Quantum optimal control (QOC) aims to find control functions that optimally steer a quantum system toward a target operation. We introduce a \emph{randomized} QOC framework where optimization is carried over an ensemble of control functions and their probabilities, instead of a single set of functions. Using this framework, we prove that randomized QOC can reach a target accuracy faster than any deterministic protocol under the same resource constraints. We also develop general symmetry-based constructions that convert a given control into an ensemble of controls that can systematically reduce the error. We benchmark these constructions for CNOT implementation and find that the resulting randomized protocol quadratically suppresses the error of the optimized deterministic solution. In addition, we introduce randomized GRAPE, which generalizes GRAPE to directly optimize control ensembles and their associated probabilities. Finally, as a related application, we discuss randomized boundary-pulse constructions {that enhance} robustness against coherent noise.
Quantum optimal control (QOC) aims to find control functions that optimally steer a quantum system toward a target operation. We introduce a \emph{randomized} QOC framework where optimization is carried over an ensemble of control functions and their probabilities, instead of a single set of functions. Using this framework, we prove that randomized QOC can reach a target accuracy faster than any deterministic protocol under the same resource constraints. We also develop general symmetry-based constructions that convert a given control into an ensemble of controls that can systematically reduce the error. We benchmark these constructions for CNOT implementation and find that the resulting randomized protocol quadratically suppresses the error of the optimized deterministic solution. In addition, we introduce randomized GRAPE, which generalizes GRAPE to directly optimize control ensembles and their associated probabilities. Finally, as a related application, we discuss randomized boundary-pulse constructions {that enhance} robustness against coherent noise.
High-fidelity quantum operations are the cornerstone of fault-tolerant quantum computation. In open quantum systems, traditional optimal control only passively resists decoherence, leaving environment-induced uncertainty as a fundamental performance bottleneck. To overcome this, we propose a new optimal control framework with flag ancillas and the Flag-GRAPE algorithm, which can actively tailor the system's noise structure. Through embedding post-selection directly into the objective function, Flag-GRAPE correlates decoherence errors with the ancilla's unexpected state. Subsequent measurement and post-selection effectively expel this uncertainty, circumventing the fidelity bounds of traditional control. Numerical simulations in a superconducting quantum circuit demonstrate a 51% reduction in infidelity compared to traditional closed-system pulses and also show that such enhancement is robust across broad noise regimes. Furthermore, by actively converting unstructured decoherence into heralded erasure errors, Flag-GRAPE is inherently compatible with quantum error correction. We demonstrate this by initializing a logical cat-code state, showing that the combination between Flag-GRAPE and QEC yields immediate state preparation enhancements. This new framework can reduce hardware overhead for fault-tolerant architectures and open up a practical path toward logical state preparation gain in near-term experiments.
The fundamental goal of quantum computing is to precisely control quantum systems to perform meaningful tasks, including implementing high-fidelity quantum gates for reliable quantum computation and accurately simulating complex quantum many- body dynamics. In this dissertation, we develop improved quantum control protocols for three distinct objectives, quantum error suppression, quantum optimal control, and analog quantum algorithms, achieving performance beyond standard approaches. First, we introduce new dynamical decoupling protocols, including both determin- istic and randomized constructions, that can substantially outperform conventional deterministic sequences. We then extend the randomized approach to dynamically corrected gates. Second, we propose a randomized quantum optimal control frame- work that offers advantages over deterministic optimal control protocols. Finally, we develop new control protocols for analog quantum algorithms to perform high-order Hamiltonian simulation and learning unknown quantum states.
This research presents an ensemble Reinforcement Learning (RL) approach that combines Deep Q-Network (DQN) and Proximal Policy Optimization (PPO) algorithms to tackle quantum control problems. This research aims to use the complementary strengths of DQN and PPO algorithms to develop robust and adaptive control policies for noisy and uncertain quantum systems. We comprehensively analyse the proposed ensemble learning, including algorithmic details, implementation specifics, and experimental results. Through extensive experimentation and evaluation, we demonstrate the effectiveness of the ensemble approach in learning control strategies for manipulating quantum systems towards a random target state. The results highlight the potential of ensemble RL techniques in addressing the challenges of quantum control tasks, such as system noise and dynamics. By integrating multiple RL agents within an ensemble framework, We aim to advance current developments in quantum control and create a new path for the development of adaptive control systems for quantum systems. The performance of the ensemble model is assessed against Gradient Ascent Pulse Engineering (GRAPE) and robust Model Predictive Control (MPC) to demonstrate its efficiency in highly challenging and noisy environments.
Superconducting-qubit control is fundamentally constrained by decoherence, finite bandwidth, and hardware-limited drive amplitudes, making high-fidelity state preparation sensitive to optimizer initialization under non-convex open-system dynamics. We propose a hybrid reinforcement learning (RL)–quantum optimal control (QOC) pipeline in which a lightweight, tabular, model-free RL agent is trained offline in simulation to generate feasible, bounded seed pulses, which are subsequently refined via GRAPE under Lindblad dynamics. Hard amplitude constraints are enforced consistently across both stages, ensuring strict feasibility throughout optimization. Performance is evaluated using a budget-matched protocol based on fidelity evaluations (F-evals), enabling controlled comparison with random-start multi-start GRAPE. On a transmon-like qubit benchmark with relaxation and dephasing, RL warm-starting reduces the median online refinement effort in the adopted finite-difference GRAPE implementation from 7568 to 3543 F-evals (2.14× reduction) while achieving terminal state fidelity ≥0.995 under identical constraints and evaluation budgets. We provide a theoretical interpretation of the improvement in terms of basin-of-attraction probability shaping in constrained control landscapes and an amortized cost analysis showing that the offline RL cost is recovered after a small number of reuse cycles. The results support the view that learning-based initialization can improve warm-start quality relative to uninformed feasible multi-start in constrained open-system quantum-control benchmarks, while broader practical comparison against stronger physics-guided seeds remains for future work.
Abstract The mathematics of optimal control of quantum systems is of great interest in connection with fundamental problems of physics as well as with existing and prospective applications to quantum technologies. One important problem is the development of methods for constructing controls for quantum systems. One of the commonly used methods is the Krotov method, which was initially proposed outside of quantum control theory in articles by Krotov and Feldman (1978, 1983). This method was used to develop a novel approach to finding optimal controls for quantum systems in [64] (Tannor, Kazakov, and Orlov, 1992), [65] (Somlói, Kazakov, and Tannor, 1993), and in many other works by various scientists. Our survey discusses mathematical aspects of this method for optimal control of closed quantum systems. It outlines various modifications with different forms of the improvement function (for example, linear or linear-quadratic), different constraints on the control spectrum and on the admissible states of the quantum system, different regularisers, and so on. The survey describes applications of the Krotov method to controlling molecular dynamics and Bose–Einstein condensates, and to quantum gate generation. This method is compared with the GRAPE (GRadient Ascent Pulse Engineering) method, the CRAB (Chopped Random-Basis) method, and the Zhu–Rabitz and Maday–Turinici methods. Bibliography: 158 titles.
This thesis is concerned with the control of quantum systems.Given a Hamiltonian model of a quantum system, we are interested in finding controls-typically shaped electromagnetic pulses-that steer the evolution of the system toward a desired target operation.For this we employ a numerical optimisation method known as the GRAPE algorithm.For particular experimental systems, we design control schemes that respect constraints of robustness and addressability, and are within the reach of the experimental hardware.A general procedure is given for specifying a Hamiltonian model of a driven N -level system and converting it to an appropriate rotating frame.This is then applied together with the numerical algorithm to design improved schemes for two different systems, where laser fields manipulate orbital and hyperfine states of Pr 3+ and Rb.The generation of cluster states in Ising-coupled systems is also studied.We find that, in the ideal case, the solution of evolving only under the coupling Hamiltonian is not time-optimal.This surprising result is in contrast to the known cases for unitary gates.For a symmetrised three-qubit example, we provide a geometrical interpretation of this.Numerically optimised control schemes are then developed for a nonideal coupling topology, modelling an experimental configuration of trapped ions.Controls for the implementation of the two-qubit Deutsch and Grover algorithms are designed for a pair of 13 C nuclear spins at a nitrogen vacancy center in diamond.These implementations are robust to experimental errors, and found to be reproduced with high accuracy on a VFG-150 pulse generator.We also consider two-qubit gate synthesis in a system of superconducting qubits coupled by mii xii CONTENTS C.4 Examples of time-optimal gates . . . . . . . .