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.
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 simulation provides a promising framework for studying non-perturbative phenomena in lattice gauge theories that are difficult to access using classical computational methods. In particular, classical Monte Carlo approaches suffer from the sign problem, limiting their applicability to real-time dynamics and finite-density regimes. Quantum computers, by directly encoding quantum dynamics, offer a natural pathway to overcoming these limitations. In this thesis, we study quantum simulations of a truncated SU(2) lattice gauge theory using a Hamiltonian formulation, representing an important non-Abelian step toward quantum chromodynamics. We focus on three-dimensional gauge-theory simulations in the noisy intermediate-scale quantum (NISQ) era, where limited qubit resources pose a significant challenge. To address this, we introduce the triamond lattice, a three-dimensional lattice geometry that enforces local gauge invariance while providing an economical encoding of gauge degrees of freedom, thereby reducing qubit overhead compared to conventional lattice constructions. We derive the corresponding Hamiltonian, construct physical gauge-invariant states, and implement quantum simulations using quantum imaginary time evolution to prepare ground states, alongside real-time evolution methods to study dynamical behavior. Error-mitigation techniques are employed to extract reliable physical observables from noisy quantum hardware. Our results demonstrate that the triamond lattice enables resource-efficient three-dimensional quantum gauge simulations and represents a practical step toward scalable quantum simulations of non-perturbative gauge theories.
Quantum computing has emerged as a transformative paradigm capable of addressing computational challenges beyond the reach of classical systems.In the current era of Noisy Intermediate-Scale Quantum (NISQ) devices, practical quantum hardware is characterized by limited qubit counts, short coherence times, gate errors, and the absence of full error correction.Despite these constraints, significant progress has been made in developing quantum machine learning (QML) techniques tailored to operate on near-term quantum processors.This paper presents a comprehensive review of Quantum Machine Learning in the context of NISQ computing.We first outline the fundamental principles of quantum computing, including qubits, superposition, entanglement, and quantum parallelism, followed by a detailed discussion of the NISQ computing model and its hardware limitations.The review then examines hybrid quantum-classical learning frameworks, variational quantum algorithms, quantum data encoding strategies, and noise mitigation techniques that enable practical implementation on existing platforms.Emerging applications across healthcare, finance, cybersecurity, climate modeling, and materials science are also surveyed to highlight the real-world potential of QML.Furthermore, key challenges such as scalability, trainability issues, and algorithmic robustness are analyzed, along with current research efforts aimed at overcoming these barriers.The paper concludes by identifying promising future directions for advancing QML toward quantum advantage.This review aims to provide researchers and practitioners with a structured understanding of the capabilities, limitations, and opportunities of quantum machine learning in the NISQ era .
Abstract The arrival of noisy intermediate-scale quantum (NISQ) devices defines an era in which quantum utility is fundamentally constrained by finite coherence times, limited qubit counts, gate infidelities, restricted connectivity, and measurement noise. Within this regime, hybrid quantum-classical frameworks have emerged as the dominant operational paradigm, particularly for quantum machine learning (QML). This review identifies a fundamental trade-off between expressivity, trainability, and noise resilience that governs the performance and scalability of NISQ-era QML systems. To contextualize these challenges, we introduce the resource-constrained iterative routing framework, a hardware-aware conceptual architecture that integrates topology-aware classical compression and distributed quantum orchestration to maintain circuit depths within device-dependent limits while routing representations toward symmetry-constrained Hilbert subspaces to mitigate noise-induced barren plateaus. Furthermore, we shift the discussion of quantum advantage away from asymptotic fault-tolerant complexity toward the notion of operational NISQ advantage based on finite-resource scaling, trainability preservation, and sampling complexity. We evaluate the practical resource efficiency of variational quantum algorithms, quantum kernel methods, and quantum neural networks across superconducting, trapped-ion, neutral-atom, and photonic platforms. The review also examines reproducibility challenges, emphasizing benchmarking against optimized classical baselines, and discusses strategies for managing the sampling overhead of error mitigation alongside distributed execution and quantum circuit compilation. Ultimately, NISQ in Practice positions hybrid QML as a physically constrained computational paradigm while outlining a pathway from contemporary noisy workflows toward early fault-tolerant quantum architectures.
This thesis investigates advances in quantum simulation methods for lattice gauge theories, with a focus on (2+1)-dimensional quantum electrodynamics (QED), which shares important features with (3+1)-dimensional quantum chromodynamics (QCD), such as confinement and asymptotic freedom. Two main projects are developed. The first project investigates the ongoing coupling in a compact pure U(1) gauge theory using a step-scaling function approach. A quantum variational method allows calculations over a wide range of couplings. Plaquette expectation value results are compared with classical Monte Carlo simulations to obtain, in principle, the physical value of the lattice spacing. This method can potentially be extended to the study of QED, which also includes fermionic matter. The second project investigates the static potential between two charges, analyzing the Coulomb, confining, and string-breaking regimes. It involves the development of a tailored variational approach that incorporates system symmetries and mutual information to represent fermionic degrees of freedom. Results from a trapped-ion quantum device agree well with classical simulations, validating the method. Furthermore, this work evaluates superconducting quantum devices, noting issues with noise but also demonstrating improvements in hardware and potential through error limitation. Overall, this work underscores the feasibility of variational quantum algorithms for lattice gauge theory simulations and demonstrates their promise for advancing theoretical physics with quantum computers. This thesis explores advancements in quantum simulation methods for lattice gauge theories, focusing on (2+1)-dimensional Quantum Electrodynamics (QED), which shares key features with (3+1)-dimensional Quantum Chromodynamics (QCD), such as confinement and asymptotic freedom. Two main projects are developed. The first investigates the running coupling in a compact U(1) pure gauge theory using a step scaling function approach. A quantum variational method enables computation across a wide range of couplings. The plaquette expectation value is matched with classical Monte Carlo simulations to obtain, in principle, the physical value of the lattice spacing. This method can be eventually extended to study QED, where fermionic matter is included. The second project examines the static potential between two charges, analyzing Coulomb, confining, and string-breaking regimes. It involves developing a custom variational Ansatz that incorporates system symmetries and mutual information to represent fermionic degrees of freedom. Results from a trapped-ion quantum device align well with exact classical simulations, validating the method. Additionally, the thesis evaluates superconducting devices, identifying noise challenges but noting improvements in hardware and the potential of error mitigation. Overall, this work highlights the viability of variational quantum algorithms for lattice gauge theory simulations and demonstrates their promise for advancing theoretical physics with quantum computing.
Quantum computing promises to revolutionize several scientific and technological domains through fundamentally new ways of processing information. Among its most compelling applications is digital quantum simulation, where quantum computers are used to replicate the behavior of other quantum systems. This could enable the study of problems that are otherwise intractable on classical computers, transforming fields such as quantum chemistry, condensed matter physics, and materials science. Despite this potential, realizations of practical quantum advantage for relevant problems are hindered by imperfections of current devices. This also affects quantum hardware based on superconducting circuits which is among the most advanced and scalable platforms. The envisaged long-term solution of fault-tolerant quantum computers that correct their own errors remains out of reach mainly due to the associated qubit number overhead. As a result, the field has developed strategies that combine quantum and classical resources, exploit hardware-native operations, and employ error mitigation techniques to extract meaningful results from noisy data. This doctoral thesis contributes to this broader effort by exploring methods for advancing quantum simulation across the full computational stack, including hardware-level innovations, refined techniques for noise modeling and error mitigation, and algorithmic improvements enabled by efficient measurement processing.
Quantum computing is in its greatest upswing, with so-called noisy-intermediate-scale-quantum devices heralding the computational power to be expected in the near future.While the field is progressing toward quantum advantage, quantum computers already have the potential to tackle classically intractable problems.Here, we consider gauge theories describing fundamental-particle interactions.On the way to their full-fledged quantum simulations, the challenge of limited resources on near-term quantum devices has to be overcome.We propose an experimental quantum simulation scheme to study ground-state properties in two-dimensional quantum electrodynamics (2D QED) using existing quantum technology.Our protocols can be adapted to larger lattices and offer the perspective to connect the lattice simulation to low-energy observable quantities, e.g., the hadron spectrum, in the continuum theory.By including both dynamical matter and a nonminimal gauge-field truncation, we provide the novel opportunity to observe 2D effects on present-day quantum hardware.More specifically, we present two variational-quantumeigensolver-(VQE) based protocols for the study of magnetic field effects and for taking an important first step toward computing the running coupling of QED.For both instances, we include variational quantum circuits for qubit-based hardware.We simulate the proposed VQE experiments classically to calculate the required measurement budget under realistic conditions.While this feasibility analysis is done for trapped ions, our approach can be directly adapted to other platforms.The techniques presented here, combined with advancements in quantum hardware, pave the way for reaching beyond the capabilities of classical simulations.