Quantum control papers on arXiv, selected and classified automatically by QOC. https://llorebaga.github.io/QOC/topics/autodiff-control/ 2026-10-04T00:00:00Z QOC https://arxiv.org/abs/2610.05086 2026-10-04T00:00:00Z 2026-10-04T00:00:00Z Melvin StroblMaja FranzLukas SchellerEileen KuehnWolfgang MauererAchim Streit

Classical simulation supports the development and validation of quantum algorithms through full-state inspection, controlled noise models and backpropagation, albeit for small quantum systems. Existing frameworks offer gate-level execution, differentiable pulse-level dynamics or optimised hardware execution. Just another quantum simulator (JAQSI) combines gate- and pulse-level simulation in one differentiable circuit model built upon JAX. Circuits are represented as pure functions of numerical inputs which support vectorised batches and JIT compilation. Within a single circuit, matrix-defined operations, gates synthesised from Hamiltonian time evolution and noise channels can be composed freely. For a fast simulation, gate and channel fusion reduces passes over the state, while adjoint differentiation computes expectation-value gradients with a constant number of statevectors. At pulse level, JAQSI reduces evolution under single-term Hamiltonians to a scalar pulse-area integral and reuses cached execution plans and compiled solvers. In a benchmark we compare JAQSI with PennyLane, Qiskit, Qibo, Qulacs, QuTiP and dynamiqs. At gate level, we observe performance either on par or an order of magnitude faster across statevector, density, noise and gradient simulation than the compared simulators up to 12 qubits. Beyond 18 qubits, JAQSI is on par with PennyLane Lightning in both statevector and gradient simulation. In the statevector and noisy density-matrix pulse benchmarks, it is at least 5 times faster than the other simulators, even with its closed-form solve disabled. Disabling the latter increases its runtime by at most a factor of 1.5. We provide JAQSI as open-source software on GitHub and PyPI.

https://arxiv.org/abs/2505.00529 2025-05-01T00:00:00Z 2025-05-01T00:00:00Z Harish S. Bhat

We derive and implement a second-order adjoint method to compute exact gradients and Hessians for a prototypical quantum optimal control problem, that of solving for the minimal energy applied electric field that drives a molecule from a given initial state to a desired target state. For small to moderately sized systems, we demonstrate a vectorized GPU implementation of a second-order adjoint method that computes both Hessians and gradients with wall times only marginally more than those required to compute gradients via commonly used first-order adjoint methods. Pairing our second-order adjoint method with a trust region optimizer (a type of Newton method), we show that it outperforms a first-order method, requiring significantly fewer iterations and wall time to find optimal controls for four molecular systems. Our derivation of the second-order adjoint method allows for arbitrary parameterizations of the controls.

https://arxiv.org/abs/2406.18155 2024-06-26T00:00:00Z 2025-04-23T00:00:00Z Ziang WangFeng WuHui-Hai ZhaoXin WanXiaotong Ni

One significant advantage of superconducting processors is their extensive design flexibility, which encompasses various types of qubits and interactions. Given the large number of tunable parameters of a processor, the ability to perform gradient optimization would be highly beneficial. Efficient backpropagation for gradient computation requires a tightly integrated software library, for which no open-source implementation is currently available. In this work, we introduce SuperGrad, a simulator that accelerates the design of superconducting quantum processors by incorporating gradient computation capabilities. SuperGrad offers a user-friendly interface for constructing Hamiltonians and computing both static and dynamic properties of composite systems. This differentiable simulation is valuable for a range of applications, including optimal control, design optimization, and experimental data fitting. In this paper, we demonstrate these applications through examples and code snippets.

https://arxiv.org/abs/2210.11595 2022-10-20T00:00:00Z 2023-06-06T00:00:00Z Daniel PuzzuoliSophia Fuhui LinMoein MalekakhlaghEmily PritchettBenjamin RosandChristopher J. Wood

We develop general purpose algorithms for computing and utilizing both the Dyson series and Magnus expansion, with the goal of facilitating numerical perturbative studies of quantum dynamics. To enable broad applications to models with multiple parameters, we phrase our algorithms in terms of multivariable sensitivity analysis, for either the solution or the time-averaged generator of the evolution over a fixed time-interval. These tools simultaneously compute a collection of terms up to arbitrary order, and are general in the sense that the model can depend on the parameters in an arbitrary time-dependent way. We implement the algorithms in the open source software package \qiskitdynamics{}, utilizing the JAX array library to enable just-in-time compilation, automatic differentiation, and GPU execution of all computations. Using a model of a single transmon, we demonstrate how to use these tools to approximate fidelity in a region of model parameter space, as well as construct perturbative robust control objectives. We also derive and implement Dyson and Magnus-based variations of the recently introduced Dysolve algorithm [Shillito et al., Physical Review Research, 3(3):033266] for simulating linear matrix differential equations. We show how the pre-computation step can be phrased as a multivariable expansion computation problem with fewer terms than in the original method. When simulating a two-transmon entangling gate on a GPU, we find the Dyson and Magnus-based solvers provide a speedup over traditional ODE solvers, ranging from roughly $2\times$ to $4\times$ for a solution and $10\times$ to $60\times$ for a gradient, depending on solution accuracy.

https://arxiv.org/abs/2210.08378 2022-10-15T00:00:00Z 2022-10-15T00:00:00Z Xian WangPaul KairysSri Hari Krishna NarayananJan HueckelheimPaul Hovland

Quantum optimal control problems are typically solved by gradient-based algorithms such as GRAPE, which suffer from exponential growth in storage with increasing number of qubits and linear growth in memory requirements with increasing number of time steps. Employing QOC for discrete lattices reveals that these memory requirements are a barrier for simulating large models or long time spans. We employ a nonstandard differentiable programming approach that significantly reduces the memory requirements at the cost of a reasonable amount of recomputation. The approach exploits invertibility properties of the unitary matrices to reverse the computation during back-propagation. We utilize QOC software written in the differentiable programming framework JAX that implements this approach, and demonstrate its effectiveness for lattice gauge theory.

https://arxiv.org/abs/2205.15044 2022-05-27T00:00:00Z 2022-12-01T00:00:00Z Michael H. GoerzSebastian C. CarrascoVladimir S. Malinovsky

We develop a framework of "semi-automatic differentiation" that combines existing gradient-based methods of quantum optimal control with automatic differentiation. The approach allows to optimize practically any computable functional and is implemented in two open source Julia packages, GRAPE.jl and Krotov.jl, part of the QuantumControl.jl framework. Our method is based on formally rewriting the optimization functional in terms of propagated states, overlaps with target states, or quantum gates. An analytical application of the chain rule then allows to separate the time propagation and the evaluation of the functional when calculating the gradient. The former can be evaluated with great efficiency via a modified GRAPE scheme. The latter is evaluated with automatic differentiation, but with a profoundly reduced complexity compared to the time propagation. Thus, our approach eliminates the prohibitive memory and runtime overhead normally associated with automatic differentiation and facilitates further advancement in quantum control by enabling the direct optimization of non-analytic functionals for quantum information and quantum metrology, especially in open quantum systems. We illustrate and benchmark the use of semi-automatic differentiation for the optimization of perfectly entangling quantum gates on superconducting qubits coupled via a shared transmission line. This includes the first direct optimization of the non-analytic gate concurrence.

https://arxiv.org/abs/2203.12717 2022-03-23T00:00:00Z 2022-03-23T00:00:00Z Sri Hari Krishna NarayananThomas PropsonMarcelo BongartiJan HueckelheimPaul Hovland

Quantum optimal control problems are typically solved by gradient-based algorithms such as GRAPE, which suffer from exponential growth in storage with increasing number of qubits and linear growth in memory requirements with increasing number of time steps. These memory requirements are a barrier for simulating large models or long time spans. We have created a nonstandard automatic differentiation technique that can compute gradients needed by GRAPE by exploiting the fact that the inverse of a unitary matrix is its conjugate transpose. Our approach significantly reduces the memory requirements for GRAPE, at the cost of a reasonable amount of recomputation. We present benchmark results based on an implementation in JAX.

https://arxiv.org/abs/2012.09282 2020-12-16T00:00:00Z 2020-12-16T00:00:00Z Ross ShillitoJonathan A. GrossAgustin Di PaoloElie GenoisAlexandre Blais

The controls enacting logical operations on quantum systems are described by time-dependent Hamiltonians that often include rapid oscillations. In order to accurately capture the resulting time dynamics in numerical simulations, a very small integration time step is required, which can severely impact the simulation run-time. Here, we introduce a semi-analytic method based on the Dyson expansion that allows us to time-evolve driven quantum systems much faster than standard numerical integrators. This solver, which we name Dysolve, efficiently captures the effect of the highly oscillatory terms in the system Hamiltonian, significantly reducing the simulation's run time as well as its sensitivity to the time-step size. Furthermore, this solver provides the exact derivative of the time-evolution operator with respect to the drive amplitudes. This key feature allows for optimal control in the limit of strong drives and goes beyond common pulse-optimization approaches that rely on rotating-wave approximations. As an illustration of our method, we show results of the optimization of a two-qubit gate using transmon qubits in the circuit QED architecture.

https://arxiv.org/abs/2008.09128 2020-08-20T00:00:00Z 2021-04-09T00:00:00Z Luuk CoopmansDi LuoGraham KellsBryan K. ClarkJuan Carrasquilla

Quantum control, which refers to the active manipulation of physical systems described by the laws of quantum mechanics, constitutes an essential ingredient for the development of quantum technology. Here we apply Differentiable Programming (DP) and Natural Evolution Strategies (NES) to the optimal transport of Majorana zero modes in superconducting nanowires, a key element to the success of Majorana-based topological quantum computation. We formulate the motion control of Majorana zero modes as an optimization problem for which we propose a new categorization of four different regimes with respect to the critical velocity of the system and the total transport time. In addition to correctly recovering the anticipated smooth protocols in the adiabatic regime, our algorithms uncover efficient but strikingly counter-intuitive motion strategies in the non-adiabatic regime. The emergent picture reveals a simple but high fidelity strategy that makes use of pulse-like jumps at the beginning and the end of the protocol with a period of constant velocity in between the jumps, which we dub the jump-move-jump protocol. We provide a transparent semi-analytical picture, which uses the sudden approximation and a reformulation of the Majorana motion in a moving frame, to illuminate the key characteristics of the jump-move-jump control strategy. We verify that the jump-move-jump protocol remains robust against the presence of interactions or disorder, and corroborate its high efficacy on a realistic proximity coupled nanowire model. Our results demonstrate that machine learning for quantum control can be applied efficiently to quantum many-body dynamical systems with performance levels that make it relevant to the realization of large-scale quantum technology.

https://arxiv.org/abs/2007.01287 2020-07-02T00:00:00Z 2021-11-17T00:00:00Z Ilia A. LuchnikovMikhail E. KrechetovSergey N. Filippov

Optimization with constraints is a typical problem in quantum physics and quantum information science that becomes especially challenging for high-dimensional systems and complex architectures like tensor networks. Here we use ideas of Riemannian geometry to perform optimization on manifolds of unitary and isometric matrices as well as the cone of positive-definite matrices. Combining this approach with the up-to-date computational methods of automatic differentiation, we demonstrate the efficacy of the Riemannian optimization in the study of the low-energy spectrum and eigenstates of multipartite Hamiltonians, variational search of a tensor network in the form of the multiscale entanglement-renormalization ansatz, preparation of arbitrary states (including highly entangled ones) in the circuit implementation of quantum computation, decomposition of quantum gates, and tomography of quantum states. Universality of the developed approach together with the provided open source software enable one to apply the Riemannian optimization to complex quantum architectures well beyond the listed problems, for instance, to the optimal control of noisy quantum systems.

https://arxiv.org/abs/2002.08376 2020-02-19T00:00:00Z 2020-02-19T00:00:00Z Frank SchäferMichal KlocChristoph BruderNiels Lörch

Optimal control is highly desirable in many current quantum systems, especially to realize tasks in quantum information processing. We introduce a method based on differentiable programming to leverage explicit knowledge of the differential equations governing the dynamics of the system. In particular, a control agent is represented as a neural network that maps the state of the system at a given time to a control pulse. The parameters of this agent are optimized via gradient information obtained by direct differentiation through both the neural network \emph{and} the differential equation of the system. This fully differentiable reinforcement learning approach ultimately yields time-dependent control parameters optimizing a desired figure of merit. We demonstrate the method's viability and robustness to noise in eigenstate preparation tasks for three systems: a~single qubit, a~chain of qubits, and a quantum parametric oscillator.

https://arxiv.org/abs/1901.05541 2019-01-16T00:00:00Z 2019-01-16T00:00:00Z Mohamed AbdelhafezDavid I. SchusterJens Koch

We present a gradient-based optimal-control technique for open quantum systems that utilizes quantum trajectories to simulate the quantum dynamics during optimization. Using trajectories allows for optimizing open systems with less computational cost than the regular density matrix approaches in most realistic optimization problems. We introduce an improved-sampling algorithm which minimizes the number of trajectories needed per optimization iteration. Together with employing stochastic gradient descent techniques, this reduces the complexity of optimizing many realistic open quantum systems to the complexity encountered with closed systems. Our optimizer harnesses automatic differentiation to provide flexibility in optimization and to suit the different constraints and diverse parameter regimes of real-life experiments. We utilize the optimizer in a variety of applications to demonstrate how the use of quantum trajectories significantly reduces the computation complexity while achieving a multitude of simultaneous optimization targets. Demonstrated targets include high state-transfer fidelities despite dissipation, faster gate times and maximization of qubit-readout fidelity while maintaining the quantum non-demolition nature of the measurement and allowing for subsequent fast resonator reset.

https://arxiv.org/abs/1612.04929 2016-12-15T00:00:00Z 2017-04-18T00:00:00Z Nelson LeungMohamed AbdelhafezJens KochDavid I. Schuster

We implement a quantum optimal control algorithm based on automatic differentiation and harness the acceleration afforded by graphics processing units (GPUs). Automatic differentiation allows us to specify advanced optimization criteria and incorporate them in the optimization process with ease. We show that the use of GPUs can speed up calculations by more than an order of magnitude. Our strategy facilitates efficient numerical simulations on affordable desktop computers, and exploration of a host of optimization constraints and system parameters relevant to real-life experiments. We demonstrate optimization of quantum evolution based on fine-grained evaluation of performance at each intermediate time step, thus enabling more intricate control on the evolution path, suppression of departures from the truncated model subspace, as well as minimization of the physical time needed to perform high-fidelity state preparation and unitary gates.