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 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.
Abstract Lattice gauge theory should be able to address significant new scientific questions when implemented on quantum computers. In practice, error-mitigation techniques have already allowed encouraging progress on small lattices. In this work we focus on a truncated version of SU(2) gauge theory, which is a familiar non-Abelian step toward quantum chromodynamics. First, we demonstrate effective error mitigation for imaginary time evolution on a lattice having two square plaquettes, obtaining the ground state using an IBM quantum computer and observing that this would have been impossible without error mitigation. Then we propose the triamond lattice as an expedient approach to lattice gauge theories in three spatial dimensions and we derive the Hamiltonian. Finally, error-mitigated imaginary time evolution is applied to the three-dimensional triamond unit cell, and its ground state is obtained from an IBM quantum computer. Future work will want to relax the truncation on the gauge fields, and the triamond lattice is increasingly valuable for such studies.
Matter under extreme conditions behaves as a non-equilibrium, strongly-interacting quantum system. Such systems are in the non-perturbative regime of quantum chromodynamics (QCD), where their time evolution is classically intractable. Quantum computing offers a promising alternative, but present-day devices are limited in qubit count and circuit depth, so efficient formulations and algorithms are key to scaling toward experimentally relevant QCD simulations. A scalable framework is established for simulating energy loss and hadronization in 1+1-dimensional SU(2) lattice gauge theory, in which a heavy quark traverses a lattice of light quarks. Classical lattice QCD methods are translated into physics-informed circuits to prepare the interacting ground state. The evolution is run on IBM's quantum processor ibm_pittsburgh, where the charge distribution and energy loss are measured. A further study develops the quantum simulation of the fully gauge-fixed SU(2) Hamiltonian in a mixed basis, a formulation that is expected to remain efficient at all gauge couplings. Digitizing the continuous gauge fields with as few as three qubits per plaquette reproduces low-energy observables with 10−3 precision. Scaling to larger systems is limited by resource overhead, which motivates truncations that preserve the relevant observables. Sequency Hierarchy Truncation (SeqHT) exploits the hierarchy in basis-operator contributions. Demonstrated on the adiabatic preparation of the λφ4 ground state on ibm_sherbrooke, SeqHT reduces circuit depth by ~30%, suppressing hardware noise in the extracted observables. All simulations in this dissertation are validated on quantum hardware against classical benchmarks. These studies advance quantum simulations of real-time QCD dynamics.
Quantum computers have the potential to expand the utility of lattice gauge theory to investigate non-perturbative particle physics phenomena that cannot be accessed using a standard Monte Carlo method due to the sign problem. Thanks to the qubit, quantum computers can store Hilbert space in a more efficient way compared to classical computers. This allows the Hamiltonian approach to be computationally feasible, leading to absolute freedom from the sign-problem. But what the current noisy intermediate scale quantum hardware can achieve is under investigation, and therefore we chose to study the energy spectrum and the time evolution of an SU(2) theory using two kinds of quantum hardware: the D-Wave quantum annealer and the IBM gate-based quantum hardware.
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.
The development of quantum technology and the advent of quantum computation have renewed interest in Hamiltonian formulations of lattice gauge theories. In contrast to Euclidean Monte Carlo calculations, Hamiltonian simulation requires a direct representation of the physical Hilbert space, an efficient treatment of enforcing Gauss' law as constraints, and a formulation of real-time dynamics in terms of degrees of freedom that can be encoded on quantum or quantum-inspired classical platforms. The starting point corresponds to finding a suitable basis for Hamiltonian lattice gauge theories. The existing literature focuses on several complementary approaches: electric basis, magnetic basis, gauge-fixed, quantum-link, qubit-regularised, finite-group, and orbifold formulations. This article primarily focuses on the prepotential and loop--string--hadron formulations, where non-Abelian Gauss laws are solved locally and the dynamics is written directly in terms of gauge-invariant loop, string and hadron excitations. The discussion covers the SU(2) and SU(3) constructions in one spatial dimension, the role of residual Abelian Gauss laws, and the extension to higher dimensions through point splitting. We conclude by highlighting its direct applications: eliminating redundant gauge degrees of freedom makes exact diagonalisation and tensor network calculations feasible for studying real-time dynamics, provides insights into thermalisation properties, enables mapping of physical degrees of freedom onto analog and digital quantum hardware, and enables quantum simulation of dynamics.
Quantum simulation of lattice gauge theories offers a path to first-principles calculations of real-time dynamics and finite-density phenomena that are inaccessible to classical Euclidean Monte Carlo methods. Realizing this potential requires a pipeline of controlled approximations---lattice discretization, truncation, digitization, state preparation, time evolution, measurement, and continuum extrapolation---each contributing errors and computational costs. General algorithmic asymptotic complexity arguments capture only part of the cost picture: the practical resources required for end-to-end simulation depend on numerical pre-factors, the cost of the subroutines that various algorithms call, and structural features of the lattice theory, all of which the asymptotic scaling leaves unspecified. This thesis develops contributions that aim to make such dependencies explicit and quantitative. We begin with a rigorous analysis of the asymptotic gate complexity of product formulas and Quantum Signal Processing (QSP) for the time evolution of general classes of lattice Hamiltonians, identifying the parameter regimes in which each method is favorable and estimating the associated pre-factors numerically. Since the cost of QSP-based simulation is dominated (in regimes of practical interest) by the block-encoding subroutine it calls, we also develop several novel block-encoding constructions tailored to bosonic lattice field theories and show that signal-processing techniques can be repurposed as highly efficient block-encoding subroutines. We then turn to the problem of truncating the Kogut--Susskind electric-field Hilbert space. Existing error bounds rely on energy-conservation arguments and require the truncation to grow with simulation time. By exploiting Hilbert space fragmentation we derive the tightest error bounds known to date: they decay factorially in the truncation parameter and are independent of simulation time. We validate them numerically for U(1) pure gauge theory and the Schwinger model. Finally, we address the continuum limit in the presence of approximate time evolution. For product formulas, we show that Trotter errors correspond to irrelevant operators that vanish in the continuum limit, which yields a renormalization trajectory independent of the Trotter step size. More generally, we introduce the Statistically-Bounded Time Evolution (SBTE) protocol, an algorithm-independent framework that treats approximation errors as a systematic uncertainty to be driven below the working statistical precision. This decouples the continuum-limit prescription from the choice of time-evolution algorithm and provides a basis for end-to-end cost comparisons across simulation methods.