Simulation of adiabatic methods on a quantum computer has been successfully used to prepare ground states of gauge theories. However, this process requires a high number of quantum gates, which is inaccessible in the NISQ era. An alternative approach is to use variational methods, which utilise a hybrid of classical and quantum computation. We show how a particular example, the Quantum Approximate Optimisation Algorithm (QAOA), can be used to prepare ground states of the Schwinger Model, with an improved circuit depth compared to the adiabatic approximation that targets current devices. In addition, we discuss how, in principle, Permutational Quantum Computing can give us better optimisation beyond the NISQ era.
Simulation of adiabatic methods on a quantum computer has been successfully used to prepare ground states of gauge theories. However, this process requires a high number of quantum gates, which is inaccessible in the NISQ era. An alternative approach is to use variational methods, which utilise a hybrid of classical and quantum computation. We show how a particular example, the Quantum Approximate Optimisation Algorithm (QAOA), can be used to prepare ground states of the Schwinger Model, with an improved circuit depth compared to the adiabatic approximation that targets current devices. In addition, we discuss how, in principle, Permutational Quantum Computing can give us better optimisation beyond the NISQ era.
The Quantum Approximate Optimization Algorithm (QAOA), whose design is underpinned by the adiabatic theorem, is one of the leading variational quantum algorithms for preparing the ground states of gauge theories. A recently proposed variant, DC-QAOA, incorporates counterdiabatic driving to accelerate the adiabatic process, reducing both circuit depth and runtime. In this work, we present a systematic analysis, from both theoretical and computational perspectives, of DC-QAOA and related counterdiabatic variants for preparing the ground state of the Schwinger model, the paradigmatic (1+1)-dimensional lattice gauge theory. Benchmarking these methods against standard QAOA, we show that counterdiabatic driving improves ground-state preparation while lowering circuit depth requirements. Our results establish counterdiabatic protocols as a practical route towards efficient quantum simulation of gauge theories.
In this thesis, I explore the domain of hybrid quantum-classical computation, the foremost approach for utilizing Noisy Intermediate-Scale Quantum (NISQ) devices. The opening chapter presents an overview of Variational Quantum Algorithms (VQAs), highlighting the primary algorithmic challenges. It offers an in-depth review of the Quantum Approximate Optimization Algorithm (QAOA), discussing its variants for ground state preparation. In the second chapter, we apply QAOA for the supervised learning of a simple Binary Neural Network. This model represents an idealized yet prototypical example of classical combinatorial optimization problems involving multi-spin interactions. In the following chapters, the discussion shifts toward quantum many-body ground state preparation, focusing on the one-dimensional Heisenberg XYZ model and the longitudinal-transverse-field Ising model (LTFIM). We have developed a novel technique that, at any point in the phase diagram, leverages the transferability of a specific class of optimal schedules from systems with small to those with larger numbers of qubits. This approach mitigates trainability issues, specifically vanishing gradients (Barren Plateaus). Next, we tailor a QAOA scheme to characterize a topological quantum phase transition within a lattice gauge theory model. This investigation is particularly significant due to its implications for high-energy physics and relevance to quantum error correction and surface codes. In the concluding chapter, I propose new stimulating research directions and help to identify core challenges and unresolved questions in variational quantum computing that transcend any particular application domain.
This research paper provides a comprehensive review of quantum simulation methods for lattice gauge theories during the current era of noisy intermediate-scale quantum computing. It focuses on the fundamental framework used to understand strong interactions in high-energy physics and explores how quantum devices can overcome the limitations of traditional computational methods, such as the sign problem found in classical simulations. The manuscript is built around three primary pillars that are critical for near-term progress. The first pillar involves encoding strategies, describing the movement away from simple mapping techniques toward more advanced, compact methods that significantly decrease the number of required quantum bits by focusing only on physically relevant states and exploiting local gauge constraints. The second pillar analyzes specific variational quantum algorithms that use flexible circuit structures to find low-energy states, comparing different approaches based on their circuit depth and suitability for current hardware. The third pillar evaluates various error mitigation techniques used to extract accurate information from imperfect quantum hardware, such as methods that amplify and then remove noise or those that use physical symmetries to detect and discard errors. Additionally, the paper compares different hardware technologies—including those based on superconducting circuits, trapped atoms, and ions—to weigh their respective benefits, such as gate speed and connectivity, against their drawbacks. It also introduces emerging hybrid approaches that combine quantum circuits with artificial neural networks to improve simulation power and state representation. Ultimately, the review identifies pathways toward achieving practical advantages in the field and discusses the challenges that remain for scaling these systems to larger sizes.
Quantum computing promises to efficiently and accurately solve many important problems in quantum chemistry which elude classical solvers, such as the electronic structure problem of highly correlated materials. Two leading methods in solving the ground state problem are the Variational Quantum Eigensolver (VQE) and Adiabatic Quantum Computing (AQC) algorithms. VQE often struggles with convergence due to the energy landscape being highly non-convex and the existence of barren plateaux, and implementing AQC is beyond the capabilities of current quantum devices as it requires deep circuits. Adiabatically-inspired algorithms aim to fill this gap. In this paper, we first present a unifying framework for these algorithms and then benchmark the following methods: the Adiabatically Assisted VQE (AAVQE) (Garcia-Saez and Latorre (2018)), the Variational Adiabatic Quantum Computing (VAQC) (Harwood et al (2022)), and the Adiabatic Quantum Computing with Parametrized Quantum Circuits (AQC-PQC) (Kolotouros et al (2025)) algorithms. Second, we introduce a novel hybrid approach termed G-AQC-PQC, which generalizes the AQC-PQC method, and combines adiabatic-inspired initialization with the low-memory BFGS optimizer, reducing the quantum computational cost of the method. Third, we compare the accuracy of the methods for chemistry applications using the beryllium hydride molecule (BeH2). We compare the approaches across a number of different choices (ansätze types, depth, discretization steps, initial Hamiltonian, adiabatic schedules and method used). Our results show that the G-AQC-PQC outperforms conventional VQE. We further discuss limitations such as the zero-gradient problem and identify regimes where adiabatically-inspired methods offer a tangible advantage for near-term quantum chemistry applications.
We report on two major hybrid applications of quantum computing, namely, the quantum approximate optimisation algorithm (QAOA) and the variational quantum eigensolver (VQE). Both are hybrid quantum classical algorithms as they require incremental communication between a classical central processing unit and a quantum processing unit to solve a problem. We find that the QAOA scales much better to larger problems than random guessing, but requires significant computational resources. In contrast, a coarsely discretised version of quantum annealing called approximate quantum annealing (AQA) can reach the same promising scaling behaviour using much less computational resources. For the VQE, we find reasonable results in approximating the ground state energy of the Heisenberg model when suitable choices of initial states and parameters are used. Our design and implementation of a general quasi-dynamical evolution further improves these results.
Quantum computers have come a long way since conception, and there is still a long way to go before the dream of universal, fault-tolerant computation is realized. In the near term, quantum computers will occupy a middle ground that is popularly known as the “Noisy, Intermediate-Scale Quantum” (or NISQ) regime. The NISQ era represents a transition in the nature of quantum devices from experimental to computational. There is significant interest in engineering NISQ devices and NISQ algorithms in a manner that will guide the development of quantum computation in this regime and into the era of fault-tolerant quantum computing. In this thesis, we study two aspects of near-term quantum computation. The first of these is the design of device architectures, covered in Chapters 2, 3, and 4. We examine different qubit connectivities on the basis of their graph properties, and present numerical and analytical results on the speed at which large entangled states can be created on nearest-neighbor grids and graphs with modular structure. Next, we discuss the problem of permuting qubits among the nodes of the connectivity graph using only local operations, also known as routing. Using a fast quantum primitive to reverse the qubits in a chain, we construct a hybrid, quantum/classical routing algorithm on the chain. We show via rigorous bounds that this approach is faster than any SWAP-based algorithm for the same problem. The second part, which spans the final three chapters, discusses variational algorithms, which are a class of algorithms particularly suited to near-term quantum computation. Two prototypical variational algorithms, quantum adiabatic optimization (QAO) and the quantum approximate optimization algorithm (QAOA), are studied for the difference in their control strategies. We show that on certain crafted problem instances, bang-bang control (QAOA) can be as much as exponentially faster than quasistatic control (QAO). Next, we demonstrate the performance of variational state preparation on an analog quantum simulator based on trapped ions. We show that using classical heuristics that exploit structure in the variational parameter landscape, one can find circuit parameters efficiently in system size as well as circuit depth. In the experiment, we approximate the ground state of a critical Ising model with long-ranged interactions on up to 40 spins. Finally, we study the performance of Local Tensor, a classical heuristic algorithm inspired by QAOA on benchmarking instances of the MaxCut problem, and suggest physically motivated choices for the algorithm hyperparameters that are found to perform well empirically. We also show that our implementation of Local Tensor mimics imaginary-time quantum evolution under the problem Hamiltonian.