Control and simulation of spin dynamics face two persistent bottlenecks: instrument-induced distortions that warp optimised pulses, and the near universal piecewise-constant approximation of the Hamiltonian. The latter is the lowest order Lie-solver that degrades under fast timing and realistic hardware responses. This thesis addresses both. From first principles, piecewise-linear and piecewise-quadratic propagators that evolve on the Lie-group manifold are derived. In simulation, these higher-order Lie-solvers achieve higher trajectory accuracy with fewer time intervals. The GRadient Ascent Pulse Engineering (GRAPE) algorithm is extended to a piecewise-linear formulation (LGRAPE). The exact analytical gradients are computed via auxiliary matrix methods, delivering higher fidelities under tight timing constraints. When significant, distortions are treated explicitly by embedding cascades of transfer functions and ensemble parameters directly into the optimisation. The resulting Response-Aware GRAPE (RAW-GRAPE) requires only the transfer functions and their Jacobians (via automatic differentiation when needed), compensating for linear/non-linear effects without brittle deconvolution. Single-pole and single-zero blocks are supplied that act as basis elements for arbitrary linear responses. When combined with non-linear elements, the framework can, in principle, incorporate any distortion cascade. Across diverse simulated experiments with representative hardware artefacts, RAW-GRAPE demonstrates higher robustness and target fidelity compared to conventional GRAPE. As machine learning use expands, well-labelled experimental datasets remain scarce. We therefore build a forward-modelled simulation pipeline that mirrors real experiments and injects hardware artefacts on the fly. The 3D data volume bottleneck is addressed by retaining Kronecker factorisations, avoiding explicit tensor expansion. Hundreds of thousands of spectra are generated in hours to train neural networks for automated protein-backbone assignment. The pipeline integrates with CcpNmr and yields accurate end-to-end predictions on proteins up to 40 kDa. All methods are implemented in Spinach with reproducible workflows.
Control and simulation of spin dynamics face two persistent bottlenecks: instrument-induced distortions that warp optimised pulses, and the near universal piecewise-constant approximation of the Hamiltonian. The latter is the lowest order Lie-solver that degrades under fast timing and realistic hardware responses. This thesis addresses both. From first principles, piecewise-linear and piecewise-quadratic propagators that evolve on the Lie-group manifold are derived. In simulation, these higher-order Lie-solvers achieve higher trajectory accuracy with fewer time intervals. The GRadient Ascent Pulse Engineering (GRAPE) algorithm is extended to a piecewise-linear formulation (LGRAPE). The exact analytical gradients are computed via auxiliary matrix methods, delivering higher fidelities under tight timing constraints. When significant, distortions are treated explicitly by embedding cascades of transfer functions and ensemble parameters directly into the optimisation. The resulting Response-Aware GRAPE (RAW-GRAPE) requires only the transfer functions and their Jacobians (via automatic differentiation when needed), compensating for linear/non-linear effects without brittle deconvolution. Single-pole and single-zero blocks are supplied that act as basis elements for arbitrary linear responses. When combined with non-linear elements, the framework can, in principle, incorporate any distortion cascade. Across diverse simulated experiments with representative hardware artefacts, RAW-GRAPE demonstrates higher robustness and target fidelity compared to conventional GRAPE. As machine learning use expands, well-labelled experimental datasets remain scarce. We therefore build a forward-modelled simulation pipeline that mirrors real experiments and injects hardware artefacts on the fly. The 3D data volume bottleneck is addressed by retaining Kronecker factorisations, avoiding explicit tensor expansion. Hundreds of thousands of spectra are generated in hours to train neural networks for automated protein-backbone assignment. The pipeline integrates with CcpNmr and yields accurate end-to-end predictions on proteins up to 40 kDa. All methods are implemented in Spinach with reproducible workflows.
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.
Real-time adaptive control of quantum systems requires rapid generation of robust, high-fidelity pulses across a continuous range of operating conditions. Standard optimization algorithms such as gradient-ascent pulse engineering (GRAPE) solve each instance independently, discarding information between runs and requiring costly reinitialization when parameters change. We present an approach to robust optimal quantum control based on model-based reinforcement learning, in which a single neural network -- embedding the Hamiltonian directly into the training pipeline -- generates robust gates across an entire family of gate configurations, without pre-computed training data. Demonstrated on a single-spin (two-level) system, the trained networks produce pulses for arbitrary rotation angles over a range of pulse durations, detunings, and field inhomogeneities in milliseconds, at fidelities comparable to multi-seed GRAPE. The framework is inherently adaptable: any parameter entering the Hamiltonian can serve as a network input, extending the approach to different systems and control settings. Beyond speed, the network reveals structure in the control landscape: it discovers the same structured phase profiles that appear in GRAPE solutions -- made identifiable through fidelity-invariant symmetry transformations -- but more consistently than independent optimization. This consistency enables smooth interpolation across the entire trained parameter space.
The gradient ascent pulse engineering (GRAPE) algorithm is a celebrated control algorithm with excellent converging rates, owing to a piecewise-constant ansatz for the control function that allows for cheap objective gradients. However, the computational effort involved in the exact simulation of quantum dynamics quickly becomes a bottleneck limiting the control of large systems. In this paper, we experiment with a modified version of GRAPE that uses Krylov approximations (K-GRAPE) to deal efficiently with high-dimensional state spaces. Even though the number of parameters required by an arbitrary control task scale linearly with the dimension of the system, we find a constant elementary computational effort (the effort per parameter). Since the elementary effort of GRAPE is superquadratic, this speed up allows us to reach dimensions far beyond. The performance of the K-GRAPE algorithm is benchmarked in the paradigmatic XXZ spin-chain model.
We present a framework combining Lie group theory and feed-forward neural networks to efficiently generate quantum optimal control pulses for arbitrary unitary operations in superconducting qubit systems, bypassing the need for explicit optimization at inference time. The exponential scaling of the Hilbert space dimension with qubit number makes standard optimization approaches computationally prohibitive when large ensembles of distinct propagators must be processed, a bottleneck that is particularly acute in Trotterized quantum simulation. Our method addresses this limitation by pre-computing a representative set of control pulses via Lie group theory and training neural networks to map target propagators to their corresponding pulses. We demonstrate the approach on superconducting qubit systems of 2, 3, and 4 qubits, finding high reconstruction fidelity for specific combinations of Lie algebra parameters. As a physically motivated benchmark, we apply the methodology to reconstruct control pulses for the Trotter propagators of a neutrino system undergoing collective flavor oscillations. The successful generalization across system types demonstrates that a single model -- trained once on hardware-specific random propagators -- can serve as a universal control-pulse generator for any target quantum system of compatible Hilbert space dimension, offering a promising route toward scalable quantum simulation.
An exquisite control over the dynamics of a quantum system is essential for realizing any quantum technology. This thesis presents some practical and efficient strategies for coherent quantum control: a paradigm for controlling quantum dynamics using electromagnetic fields. Coherent control is a common framework for describing the physical implementation of quantum logic gates in several quantum information processing platforms including superconducting qubits and trapped ions. For the purpose of demonstration, however, liquid-state Nuclear Magnetic Resonance (NMR) is used in this thesis as it is an ideal test-bed for developing, testing and benchmarking coherent control tools and techniques. Coherent control was revitalised in 2005 by the development of Gradient Ascent Pulse Engineering (GRAPE), a powerful optimal control technique that is widely used for designing shaped pulses for a variety of tasks. GRAPE, like any other closed-loop optimal control algorithm, requires multiple evaluations of the computationally expensive matrix exponential and the full time-evolution propagator. To this end, I present strategies to sidestep the explicit evaluation of matrix exponentials, thereby offering substantial speed-ups over conventional implementations of the GRAPE algorithm. The results are demonstrated experimentally in NMR, but also in simulations of ultracold molecules and superconducting qubits. Beyond GRAPE, this thesis also considers methods for designing spin-echo sequences for implementing any arbitrary network of controlled-Z gates in a system of qubits with zz-couplings. First, a method based on linear-programming provides near time-optimal sequences in fully-coupled systems having up to a few hundred qubits. Further, an analytic method based on graph colouring finds near time-optimal spin echo sequences in engineered systems with any number of qubits having only nearest and next-nearest neighbour-couplings.
We investigate how pulse-sequences and operation times of elementary quantum gates can be optimized for silicon-based donor electron spin quantum computer architecture, complementary to the original Kane's nuclear spin proposal. This gate-sequence-optimal or time-optimal quantum gate control in a quantum circuit is in addition to the more conventional concept of optimality in terms of the number of elementary gates needed in a quantum transformation. The optimal control method we use is the so-called gradient ascent pulse engineering (GRAPE) scheme. We focus on the high fidelity controlled-NOT (CNOT) gate and explicitly find the digitized control sequences by optimizing the effective, reduced donor electron spin Hamiltonian, with external controls over the hyperfine A and exchange J interactions. We first try different piecewise constant control steps and numerically calculate the fidelity (error) against the time needed to implement a CNOT gate with stopping criteria of error in the optimizer set to 〖10〗^(-9) in order to economize the simulation time. Here, the error is defined as 1-F, where F is fidelity. The error is less than 〖10〗^(-8) for times longer than 100ns, and it is found that 30 piecewise constant control steps for the CNOT gate operation will be sufficient to meet the required fidelity (error), and the performance would not be improved further with more steps. With operation time t=100ns and stopping criteria of error set to 〖10〗^(-16), we can find that the near time-optimal, high-fidelity CNOT gate control sequence has an error of 〖1.11×10〗^(-16). We then simulate the control sequences of the CNOT gate, obtained from reduced Hamiltonian simulations, with the full spin Hamiltonian. We find the error of about 〖10〗^(-6) which is below the error threshold required for fault-tolerant (〖10〗^(-4)) quantum computation. The CNOT gate operation time of 100ns is 3 times faster than the globally controlled electron spin scheme of 297ns. One of the great advantages of this near optimal-time high fidelity CNOT gate is that the exchange interaction is not required to be strong (the maximum value is J/h=20MHz compared to the typical value of 10.2GHz. This relaxes significantly the stringent distance constraint of two neighboring donor atoms of about 10nm as reported in the original Kane's proposal to be about 30nm which is within the reach of the current fabrication technology.