Quantum control papers on arXiv, selected and classified automatically by QOC. https://llorebaga.github.io/QOC/topics/pmp/ 2026-09-10T00:00:00Z QOC https://arxiv.org/abs/2609.11213 2026-09-10T00:00:00Z 2026-09-10T00:00:00Z Bereket Sitotaw KidaneMd Samiul Haque MotayedShuo Wang

Optimal scheduling of combined chemo-immunotherapy is often formulated as a control-affine optimal control problem, which generically yields boundary-selected (bang-bang-type) protocols unless singular arcs occur. This structure, while convenient, neglects saturating pharmacodynamics at high dose rates. We incorporate Michaelis-Menten saturation directly into the therapy channels, making the dynamics non-control-affine and the Hamiltonian nonlinear in each control. With strictly positive exposure penalties, the Hamiltonian admits an explicit three-regime pointwise minimization law: each input is chosen at the lower bound, the upper bound, or as a unique interior minimizer. On interior intervals the strict Legendre condition holds, so continuously modulated dosing arises as a regular interior extremal rather than a singular-arc or smoothing artifact. The resulting transcription is nonconvex; we therefore use a hybrid Quantum Particle Swarm Optimization (QPSO)-Sequential Quadratic Programming (SQP) pipeline, where QPSO provides a constraint-aware warm start and SQP enforces feasibility and Karush-Kuhn-Tucker (KKT) optimality on a collocation grid. Costate reconstruction corroborates the Pontryagin Minimum Principle (PMP) structure and the predicted boundary/interior regime transitions.

https://arxiv.org/abs/2609.11197 2026-09-10T00:00:00Z 2026-09-10T00:00:00Z Bereket Sitotaw KidaneMd Samiul Haque MotayedShuo Wang

Optimal control in cancer chemotherapy is challenged by tumor heterogeneity and mutations, which complicate treatment effectiveness. Traditional methods, such as Pontryagin's maximum principle (PMP), are often hindered by their reliance on an initial guess for the costate equation, affecting accuracy and convergence. To address these limitations, this work introduces a hybrid quantum particle swarm optimization (QPSO) method based on regularization. QPSO is employed for global exploration to approximate the optimal control trajectory, followed by a regularization-based refinement to ensure smoothness and consistency with optimality conditions. The Hamiltonian function is used for first- and second-order optimality checks, verifying solution quality. Numerical case studies explore various drug effectiveness functions, demonstrating the role of periodic and localized drug delivery in achieving robust tumor suppression and providing insights into the impact of different drug combinations on optimal chemotherapy strategies.

https://arxiv.org/abs/2606.22212 2026-06-20T00:00:00Z 2026-09-21T00:00:00Z Denis JankovićSaba TaherpourPaul-Louis EtienneyPaul-Antoine HervieuxChristoph Wolf

A central goal of quantum optimal control is to achieve high-fidelity and low-energy control pulses. When quantum optimal control methods optimize every point of a pulse discretized over small time steps independently this can yield high fidelity control but also results in broadband and energy-hungry waveforms. We extend MAGICARP, a shooting method inspired by Pontryagin's maximum principle on energy that generates an entire pulse from a small set of parameters, making it smooth and energy-efficient by construction, from driftless systems to closed systems with the constant drift Hamiltonian of two exchange-coupled spins in an external magnetic field. The optimization proceeds in stages: the dressed states of the drift Hamiltonian structure the target, an initial shooting optimization is performed in the rotating-wave frame, and an exact laboratory-frame refinement follows. Benchmarked against Krotov and GRAPE at matched gate infidelity, MAGICARP consistently achieves the lowest energy and a conserved pulse area, concentrates its spectral weight on the gate-relevant transitions, and is the most robust to fluctuations in the exchange coupling; GRAPE independently converges to essentially the same pulse while black-box Krotov meets the same error at an order-of-magnitude energy premium. This method-independence is what qualifies the bounded solver as a measurement instrument, and the central result follows: a large statistical survey of unselected optimization runs resolves a weak-driving quantum speed limit for two exchange-coupled electron spins: low-amplitude realizations of the two-qubit quantum Fourier transform cease to exist below a critical gate time, and the minimum control energy diverges on approach to this limit. The divergence obeys a simple two-parameter area--pole law, $E_2^{\mathrm{law}}(T)=A/T+B/(T-T^*)$.

https://arxiv.org/abs/2604.25760 2026-04-28T00:00:00Z 2026-06-25T00:00:00Z Tianen ChenYun Shang

The Quantum Approximate Optimization Algorithm (QAOA) follows a single, fixed evolution path, overlooking the potential computational advantage of coherently superposing multiple trajectories. Here we overcome this limitation with a hybrid quantum walk (HQW) ansatz that super poses multiple Hamiltonian-driven paths coherently within each circuit layer via a dynamical coin operator. QAOA emerges as a special case of this framework with a static Pauli-X coin. Using Pontryagin's minimum principle, we derive the optimal form of the coin operator, demonstrating that it generally differs from a constant gate. A dynamical Lie algebra analysis reveals that HQW generates a strictly larger Jordan-Lie algebra, providing an algebraic foundation for its enhanced expressivity. Especially, we reveal the connection between the unique Jordan product negativity in HQW's DLA and its performance advantages. Numerical experiments on Max-Cut and Maximum Independent Set problems show that HQW systematically outperforms QAOA in convergence speed, solution accuracy, and robustness. Our work establishes a path-superposition paradigm for quantum optimization, combining optimal control theory with algebraic structure to guide the design of advanced quantum algorithms.

https://arxiv.org/abs/2604.15886 2026-04-17T00:00:00Z 2026-08-06T00:00:00Z Kun ZhangKang-Yuan ChenXiao-Hui WangVladimir Korepin

Grover's algorithm is a cornerstone of quantum algorithms and is strictly optimal in oracle-query complexity. While the full search problem admits no further improvement, one may trade accuracy for speed in the partial search problem, where the task is to identify only the block containing the target item. The best known quantum algorithm for the partial search problem is the Grover-Radhakrishnan-Korepin (GRK) algorithm, whose optimality has long been conjectured but not proved. In this work, we prove the optimality of GRK in the large-block limit. We formulate partial search as a time-optimal control problem and apply the Pontryagin maximum principle to derive the switching-function dynamics, establish the bang-bang structure of regular extremals, and exclude non-optimal switching patterns. As a result, we show that the optimal regular extremal has the global-local-global form, which yields a control-theoretic proof of the asymptotic optimality of the GRK algorithm in oracle-query complexity.

https://arxiv.org/abs/2604.09196 2026-04-10T00:00:00Z 2026-09-14T00:00:00Z Xiao-Yu DongXi-Lai WangWen-Long Ma

The standard stimulated Raman adiabatic passage (STIRAP) protocol enables high-fidelity quantum state transfer in an ideal three-level system via adiabatic following of a dark state. However, in practical systems with more energy levels, control pulses with finite spectral selectivity often couple the three-level subspace to the remaining subspace, introducing leakage that fundamentally limits the transfer performance. Here, we adopt a multilevel chain model for STIRAP that explicitly incorporates this leakage subspace. Using Pontryagin's maximum principle, we formulate a leakage-penalized quantum optimal control problem with the control pulses constrained to experimentally feasible Gaussian pulse families. We derive explicit gradients of the objective functional with respect to the pulse parameters, enabling efficient low-dimensional optimization that suppresses leakage while preserving the counterintuitive STIRAP pulse ordering. Numerical simulations for a superconducting transmon platform demonstrate that the optimized control pulses significantly enhance the target-state transfer fidelity and improve robustness against amplitude miscalibration and detuning drifts.

https://arxiv.org/abs/2512.18879 2025-12-21T00:00:00Z 2025-12-21T00:00:00Z Leonardo Colombo

We develop a discrete Pontryagin Maximum Principle (PMP) for controlled open quantum systems governed by Lindblad dynamics, and introduce a second--order \emph{contact Lie--group variational integrator} (contact LGVI) that preserves both the CPTP (completely positive and trace--preserving) structure of the Lindblad flow and the contact geometry underlying the discrete PMP. A type--II discrete contact generating function produces a strict discrete contactomorphism under which the state, costate, and cost propagate in exact agreement with the variational structure of the discrete contact PMP. We apply this framework to the optimal control of a dissipative qubit and compare it with a non--geometric explicit RK2 discretization of the Lindblad equation. Although both schemes have the same formal order, the RK2 method accumulates geometric drift (loss of trace, positivity violations, and breakdown of the discrete contact form) that destabilizes PMP shooting iterations, especially under strong dissipation or long horizons. In contrast, the contact LGVI maintains exact CPTP structure and discrete contact geometry step by step, yielding stable, physically consistent, and geometrically faithful optimal control trajectories.

https://arxiv.org/abs/2512.13549 2025-12-15T00:00:00Z 2026-05-15T00:00:00Z Federico Alberto AstolfiSven JanduraGuido Pupillo

We study time-optimal state-to-state control for two- and multi-qubit operations motivated by neutral-atom quantum processors within the Rydberg blockade regime. Block-diagonalization of the Hamiltonian simplifies the dynamics and enables the application of a semi-analytic approach to the Pontryagin Maximum Principle to derive optimal laser controls. We provide a general formalism for $N$ qubits. For $N=2$ qubits, we classify normal and abnormal extremals, showcasing examples where abnormal solutions are either absent or suboptimal. For normal extremals, we establish a correspondence between the laser detuning from atomic transitions and the motion of a classical particle in a quartic potential, yielding a reduced, semi-analytic formulation of the control problem. Combining PMP-based insights with numerical optimization, our approach bridges analytic and computational methods for high-fidelity, time-optimal control.

https://arxiv.org/abs/2512.10093 2025-12-10T00:00:00Z 2025-12-10T00:00:00Z Oleg V. Morzhin

This article (I) considers the known optimal control model of a quantum information transfer along a spin chain with controlled external parabolic magnetic field, with an arbitrary length. The article adds certain lower and upper pointwise constraints on controls, adds the problem of keeping the signal at the last spin, considers various classes of controls. For these problems under piecewise continuous controls, the projection-type linearized Pontryagin maximum principle, gradient projection method's constructions in its one- and two- and three-step forms were adapted by analogy with [Morzhin O.V., Pechen A.N. J. Phys. A: Math. Theor., 2025]. Moreover, an example with a genetic algorithm's successful use under a special class of controls is given.

https://arxiv.org/abs/2511.06097 2025-11-08T00:00:00Z 2025-11-08T00:00:00Z Julia CenDomenico D'Alessandro

In various physical implementations of quantum information processing, qubits are realized in a Lambda type system configuration as two stable lower energy levels coupled indirectly via an unstable higher energy level, that is, in comparison, a lot more susceptible to decoherence. We consider the quantum control problem of optimal state transfer between two isospectral density matrices, over an arbitrary finite time horizon, for the quantum Lambda system. The cost considered is a compromise between the energy of the control field and the average occupancy in the highest energy level. We apply a geometric approach that combines the use of the Pontryagin Maximum Principle, a symmetry reduction technique to reduce the number of parameters in the resulting optimization problem, and several auxiliary techniques to bound the parameter space in the search for the optimal solution. We prove several properties of the optimal control and trajectories for this problem, including their normality and smoothness. We obtain a system of differential equations that must be satisfied by the optimal pair of control and trajectory we treat in detail, with numerical simulations, and solve a case study involving a Hadamard-like transformation. Our techniques can be adapted to other contexts and promise to push to a more consequential level, the application of geometric control in quantum systems.

https://arxiv.org/abs/2510.05074 2025-10-06T00:00:00Z 2025-10-06T00:00:00Z Farhan T. ChowdhuryLuke D. SmithDaniel R. Kattnig

The quantum control of spin-correlated radical pairs (SCRPs) holds promise for the targeted manipulation of magnetic field effects, with potential applications ranging from the design of noise-resilient quantum information processors to genetically encodable quantum sensors. However, achieving precise handles over the intricate interplay between coherent electron spin dynamics and incoherent relaxation processes in photoexcited radical-pair reactions requires tractable approaches for numerically obtaining controls for large, complex open quantum systems. Employing techniques relying on full Liouville-space propagators becomes computationally infeasible for large spin systems of realistic complexity. Here, we demonstrate how a control engineering approach based on the Pontryagin Maximum Principle (PMP) can offer a viable alternative by reporting on the successful application of PMP-optimal control to steer the coherent and incoherent spin dynamics of noisy radical pairs. This enables controls for prototypical radical-pair models that exhibit robustness in the face of relevant noise sources and paves the way to incoherent control of radical-pair spin dynamics.

https://arxiv.org/abs/2508.01806 2025-08-03T00:00:00Z 2026-04-30T00:00:00Z Ugur G. AbdullaJose H. RodriguesJean-Jacques Slotine

This paper aims to devise the shape of the external electromagnetic field that drives the spin dynamics of radical pairs to a quantum coherent state through maximization of the triplet-born singlet yield in biochemical reactions. The model is a Schrödinger system with spin Hamiltonians given by the sum of Zeeman interaction and hyperfine coupling interaction terms. We introduce a one-parameter family of optimal control problems by coupling the Schrödinger system to a control field through filtering equations for the electromagnetic field. Fréchet differentiability and the Pontryagin Maximum Principle in Hilbert space are proved, and the bang-bang structure of the optimal control is established. A new iterative Pontryagin Maximum Principle (IPMP) method for the identification of the bang-bang optimal control is developed. Numerical simulations based on IPMP and the gradient projection method (GPM) in Hilbert spaces are pursued, and the convergence, stability, and the regularization effect are demonstrated. Comparative analysis of filtering with regular optimal electromagnetic field versus non-filtering with bang-bang optimal field ({\it Abdulla et al, Quantum Sci. Technol., {\bf9}, 4, 2024}) demonstrates that the change of the maxima of the singlet yield is less than 1\%. The results open a venue for a potential experimental work on magnetoreception as a manifestation of quantum biological phenomena.

https://arxiv.org/abs/2507.09844 2025-07-14T00:00:00Z 2025-07-14T00:00:00Z Nahid Binandeh DehaghaniAntonio Pedro AguiarRafal Wisniewski

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.

https://arxiv.org/abs/2505.21203 2025-05-27T00:00:00Z 2026-06-24T00:00:00Z Denis JankovićJean-Gabriel HartmannPaul-Louis EtienneyKillian LutzYannick PrivatPaul-Antoine Hervieux

We introduce the MAGICARP algorithm, a numerical optimization method for quantum optimal control problems that combines the structure provided by Pontryagin's Maximum Principle (PMP) and the robustness of gradient ascent techniques, such as GRAPE. MAGICARP is formulated as a "shooting technique", aiming to determine the appropriate initial adjoint momentum to realize a target quantum gate. This method naturally incorporates time and energy optimal constraints through a PMP-informed pulse structure. We demonstrate MAGICARP's effectiveness through illustrative numerical examples, comparing its performance to GRAPE and highlighting its advantages in specific scenarios.

https://arxiv.org/abs/2504.08173 2025-04-10T00:00:00Z 2026-03-14T00:00:00Z Tathagata KarmakarAndrew N. Jordan

The Chantasri-Dressel-Jordan (CDJ) stochastic path integral formalism (Chantasri et al. 2013 and 2015) characterizes the statistics of the readouts and the most likely conditional evolution of continuously monitored quantum systems. In our work, we generalize the CDJ formalism to arbitrary continuously monitored systems by introducing a costate operator. We then prescribe a generalized Pontryagin's maximum principle for quantum systems undergoing arbitrary evolution and find conditions on optimal control protocols. We show that the CDJ formalism's most likely path can be cast as a quantum Pontryagin's maximum principle, where the cost function is the readout probabilities along a quantum trajectory. This insight allows us to derive general optimal control equations for arbitrary control parameters. We apply our results to a monitored oscillator in the presence of a parametric quadratic potential and variable quadrature measurements. We find the optimal potential strength and quadrature angle for fixed-end point problems. The optimal parametric potential is analytically shown to have a "bang-bang" form. We apply our protocol to three quantum oscillator examples relevant to Bosonic quantum computing. The first example considers a binomial codeword preparation from an error word, the second example looks into cooling to the ground state from an even cat state, and the third example investigates a cat state to cat state evolution. We compare the statistics of the fidelities of the final state with respect to the target state for trajectories generated under the optimal control with those generated under a sample control. Compared to the latter case, we see a 40-196% increase in the number of trajectories reaching more than 95% fidelities under the optimal control. Our work provides a systematic prescription for finding quantum optimal control for continuously monitored systems.

https://arxiv.org/abs/2503.11830 2025-03-14T00:00:00Z 2025-03-14T00:00:00Z O. Fresse-ColsonStéphane GuérinXi ChenDominique Sugny

We study the time-optimal robust control of a two-level quantum system subjected to field inhomogeneities. We apply the Pontryagin Maximum Principle and we introduce a reduced space onto which the optimal dynamics is projected down. This reduction leads to a complete analytical derivation of the optimal solution in terms of elliptic functions and elliptic integrals. Necessary optimality conditions are then obtained for the original system. These conditions are verified numerically and lead to the optimal control protocol. Various examples, ranging from state-to-state transfer to the generation of a Not gate, illustrate this study. The connection with other geometric optimization approaches that have been used to solve this problem is also discussed.

https://arxiv.org/abs/2502.19666 2025-02-27T00:00:00Z 2025-02-27T00:00:00Z Wang PenghuiWang ShanZhao Shengkai

In this paper, we investigate the closed-loop solvability of the quantum stochastic linear quadratic optimal control problem. We derive the Pontryagin maximum principle for the linear quadratic control problem of infinite-dimensional quantum stochastic systems. The equivalence between unique closed-loop solvability for quantum stochastic linear quadratic optimal control problems and the well-posedness of the corresponding quantum Riccati equations is established. Notably, although the quantum Riccati equation is an infinite-dimensional deterministic operator-valued ordinary differential equation, classical methods are not applicable. Inspired by Lü and Zhang's approach [Q. Lü and X. Zhang, Probability Theory and Stochastic Modelling, 101. Springer, Cham, (2021) \& Mem. Amer. Math. Soc. 294 (2024)] to stochastic Riccati equations, we prove the existence and uniqueness of its solutions. The results provide a theoretical foundation for the optimal design of quantum control.

https://arxiv.org/abs/2412.20149 2024-12-28T00:00:00Z 2024-12-28T00:00:00Z Mo ZhouFrancisco Andrés Cárdenas-LópezSugny DominiqueXi Chen

We propose a quantum optimal control framework based on the Pontryagin Maximum Principle to design energy- and time-efficient pulses for open quantum systems. By formulating the Langevin equation of a dissipative LC circuit as a linear control problem, we derive optimized pulses with exponential scaling in energy cost, outperforming conventional shortcut-to-adiabaticity methods such as counter-diabatic driving. When applied to a resonator dispersively coupled to a qubit, these optimized pulses achieve an excellent signal-to-noise ratio comparable to longitudinal coupling schemes across varying critical photon numbers. Our results provide a significant step toward efficient control in dissipative open systems and improved qubit readout in circuit quantum electrodynamics.

https://arxiv.org/abs/2412.05170 2024-12-06T00:00:00Z 2025-02-12T00:00:00Z Etienne DionisBruno PeaudecerfStéphane GuérinDavid Guéry-OdelinDominique Sugny

We numerically study the optimal control of an atomic Bose-Einstein condensate in an optical lattice. We present two generalizations of the gradient-based algorithm, GRAPE, in the non-linear case and for a two-dimensional lattice. We show how to construct such algorithms from Pontryagin's maximum principle. A wide variety of target states can be achieved with high precision by varying only the laser phases setting the lattice position. We discuss the physical relevance of the different results and the future directions of this work.

https://arxiv.org/abs/2411.19644 2024-11-29T00:00:00Z 2025-08-30T00:00:00Z Oleg V. MorzhinAlexander Pechen

In this work, we adopt the Gradient Projection Method (GPM) to problems of quantum control. For general $N$-level closed and open quantum systems, we derive the corresponding adjoint systems and gradients of the objective functionals, and provide the projection versions of the Pontryagin maximum principle and the GPM, all directly in terms of quantum objects such as evolution operator, Hamiltonians, density matrices, etc. Various forms of the GPM, including one- and two-step, are provided and compared. We formulate the GPM both for closed and open quantum systems, latter for the general case with simultaneous coherent and incoherent controls. The GPM is designed to perform local gradient based optimization in the case when bounds are imposed on the controls. The main advantage of the method is that it allows to exactly satisfy the bounds, in difference to other approaches such as adding constraints as weight to objective. We apply the GPM to several examples including generation of one- and two-qubit gates and two-qubit Bell and Werner states for models of superconducting qubits under the constraint when controls are zero at the initial and final times, and steering an open quantum system state to a target density matrix for simulating action of the Werner-Holevo channel, etc.

https://arxiv.org/abs/2411.10840 2024-11-16T00:00:00Z 2024-11-16T00:00:00Z Nahid Binandeh DehaghaniAntonio Pedro AguiarRafal Wisniewski

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.

https://arxiv.org/abs/2409.12287 2024-09-18T00:00:00Z 2024-09-18T00:00:00Z Joshua HansonDennis Lucarelli

Reliable quantum information technologies depend on precise actuation and techniques to mitigate the effects of undesired disturbances such as environmental noise and imperfect calibration. In this work, we present a general framework based in geometric optimal control theory to synthesize smooth control pulses for implementing arbitrary noise-robust quantum gates. The methodology applies to generic unitary quantum dynamics with any number of qubits or energy levels, any number of control fields, and any number of disturbances, extending existing dynamical decoupling approaches that are only applicable for limited gate sets or small systems affected by one or two disturbances. The noise-suppressing controls are computed via indirect trajectory optimization based on Pontryagin's maximum principle, eliminating the need to make heuristic structural assumptions on parameterized pulse envelopes.

https://arxiv.org/abs/2409.01684 2024-09-03T00:00:00Z 2024-09-03T00:00:00Z Penghui WangShan Wang

In the present paper, by using the relaxed transposition method[29], we solve the second-order adjoint equations, corresponding to the optimal control of quantum stochastic systems in fermion fields, which plays the fundamental roles in the study of the Pointryagin-type maximum principle in quantum stochastic optimal control. The second-order adjoint equation is a backard operator valued quantum stochastic differential equation, which has no definition in the algebra of bounded operators, and the solution derived from the relaxed transposition method makes sense in W*-topology.

https://arxiv.org/abs/2408.06782 2024-08-13T00:00:00Z 2024-09-16T00:00:00Z Niklas FunckeJulian Berberich

Noise in quantum computing devices poses a key challenge in their realization. In this paper, we study the robustness of optimal quantum annealing protocols against coherent control errors, which are multiplicative Hamlitonian errors causing detrimental effects on current quantum devices. We show that the norm of the Hamiltonian quantifies the robustness against these errors, motivating the introduction of an additional regularization term in the cost function. We analyze the optimality conditions of the resulting robust quantum optimal control problem based on Pontryagin's maximum principle, showing that robust protocols admit larger smooth annealing sections. This suggests that quantum annealing admits improved robustness in comparison to bang-bang solutions such as the quantum approximate optimization algorithm. Finally, we perform numerical simulations to verify our analytical results and demonstrate the improved robustness of the proposed approach.

https://arxiv.org/abs/2406.08153 2024-06-12T00:00:00Z 2024-06-12T00:00:00Z Penghui WangShan Wang

In this paper, the Pontryagin-type maximum principle for optimal control of quantum stochastic systems in fermion fields is obtained. These systems have gained significant prominence in numerous quantum applications ranging from physical chemistry to multi-dimensional nuclear magnetic resonance experiments. Furthermore, we establish the existence and uniqueness of solutions to backward quantum stochastic differential equations driven by fermion Brownian motion. The application of noncommutative martingale inequalities and the martingale representation theorem enables this achievement.

https://arxiv.org/abs/2405.20034 2024-05-30T00:00:00Z 2024-05-30T00:00:00Z Emanuel MalvettiLéo Van Damme

Closed bipartite quantum systems subject to fast local unitary control are studied using quantum optimal control theory and a method of reduced control systems based on the Schmidt decomposition. Particular focus is given to the time-optimal generation of maximally entangled states and product states, as well as to the problem of stabilizing quantum states with a certain amount of entanglement. Explicit analytical solutions are given for general systems consisting of two qubits (as well as for bosonic and fermionic analogues) and also for a class of systems consisting of two coupled qutrits which is studied using the Pontryagin Maximum Principle.

https://arxiv.org/abs/2405.11170 2024-05-18T00:00:00Z 2024-05-18T00:00:00Z Shingo KukitaHaruki KiyaYasushi Kondo

Precise control of quantum systems is one of the most important milestones for achieving practical quantum technologies, such as computation, sensing, and communication. Several factors deteriorate the control precision and thus their suppression is strongly demanded. One of the dominant factors is systematic errors, which are caused by discord between an expected parameter in control and its actual value. Error-robust control sequences, known as composite pulses, have been invented in the field of nuclear magnetic resonance (NMR). These sequences mainly focus on the suppression of errors in one-qubit control. The one-qubit control, which is the most fundamental in a wide range of quantum technologies, often suffers from detuning error. As there are many possible control sequences robust against the detuning error, it will practically be important to find ``optimal" robust controls with respect to several cost functions such as time required for operation, and pulse-area during the operation, which corresponds to the energy necessary for control. In this paper, we utilize the Pontryagin's maximum principle (PMP), a tool for solving optimization problems under inequality constraints, to solve the time and pulse-area optimization problems. We analytically obtain pulse-area optimal controls robust against the detuning error. Moreover, we found that short-CORPSE, which is the shortest known composite pulse so far, is a probable candidate of the time optimal solution according to the PMP. We evaluate the performance of the pulse-area optimal robust control and the short-CORPSE, comparing with that of the direct operation.

https://arxiv.org/abs/2404.15015 2024-04-23T00:00:00Z 2024-04-23T00:00:00Z Nahid Binandeh DehaghaniAntonio Pedro AguiarRafal Wisniewski

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.

https://arxiv.org/abs/2403.16321 2024-03-24T00:00:00Z 2025-02-20T00:00:00Z Nahid Binandeh DehaghaniAntonio Pedro AguiarRafal Wisniewski

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.

https://arxiv.org/abs/2403.00532 2024-03-01T00:00:00Z 2024-06-14T00:00:00Z Quentin AnselEtienne DionisFloriane ArrouasBruno PeaudecerfStéphane GuérinDavid Guéry-OdelinDominique Sugny

Quantum optimal control is a set of methods for designing time-varying electromagnetic fields to perform operations in quantum technologies. This tutorial paper introduces the basic elements of this theory based on the Pontryagin maximum principle, in a physicist-friendly way. An analogy with classical Lagrangian and Hamiltonian mechanics is proposed to present the main results used in this field. Emphasis is placed on the different numerical algorithms to solve a quantum optimal control problem. Several examples ranging from the control of two-level quantum systems to that of Bose-Einstein Condensates (BEC) in a one-dimensional optical lattice are studied in detail, using both analytical and numerical methods. Codes based on shooting method and gradient-based algorithms are provided. The connection between optimal processes and the quantum speed limit is also discussed in two-level quantum systems. In the case of BEC, the experimental implementation of optimal control protocols is described, both for two-level and many-level cases, with the current constraints and limitations of such platforms. This presentation is illustrated by the corresponding experimental results.