequently, the online SMPC step requires only deterministic propagation of the filter and a terminal fidelity evaluation. An advantage of this method is that it eliminates per-horizon Monte Carlo scenario sampling and significantly reduces computational load while retaining the essential stochastic dynamics. We establish equivalence and mean-square stability guarantees, and validate the approach on multi-level and Ising-type systems, demonstrating favorable scalability compared to sampling-based SMPC.

https://arxiv.org/abs/2510.18852 2025-10-21T00:00:00Z 2025-10-21T00:00:00Z Nutkritta KraipatthanapongNatthaphat ThathongPannita SuksawasThanunnut KlunklinKritin VongthongluaKrit AttahakulAueaphum Aueawatthanaphisut

This paper presents a novel Lyapunov-Based Quantum Reinforcement Learning (LQRL) framework that integrates quantum policy optimization with Lyapunov stability analysis for continuous-time vehicle control. The proposed approach combines the representational power of variational quantum circuits (VQCs) with a stability-aware policy gradient mechanism to ensure asymptotic convergence and safe decision-making under dynamic environments. The vehicle longitudinal control problem was formulated as a continuous-state reinforcement learning task, where the quantum policy network generates control actions subject to Lyapunov stability constraints. Simulation experiments were conducted in a closed-loop adaptive cruise control scenario using a quantum-inspired policy trained under stability feedback. The results demonstrate that the LQRL framework successfully embeds Lyapunov stability verification into quantum policy learning, enabling interpretable and stability-aware control performance. Although transient overshoot and Lyapunov divergence were observed under aggressive acceleration, the system maintained bounded state evolution, validating the feasibility of integrating safety guarantees within quantum reinforcement learning architectures. The proposed framework provides a foundational step toward provably safe quantum control in autonomous systems and hybrid quantum-classical optimization domains.

https://arxiv.org/abs/2509.05167 2025-09-05T00:00:00Z 2025-09-05T00:00:00Z Eya GuizaniJulian Berberich

Model predictive control (MPC) is one of the most successful modern control methods. It relies on repeatedly solving a finite-horizon optimal control problem and applying the beginning piece of the optimal input. In this paper, we develop a modular framework for improving efficiency and robustness of quantum optimal control (QOC) via MPC. We first provide a tutorial introduction to basic concepts of MPC from a QOC perspective. We then present multiple MPC schemes, ranging from simple approaches to more sophisticated schemes which admit stability guarantees. This yields a modular framework which can be used 1) to improve efficiency of open-loop QOC and 2) to improve robustness of closed-loop quantum control by incorporating feedback. We demonstrate these benefits with numerical results, where we benchmark the proposed methods against competing approaches.

https://arxiv.org/abs/2507.15191 2025-07-21T00:00:00Z 2025-07-21T00:00:00Z Weichao LiangGaoyue Guo

We address the stabilization of both classical and quantum systems modeled by jump-diffusion stochastic differential equations using a novel hysteresis switching strategy. Unlike traditional methods that depend on global Lyapunov functions or require each subsystem to stabilize the target state individually, our approach employs local Lyapunov-like conditions and state-dependent switching to achieve global asymptotic or exponential stability with finitely many switches almost surely. We rigorously establish the well-posedness of the resulting switched systems and derive sufficient conditions for stability. The framework is further extended to quantum feedback control systems governed by stochastic master equations with both diffusive and jump dynamics. Notably, our method relaxes restrictive invariance assumptions often necessary in prior work, enhancing practical applicability in experimental quantum settings. Additionally, the proposed strategy offers promising avenues for robust control under model uncertainties and perturbations, paving the way for future developments in both classical and quantum control.

https://arxiv.org/abs/2506.09214 2025-06-10T00:00:00Z 2025-06-10T00:00:00Z Takuya Hatomura

We propose a quantum-inspired classical algorithm for combinatorial optimization problems, named the counterdiabaticity-assisted classical algorithm for optimization (CACAO). In this algorithm, a solution of a given combinatorial optimization problem is heuristically searched with classical spin dynamics based on quantum Lyapunov control of local counterdiabatic driving. We compare the performance of CACAO with that of quantum time-evolution algorithms, i.e., quantum annealing, the feedback-based algorithm for quantum optimization (known as FALQON), and the counterdiabatic feedback-based quantum algorithm (known as CD-FQA). We also study the performance of CACAO applied to large systems up to $10,000$ spins.

https://arxiv.org/abs/2503.20426 2025-03-26T00:00:00Z 2025-09-29T00:00:00Z Oleksandr PovitchanDenys I. BondarAndrii G. Sotnikov

We demonstrate that quantum Lyapunov control provides an effective strategy for enhancing superconducting correlations in the Fermi-Hubbard model without requiring careful parameter tuning. While photoinduced superconductivity is sensitive to the frequency and amplitude of a monochromatic laser pulse, our approach employs a simple feedback-based protocol that prevents the decrease of superconducting correlations once they begin to form. This method enables robust enhancement of pairing across a broad range of initial pumping conditions, eliminating the need for intricate frequency and amplitude optimization. We also show that an alternative implementation, asymptotic quantum control, achieves comparable results. Furthermore, our approach can be adapted to suppress previously induced superconducting correlations, providing bidirectional control over quantum pairing states. These findings suggest practical pathways for manipulating quantum correlations in strongly interacting systems with minimal experimental complexity.

https://arxiv.org/abs/2502.14369 2025-02-20T00:00:00Z 2025-06-13T00:00:00Z Salahuddin Abdul RahmanÖzkan KarabacakRafal Wisniewski

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.

https://arxiv.org/abs/2409.15426 2024-09-23T00:00:00Z 2024-09-23T00:00:00Z Lucas T. BradyStuart Hadfield

Quantum optimization, both for classical and quantum functions, is one of the most well-studied applications of quantum computing, but recent trends have relied on hybrid methods that push much of the fine-tuning off onto costly classical algorithms. Feedback-based quantum algorithms, such as FALQON, avoid these fine-tuning problems but at the cost of additional circuit depth and a lack of convergence guarantees. In this work, we take the local greedy information collected by Lyapunov feedback control and develop an analytic framework to use it to perturbatively update previous control layers, similar to the global optimal control achievable using Pontryagin optimal control. This perturbative methodology, which we call Feedback Optimally Controlled Quantum States (FOCQS), can be used to improve the results of feedback-based algorithms, like FALQON. Furthermore, this perturbative method can be used to push smooth annealing-like control protocol closer to the control optimum, even providing and iterative approach, albeit with diminishing returns. In numerical testing, we show improvements in convergence and required depth due to these methods over existing quantum feedback control methods.

https://arxiv.org/abs/2409.12525 2024-09-19T00:00:00Z 2024-09-19T00:00:00Z Pranav ChandaranaKoushik PaulKasturi Ranjan SwainXi ChenAdolfo del Campo

We introduce a quantum algorithm integrating counterdiabatic (CD) protocols with quantum Lyapunov control (QLC) to tackle combinatorial optimization problems. This approach offers versatility, allowing implementation as either a digital-analog or purely digital algorithm based on selected control strategies. By examining spin-glass Hamiltonians, we illustrate how the algorithm can explore alternative paths to enhance solution outcomes compared to conventional CD techniques. This method reduces the dependence on extensive higher-order CD terms and classical optimization techniques, rendering it more suitable for existing quantum computing platforms. The combination of digital compression via CD protocols and the adaptable nature of QLC methods positions this approach as a promising candidate for near-term quantum computing.

https://arxiv.org/abs/2408.05943 2024-08-12T00:00:00Z 2024-08-12T00:00:00Z Shikun ZhangGuofeng Zhang

Quantum Lyapunov control, an important class of quantum control methods, aims at generating converging dynamics guided by Lyapunov-based theoretical tools. However, unlike the case of classical systems, disturbance caused by quantum measurement hinders direct and exact realization of the theoretical feedback dynamics designed with Lyapunov theory. Regarding this issue, the idea of closed-loop designed open-loop control has been mentioned in literature, which means to design the closed-loop dynamics theoretically, simulate the closed-loop system, generate control pulses based on simulation and apply them to the real plant in an open-loop fashion. Based on bilinear quantum control model, we analyze in this article the error, i.e., difference between the theoretical and real systems' time-evolved states, incurred by the procedures of closed-loop designed open-loop control. It is proved that the error at an arbitrary time converges to a unitary transformation of initialization error as the number of simulation grids between 0 and that time tends to infinity. Moreover, it is found that once the simulation accuracy reaches a certain level, adopting more accurate (thus possibly more expensive) numerical simulation methods does not efficiently improve convergence. We also present an upper bound on the error norm and an example to illustrate our results.

https://arxiv.org/abs/2406.08169 2024-06-12T00:00:00Z 2024-07-19T00:00:00Z Salahuddin Abdul RahmanÖzkan KarabacakRafal Wisniewski

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.

https://arxiv.org/abs/2404.19386 2024-04-30T00:00:00Z 2024-07-21T00:00:00Z Salahuddin Abdul RahmanÖzkan KarabacakRafal Wisniewski

Drawing inspiration from the Lyapunov control technique for quantum systems, feedback-based quantum algorithms have been proposed for calculating the ground states of Hamiltonians. In this work, we consider extending these algorithms to tackle calculating excited states. Inspired by the weighted subspace-search variational quantum eigensolver algorithm, we propose a novel weighted feedback-based quantum algorithm for excited state calculation. We show that depending on how we design the weights and the feedback law, we can prepare the $p$th excited state or lowest energy states up to the $p$th excited state. Through an application in quantum chemistry, we show the effectiveness of the proposed algorithm, evaluating its efficacy via numerical simulations.

https://arxiv.org/abs/2404.04620 2024-04-06T00:00:00Z 2026-01-19T00:00:00Z Salahuddin Abdul RahmanÖzkan KarabacakRafal Wisniewski

Recently, feedback-based quantum algorithms have been introduced to calculate the ground states of Hamiltonians, inspired by quantum Lyapunov control theory. This paper aims to generalize these algorithms to the problem of calculating an eigenstate of a given Hamiltonian, assuming that the lower energy eigenstates are known. To this aim, we propose a new design methodology that combines the layer-wise construction of the quantum circuit in feedback-based quantum algorithms with a new feedback law based on a new Lyapunov function to assign the quantum circuit parameters. We present two approaches for evaluating the circuit parameters: one based on the expectation and overlap estimation of the terms in the feedback law and another based on the gradient of the Lyapunov function. We demonstrate the algorithm through an illustrative example and through an application in quantum chemistry. To assess its performance, we conduct numerical simulations and execution on IBM's superconducting quantum computer.

https://arxiv.org/abs/2403.07021 2024-03-09T00:00:00Z 2024-07-07T00:00:00Z Nahid Binandeh DehaghaniAntonio Pedro AguiarRafal Wisniewski

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.

https://arxiv.org/abs/2402.07396 2024-02-12T00:00:00Z 2024-02-12T00:00:00Z Yunyan LeeIan R. PetersenDaoyi Dong

This article presents a robust control strategy using Time-Optimal Model Predictive Control (TOMPC) for a two-level quantum system subject to bounded uncertainties. In this method, the control field is optimized over a finite horizon using a nominal quantum system as the reference and then the optimal control for the first time interval is applied and a projective measurement is implemented on the uncertain system. The new control field for the next time interval will be iteratively optimized based on the measurement result. We present theoretical results to guarantee the stability of the TOMPC algorithm. We also characterize the robustness and the convergence rate of the TOMPC strategy for the control of two-level systems. Numerical simulations further demonstrate that, in the presence of uncertainties, our quantum TOMPC algorithm enhances robustness and steers the state to the desired state with high fidelity. This work contributes to the progress of Model Predictive Control in quantum control and explores its potential in practical applications of quantum technology.

https://arxiv.org/abs/2401.15303 2024-01-27T00:00:00Z 2024-10-09T00:00:00Z Rajesh K. MallaHiroki SukenoHongye YuTzu-Chieh WeiAndreas WeichselbaumRobert M. Konik

In recent quantum algorithmic developments, a feedback-based approach has shown promise for preparing quantum many-body system ground states and solving combinatorial optimization problems. This method utilizes quantum Lyapunov control to iteratively construct quantum circuits. Here, we propose a substantial enhancement by implementing a protocol that uses ideas from quantum Lyapunov control and the counterdiabatic driving protocol, a key concept from quantum adiabaticity. Our approach introduces an additional control field inspired by counterdiabatic driving. We apply our algorithm to prepare ground states in one-dimensional quantum Ising spin chains. Comprehensive simulations demonstrate a remarkable acceleration in population transfer to low-energy states within a significantly reduced time frame compared to conventional feedback-based quantum algorithms. This acceleration translates to a reduced quantum circuit depth, a critical metric for potential quantum computer implementation. We validate our algorithm on the IBM cloud computer, highlighting its efficacy in expediting quantum computations for many-body systems and combinatorial optimization problems.

https://arxiv.org/abs/2307.14599 2023-07-27T00:00:00Z 2023-07-27T00:00:00Z Yanan LiuDaoyi DongSen KuangIan R. PetersenHidehiro Yonezawa

Quantum entanglement plays a fundamental role in quantum computation and quantum communication. Feedback control has been widely used in stochastic quantum systems to generate given entangled states since it has good robustness, where the time required to compute filter states and conduct filter based control usually cannot be ignored in many practical applications. This paper designed two control strategies based on the Lyapunov method to prepare a class of entangled states for qubit systems with a constant delay time. The first one is bang bang like control strategy, which has a simple form with switching between a constant value and zero, the stability of which is proved. Another control strategy is switching Lyapunov control, where a constant delay time is introduced in the filter-based feedback control law to compensate for the computation time. Numerical results on a two qubit system illustrate the effectiveness of these two proposed control strategies.

https://arxiv.org/abs/2304.09023 2023-04-18T00:00:00Z 2023-04-18T00:00:00Z Henrik Glavind ClausenSalahuddin Abdul RahmanÖzkan KarabacakRafal Wisniewski

In variational quantum algorithms (VQAs), the most common objective is to find the minimum energy eigenstate of a given energy Hamiltonian. In this paper, we consider the general problem of finding a sufficient control Hamiltonian structure that, under a given feedback control law, ensures convergence to the minimum energy eigenstate of a given energy function. By including quantum non-demolition (QND) measurements in the loop, convergence to a pure state can be ensured from an arbitrary mixed initial state. Based on existing results on strict control Lyapunov functions, we formulate a semidefinite optimization problem, whose solution defines a non-unique control Hamiltonian, which is sufficient to ensure almost sure convergence to the minimum energy eigenstate under the given feedback law and the action of QND measurements. A numerical example is provided to showcase the proposed methodology.

https://arxiv.org/abs/2303.02917 2023-03-06T00:00:00Z 2023-09-26T00:00:00Z James B. LarsenMatthew D. GraceAndrew D. BaczewskiAlicia B. Magann

The ground state properties of quantum many-body systems are a subject of interest across chemistry, materials science, and physics. Thus, algorithms for finding ground states can have broad impacts. Variational quantum algorithms are one class of ground state algorithms that has received significant attention in recent years. These algorithms utilize a hybrid quantum-classical computing framework to prepare ground states on quantum computers. However, this requires solving a classical optimization problem that can become prohibitively expensive in high dimensions. Here, we develop formulations of feedback-based quantum algorithms for ground state preparation that can be used to address this challenge for two broad classes of Hamiltonians: Fermi-Hubbard Hamiltonians, and molecular Hamiltonians represented in second quantization. Feedback-based quantum algorithms are optimization-free; in place of classical optimization, quantum circuit parameters are set according to a deterministic feedback law derived from quantum Lyapunov control principles. This feedback law guarantees a monotonic improvement in solution quality with respect to the depth of the quantum circuit. A variety of numerical illustrations are provided that analyze the convergence and robustness of feedback-based quantum algorithms for these problem classes.

https://arxiv.org/abs/2203.00182 2022-03-01T00:00:00Z 2024-06-17T00:00:00Z Yunyan LeeDaoyi DongCiann-Dong Yang

Maximally entangled states (MES) are highly valued in quantum information processing. In quantum control, the creation of MES is typically treated as a state transfer problem with a predefined MES as the target. However, this approach is limited by the requirement to predetermine the MES structure. This paper introduces an improved quantum Lyapunov control approach that relies on the quantum entanglement measure to construct the Lyapunov function, instead of using the distance between quantum states. This strategy enables the preparation of any MES, regardless of whether its structure is known beforehand, using a single control scheme. The proposed entanglement control technique is unaffected by the number of entangled subsystems since it targets the entanglement measure as a scalar. Initially applied to bipartite pure states, this method demonstrates its capability to generate Bell states and their equivalents. Subsequent applications to bipartite mixed states and multipartite systems illustrate that the technique can produce MES with unspecified structures.