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A Framework for Automated, Unsupervised Control Synthesis in Noiseless Subspaces of Open Quantum Systems

Eric Benjamin Kopp

Published Mar 1, 2024• 0 citations
OpenAlex

Abstract

In this thesis, we develop an automated framework for open-loop quantum control design, called the Generalized Control of Noiseless Subspaces (GCNS) framework, that targets a broad class of open quantum systems subject to the Born-Markov approximation. The framework is automated, highly generalized, computationally efficient, and extensible. It rests on an eleven-point Formal Framework Scope that specifies the model classes, control standards, information preservation standards, and control input classes it supports. It additionally rests on a nine-point set of Software Implementation Guidelines (SIG) that specifies how any software implementation of the framework should ideally perform with respect to efficiency, automaticity, and scalability. In constructing the framework, we develop novel theorems for controllability in Quantum Noiseless Subsystems, novel algorithms for the efficient, automated detection and parameterization of subsystem codes, and novel algorithms for the systematic selection and synthesis of control Hamiltonians from large candidate sets of feasible controls. Additionally, we develop the theory of Transition-Effort-based Control Input Synthesis: a versatile approach to generating control input signals, subject to a wide potential range of constraints, for the purpose of noiselessly effecting quantum operations on encoded quantum states. The thesis provides a comprehensive examination of a MATLAB- and Java-based implementation of the framework called the QBox library. The examination covers supporting algorithms critical for meeting the efficiency and extensibility guidelines in the SIG. It additionally covers all major aspects of the software library's anatomy, its application programming interface, and its suite of supplementary tools assisting control design. To validate the GCNS framework, its principal workflow is applied to two open quantum system models selected from the quantum information processing literature, based on trapped ions and superconducting transmon qutrits. The models and workflow parameters are selected to demonstrate a broad cross-section of the algorithms, subroutines, and software tools developed in the thesis. The examples further establish the exceptional scope and configurability of the framework, highlighting its importance to rapid design iteration in the noisy intermediate-scale quantum computing era.

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In this thesis, we develop an automated framework for open-loop quantum control design, called the Generalized Control of Noiseless Subspaces (GCNS) framework, that targets a broad class of open quantum systems subject to the Born-Markov approximation. The framework is automated, highly generalized, computationally efficient, and extensible. It rests on an eleven-point Formal Framework Scope that specifies the model classes, control standards, information preservation standards, and control input classes it supports. It additionally rests on a nine-point set of Software Implementation Guidelines (SIG) that specifies how any software implementation of the framework should ideally perform with respect to efficiency, automaticity, and scalability. In constructing the framework, we develop novel theorems for controllability in Quantum Noiseless Subsystems, novel algorithms for the efficient, automated detection and parameterization of subsystem codes, and novel algorithms for the systematic selection and synthesis of control Hamiltonians from large candidate sets of feasible controls. Additionally, we develop the theory of Transition-Effort-based Control Input Synthesis: a versatile approach to generating control input signals, subject to a wide potential range of constraints, for the purpose of noiselessly effecting quantum operations on encoded quantum states. The thesis provides a comprehensive examination of a MATLAB- and Java-based implementation of the framework called the QBox library. The examination covers supporting algorithms critical for meeting the efficiency and extensibility guidelines in the SIG. It additionally covers all major aspects of the software library's anatomy, its application programming interface, and its suite of supplementary tools assisting control design. To validate the GCNS framework, its principal workflow is applied to two open quantum system models selected from the quantum information processing literature, based on trapped ions and superconducting transmon qutrits. The models and workflow parameters are selected to demonstrate a broad cross-section of the algorithms, subroutines, and software tools developed in the thesis. The examples further establish the exceptional scope and configurability of the framework, highlighting its importance to rapid design iteration in the noisy intermediate-scale quantum computing era.
Abstract Effectively manipulating quantum computing (QC) hardware in the presence of imperfect devices and control systems is a central challenge in realizing useful quantum computers. Susceptibility to noise critically limits the performance and capabilities of today’s so-called noisy intermediate-scale quantum devices, as well as any future QC technologies. Fortunately, quantum control enables efficient execution of quantum logic operations and quantum algorithms with built-in robustness to errors, and without the need for complex logical encoding. In this manuscript we introduce software tools for the application and integration of quantum control in QC research, serving the needs of hardware R&D teams, algorithm developers, and end users. We provide an overview of a set of Python-based classical software tools for creating and deploying optimized quantum control solutions at various layers of the QC software stack. We describe a software architecture leveraging both high-performance distributed cloud computation and local custom integration into hardware systems, and explain how key functionality is integrable with other software packages and quantum programming languages. Our presentation includes a detailed mathematical overview of key features including a flexible optimization toolkit, engineering-inspired filter functions for analyzing noise susceptibility in high-dimensional Hilbert spaces, and new approaches to noise and hardware characterization. Pseudocode is presented in order to elucidate common programming workflows for these tasks, and performance benchmarking is reported for numerically intensive tasks, highlighting the benefits of the selected cloud-compute architecture. Finally, we present a series of case studies demonstrating the application of quantum control solutions derived from these tools in real experimental settings using both trapped-ion and superconducting quantum computer hardware.
The scaling of effort to achieve control objectives with system size is an important consideration in the development of many quantum devices, especially in those intended for quantum information processing. This thesis investigates the scaling with system size of effort required to control manybody quantum systems, and asks whether this is sufficiently favourable to enable supremacy in quantum computation. This is tested using quantum control theory and numerical control optimisation, which are well established tools for investigating the dynamics of driven quantum systems, in a variety of theoretical models related to state-of-the-art quantum devices. Gates acting on a chain of coupled oscillators are found to achievable in times that scale approximately linear with chain length, where the control is over only a single oscillator. The scalability of a scheme for implementing quantum gates in a many-body quantum simulator is shown to be favourable enough to allow for them to be configured to perform quantum computations. A state measurement protocol is proposed as part of the scheme. The scalability is validated through numerical simulation of simulator models composed of up to 9 qubits. The reachable set of operations for systems with quadratic Hamiltonians and infinite-dimensional Hilbert spaces is investigated. The passive operations in quantum optics are proven to be unreachable for single-mode systems with ‘unstable’ Hamiltonians. Further characterisation of the reachable set is made through numerical simulation of control optimisation. Some progress is made in extending the reachability result to n-modes. A non-Markovian noise model is used in simulating control optimisation of a dynamical decoupling scheme, which would be impossible to simulate with Markovian dynamics. The popular QuTiP Python library has been extended to allow simulation of control optimisation with a range of dynamical models. A description of these software modules and their method of use is given. Many of the software tools developed for the study are made available through open-source repositories. Some outlook is given for the use of in-situ open-loop control in optimising controls in quantum system experiments.
Quantum control is essential for quantum information science and technology, yet designing high-fidelity control protocols remains challenging due to complex optimization landscapes, hardware noise, and long pulse sequences. Existing numerical solvers often require problem-specific engineering and produce opaque control amplitudes, while naive large language models (LLMs) lack the physical consistency and long-horizon precision for reliable quantum control synthesis. Here we introduce VF-QCTRL, a physics-informed large language model framework for general quantum control that combines symbolic reasoning with optimization to propose analytic control ansätze and coherently refine their parameters through feedback. To systematically evaluate LLM-driven quantum control, we develop QCTRL-BENCH, a benchmark spanning sixteen tasks across single- and multi-qubit systems, closed and open quantum dynamics, noiseless and noisy settings, and both analytic and numerical protocols. Across the benchmark, VF-QCTRL demonstrates strong universality, accuracy, efficiency, and interpretability: it applies to generic quantum control systems without task-specific training, achieves performance competitive with or exceeding state-of-the-art conventional solvers in both noiseless and noisy regimes with query efficiency, exhibits favorable inference-time scaling and pulse resolution scaling, and derives physically interpretable analytical protocols directly from prompts. Our results establish physics-informed LLM-based quantum control as a promising paradigm for accurate, efficient, interpretable, and training-free quantum control protocol design across a broad range of quantum systems.
For paving the way to novel applications in quantum simulation, computation, and technology, increasingly large quantum systems have to be steered with high precision. It is a typical task amenable to numerical optimal control to turn the time course of pulses, i.e., piecewise constant control amplitudes, iteratively into an optimized shape. Here, we present a comparative study of optimal-control algorithms for a wide range of finite-dimensional applications. We focus on the most commonly used algorithms: GRAPE methods which update all controls concurrently, and Krotov-type methods which do so sequentially. Guidelines for their use are given and open research questions are pointed out. Moreover, we introduce a unifying algorithmic framework, DYNAMO (dynamic optimization platform), designed to provide the quantum-technology community with a convenient matlab-based tool set for optimal control. In addition, it gives researchers in optimal-control techniques a framework for benchmarking and comparing newly proposed algorithms with the state of the art. It allows a mix-and-match approach with various types of gradients, update and step-size methods as well as subspace choices. Open-source code including examples is made available at http://qlib.info.
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 . . . . . . . .
We introduce QiboAgent, a reference implementation designed to serve as a practitioner's guideline for developing specialized coding assistants in Quantum Computing middleware. Addressing the limitations in scientific software development of general-purpose proprietary models, we explore how lightweight, open-source Large Language Models (LLMs) provided with a custom workflow architecture compare. In detail, we experiment with two complementary paradigms: a Retrieval-Augmented Generation pipeline for high-precision information retrieval, and an autonomous agentic workflow for complex software engineering tasks. We observe that this hybrid approach significantly reduces hallucination rates in code generation compared to a proprietary baseline, achieving a peak accuracy of 90.2% with relatively small open-source models of size up to 30B parameters. Furthermore, the agentic framework exhibits advanced coding capabilities, automating the resolution of maintenance issues and new features requests, or by prototyping larger-scale refactors of the codebase, such as producing a compiled Rust module with bindings of an original pure python package, Qibo in our case. The LLM workflows used for our analysis are integrated into a user interface and a Model Context Protocol server, providing an accessible tool for Qibo developers.