Quantum Optimal Control Research Articles

Abstract Quantum optimal control (QOC) relies on accurately modeling system dynamics and is often challenged by unknown or inaccessible interactions in real systems. Taking an unknown collective spin system as an example, this work introduces a machine-learning-based, data-driven scheme to overcome the challenges encountered, with a trained neural network (NN) assuming the role of a surrogate model that captures the system’s dynamics and subsequently enables QOC to be performed on the NN instead of on the real system. The trained NN surrogate proves effective for practical QOC tasks and is further demonstrated to be adaptable to different experimental conditions, remaining robust across varying system sizes and pulse durations.

We present QuantumToolbox.jl, an open-source Julia package for simulating open quantum systems. Designed with a syntax familiar to users of QuTiP (Quantum Toolbox in Python), it harnesses Julia's high-performance ecosystem to deliver fast and scalable simulations. The package includes a suite of time-evolution solvers supporting distributed computing and GPU acceleration, enabling efficient simulation of large-scale quantum systems. We also show how QuantumToolbox.jl can integrate with automatic differentiation tools, making it well-suited for gradient-based optimization tasks such as quantum optimal control. Benchmark comparisons demonstrate substantial performance gains over existing frameworks. With its flexible design and computational efficiency, QuantumToolbox.jl serves as a powerful tool for both theoretical studies and practical applications in quantum science.

We present a self-consistent algorithm for optimal control simulations of many-body quantum systems. The algorithm features a two-step synergism that combines discrete real-time machine learning (DRTL) with Quantum Optimal Control Theory (QOCT) using the time-dependent Schrödinger equation. Specifically, in step (1), DRTL is employed to identify a compact working space (i.e., the important portion of the Hilbert space) for the time evolution of the many-body quantum system in the presence of a control field (i.e., the initial or previously updated field), and in step (2), QOCT utilizes the DRTL-determined working space to find a newly updated control field for a chosen objective. Steps 1 and 2 are iterated until a self-consistent control objective value is reached such that the resulting optimal control field yields the same targeted objective value when the corresponding working space is systematically enlarged. To demonstrate this two-step self-consistent DRTL-QOCT synergistic algorithm, we perform optimal control simulations of strongly interacting 1D as well as 2D Heisenberg spin systems. In both scenarios, only a single spin (at the left end site for 1D and the upper left corner site for 2D) is driven by the time-dependent control fields to create an excitation at the opposite site as the target. It is found that, starting from all spin-down zero excitation states, the synergistic method is able to identify working spaces and convergence of the desired controlled dynamics with just a few iterations of the overall algorithm. In the cases studied, the dimensionality of the working space scales only quasi-linearly with the number of spins.

In optimal quantum control, control landscape phase transitions (CLPTs) indicate sharp changes occurring in the set of optimal protocols, as a physical model parameter is varied. Here, we demonstrate the existence of a new class of CLPTs, associated with changes in the topological properties of the optimal level set in a two-qubit state-preparation problem. In particular, the distance distribution of control protocols sampled through stochastic homotopic dynamics reveals discontinuous changes in the number of connected components in the optimal level set, as a function of the protocol duration. We demonstrate how topological CLPTs can be detected in modern-day experiments.

Enhancing the Ramsey contrast of an NV-ensemble in diamond using quantum optimal control

Ultracold atoms trapped in optical lattices have emerged as a scalable and promising platform for quantum simulation and computation; however, gate speeds remain a significant limitation for practical applications. In this work, we employ quantum optimal control to design fast, collision-based two-qubit gates within a superlattice based on a Fermi-Hubbard description, reaching errors in the range 10−3 for realistic parameters. Numerically optimizing the lattice depths and the scattering length, we effectively manipulate hopping and interaction strengths intrinsic to the Fermi-Hubbard model. Our results provide five times shorter gate durations by allowing for higher energy bands in the optimization, suggesting that standard modeling with a two-band Fermi-Hubbard model is insufficient for describing the dynamics of fast gates, and we find that four to six bands are required. Additionally, we achieve nonadiabatic gates by employing time-dependent lattice depths rather than using only fixed depths. The optimized control pulses not only maintain high efficacy in the presence of laser-intensity and phase noise but also result in negligible interwell couplings.

Dark excitons in quantum dots are not directly optically accessible, which has limited their use in practical applications. Nevertheless, they offer promising features such as substantially longer lifetimes compared to bright excitons, making them attractive candidates for quantum information processing. While previous theoretical and experimental studies have explored their potential, their full capabilities remain largely untapped. In this work, we demonstrate an all-optical storage and retrieval of the spin-forbidden dark exciton in a quantum dot from the ground state using chirped pulses and an in-plane magnetic field. Our experimental findings are in excellent agreement with theoretical predictions of the dynamics calculated using state-of-the-art product tensor methods. Our scheme enables an all-optical control of dark states without relying on any preceding decays. This opens up an unexplored dimension for optimal quantum control and time-bin entangled photon pair generation from quantum dots.

Abstract We present a robust quantum optimal control framework for implementing fast entangling gates on ion-trap quantum processors. The framework leverages tailored laser pulses to drive the multiple vibrational sidebands of the ions to create phonon-mediated entangling gates and, unlike the state of the art, requires neither weak-coupling Lamb–Dicke approximation nor perturbation treatment. With the application of gradient-based optimal control, it enables finding amplitude- and phase-modulated laser control protocols that work without the Lamb–Dicke approximation, promising gate speeds on the order of microseconds comparable to the characteristic trap frequencies. Also, robustness requirements on the temperature of the ions and initial optical phase can be conveniently included to pursue high-quality fast gates against experimental imperfections. Our approach represents a step in speeding up quantum gates to achieve larger quantum circuits for quantum computation and simulation, and thus can find applications in near-future experiments.

Quantum noise reduction below the shot-noise limit is a signature of light-matter quantum interaction. A limited amount of squeezing can be obtained along the transient evolution of a two-level system resonantly interacting with a harmonic mode. We propose the use of optimal quantum control over the two-level system to enhance the transient noise reduction in the bosonic mode in a system described by the Jaynes-Cummings model. Specifically, we propose the use of a sequence of Gaussian pulses in a time window where the dissipative effects are negligible. We find that the correct choice of pulse times can reduce the noise in the quadrature field mode well below the shot noise, reaching reductions of over 80%. As the Jaynes-Cummings model describes a pivotal light-matter quantum system, our approach for noise reduction provides an experimentally feasible protocol to produce a nontrivial amount of squeezing with current technology.

Fock states of the quantum harmonic oscillator are fundamental to quantum sensing and information processing, serving as key resources for exploiting bosonic degrees of freedom. Here, we prepare high Fock states in a high-overtone bulk acoustic wave resonator by coupling it to a superconducting qubit and applying microwave pulses designed using quantum optimal control. We characterize the experimentally realized states by employing a criterion for genuine quantum non-Gaussianity (QNG) designed to reveal multiphonon contributions. Although energy relaxation and decoherence limit the achievable fidelities, we demonstrate genuine QNG features compatible with a Fock state |6⟩, confirming that the prepared states cannot be generated through Gaussian operations on states with up to Fock state |5⟩ contributions. We further investigate the robustness of these QNG features to losses and their utility in sensing displacement amplitudes. In particular, we introduce a hierarchy based on the quantum Fisher information and show that, despite decoherence and measurement imperfections, the prepared states achieve a displacement sensitivity surpassing that of an ideal Fock state |3⟩. Our results have immediate applications in quantum sensing and simulations with high-overtone bulk acoustic wave resonator devices.

Quantum optimal control methods, such as gradient ascent pulse engineering (GRAPE), are used for precise manipulation of quantum states. Many of those methods were pioneered in magnetic resonance spectroscopy, where instrumental distortions are often negligible. However, that is not the case elsewhere: the usual jumble of cables, resonators, modulators, splitters, amplifiers, and filters can and would distort control signals. Those distortions may be non-linear; their inverse functions may be ill-defined and unstable; they may even vary from one day to the next and across the sample. Here we introduce the response-aware gradient ascent pulse engineering framework, which accounts for any cascade of differentiable distortions within the GRAPE optimization loop, does not require filter function inversion, and produces control sequences that are resilient to user-specified distortion cascades with user-specified parameter ensembles. The framework is implemented into the optimal control module supplied with versions 2.10 and later of the open-source Spinach library; the user needs to provide function handles returning the actions by the distortions and, optionally, parameter ensembles for those actions.

Quantum optimal control theory for the shaping of flying qubits

Abstract This research investigates the possibility of using quantum optimal control techniques to co‐optimize the energetic cost and the process fidelity of a quantum unitary gate. The energetic cost is theoretically defined, and thereby, the gradient of the energetic cost for pulse engineering is derived. The Pareto optimality is empirically demonstrated in the trade‐off between process fidelity and energetic cost. Thereafter, two novel numerical quantum optimal control approaches are proposed: i) energy‐optimized gradient ascent pulse engineering (EO‐GRAPE) as an open‐loop gradient‐based method, and ii) energy‐optimized deep reinforcement learning for pulse engineering (EO‐DRLPE) as a closed‐loop method. The performance of both methods is probed in the presence of increasing noise. It is found that the EO‐GRAPE method performs better than the EO‐DRLPE methods with and without a warm start for most experimental settings. Additionally, for one qubit unitary gate, the correlation between the Bloch sphere path length and the energetic cost is illustrated.

Abstract Quantum optimal control theory (QOCT) can be used to design the shape of electromagnetic pulses that implement operations on quantum devices. By using non-trivially shaped waveforms, gates can be made significantly faster than those built by concatenating monochromatic pulses. Recently, we applied this idea to the control of molecular spin qudits modelled with Schrödinger’s equation and showed it can speed up operations, helping mitigate the effects of decoherence [Phys. Rev. Appl. 17, 064028 (2022)]. However, short gate times require large optimal pulse amplitudes, which may not be experimentally accessible. Introducing bounds to the amplitudes then unavoidably leads to longer operation times, for which decoherence can no longer be neglected. Here, we study how to improve this procedure by applying QOCT on top of Lindblad’s equation, to design control pulses accounting for decoherence already in the optimization process. We define the control signal in terms of generic parameters, which permits the introduction of bounds and constraints. This is convenient, as amplitude and frequency limitations are inherent to waveform generators. The pulses that we obtain consistently enhance operation fidelities compared to those achieved with the optimization based on Schrödinger’s equation, demonstrating the flexibility and robustness of our method. The improvement is larger the shorter the spin coherence time T2.

Abstract We propose a protocol to construct narrowband (NB) composite pulses using quantum optimal control in a full-parameter adjustable two-level system. The optimal NB composite pulses are highly sensitive to various types of parameter deviations. The optimal modulation parameters are obtained by minimizing the cost function composed of the weight factor and the expansion coefficients of transition probabilities. In this way, the problem of multi-parameter modulations and incomplete nullification of expansion coefficients can be effectively solved. Furthermore, the NB composite pulses with arbitrary population transfer can be flexibly achieved by only changing the constraint of the cost function, and the current protocol is easily extended to implement passband composite pulses.

A time-parallel multiple-shooting method for large-scale quantum optimal control

Recent advancements in quantum technologies have highlighted the importance of mitigating system imperfections, including parameter uncertainties and decoherence effects, to improve the performance of experimental platforms. However, most of the previous efforts in quantum control are devoted to the realization of arbitrary unitary operations in a closed quantum system. Here, we improve the algorithm that suppresses system imperfections and noises, providing notably enhanced scalability for robust and optimal control of open quantum systems. Through experimental validation in a superconducting quantum circuit, we demonstrate that our approach outperforms its conventional counterpart for closed quantum systems with an ultralow infidelity of about 0.60%, while the complexity of this algorithm exhibits the same scaling, with only a modest increase in the prefactor. This work represents a notable advancement in quantum optimal control techniques, paving the way for realizing quantum-enhanced technologies in practical applications.

State preparation of lattice field theories using quantum optimal control

Deep reinforcement learning is considered an effective technology in quantum optimization and can provide strategies for optimal control of complex quantum systems. More precise measurements require simulation control at multiple experimental stages. Based on this, we improved a multi-objective deep reinforcement learning method in mathematical convex optimization theory for multi-process quantum optimal control optimization. By setting the single-process quantum control optimization result as a multi-objective optimization truncation threshold and reward function transfer strategy, we finally gave a global optimal solution that considers multiple influencing factors, rather than a local optimal solution that only targets a certain error. This method achieved excellent computational results on superconducting qubits. Optimum control of multi-process quantum computing can be achieved only by regulating the microwave pulse parameters of superconducting qubits, and such a set of global parameter values and control strategies are given.

Quantum optimal control is a technique for controlling the evolution of a quantum system and has been applied to a wide range of problems in quantum physics. We study a binary quantum control optimization problem, where control decisions are binary-valued and the problem is solved in diverse quantum algorithms. In this paper, we utilize classical optimization and computing techniques to develop an algorithmic framework that sequentially optimizes the number of control switches and the duration of each control interval on a continuous time horizon. Specifically, we first solve the continuous relaxation of the binary control problem based on time discretization and then use a heuristic to obtain a controller sequence with a penalty on the number of switches. Then, we formulate a switching time optimization model and apply sequential least-squares programming with accelerated time-evolution simulation to solve the model. We demonstrate that our computational framework can obtain binary controls with high-quality performance and also reduce computational time via solving a family of quantum control instances in various quantum physics applications.