Quantum computing has long been an experimental technology with the potential to simulate, at scale, phenomena which on classical devices would be too expensive to simulate at any but the smallest scales. Over the last several years, however, it has entered the NISQ era, where the number of qubits are sufficient for quantum advantage but substantial noise on hardware stands in the way of this achievement. This thesis details NISQ device-centered improvements to techniques of quantum simulation of the out-of-equilbrium real-time dynamics of lattice quantum chromodynamics (LQCD) and of dense 3-flavor neutrino systems on digital quantum devices. The first project concerning LQCD is a comparison of methods for implementing the variational quantum eigensolver (VQE) that initializes the ground state of an SU(3) plaquette-chain. The thesis then pivots to a 1+1D lattice of quarks interacting with an SU(3) gauge-field. A VQE-based state-preparation for the vacua and a Trotterized time-evolution circuit is designed and applied to the problems of simulating beta and neutrinoless double beta decay. Finally, these circuits are adapted to a version useable on quantum devices with nearest-neighbor connectivity with minimal overhead, with an eye towards utilizing the higher qubit count of such devices for hadron dynamics and scattering. This thesis covers two projects that concern dense 3-flavor neutrino systems. The first details design and testing of Trotterized time-evolution circuits on state-of-the-art quantum devices. The second, motivated by the Gottesman-Knill theorem's result that deviation from stabilizer states ("magic") is necessary for a problem to exhibit quantum advantage, details results with implications for the Standard Model in general that the 3 flavor ultradense neutrino systems with the highest, most-persistent magic are those that start with neutrinos in all 3 flavors.
Quantum computing has long been an experimental technology with the potential to simulate, at scale, phenomena which on classical devices would be too expensive to simulate at any but the smallest scales. Over the last several years, however, it has entered the NISQ era, where the number of qubits are sufficient for quantum advantage but substantial noise on hardware stands in the way of this achievement. This thesis details NISQ device-centered improvements to techniques of quantum simulation of the out-of-equilbrium real-time dynamics of lattice quantum chromodynamics (LQCD) and of dense 3-flavor neutrino systems on digital quantum devices. The first project concerning LQCD is a comparison of methods for implementing the variational quantum eigensolver (VQE) that initializes the ground state of an SU(3) plaquette-chain. The thesis then pivots to a 1+1D lattice of quarks interacting with an SU(3) gauge-field. A VQE-based state-preparation for the vacua and a Trotterized time-evolution circuit is designed and applied to the problems of simulating beta and neutrinoless double beta decay. Finally, these circuits are adapted to a version useable on quantum devices with nearest-neighbor connectivity with minimal overhead, with an eye towards utilizing the higher qubit count of such devices for hadron dynamics and scattering. This thesis covers two projects that concern dense 3-flavor neutrino systems. The first details design and testing of Trotterized time-evolution circuits on state-of-the-art quantum devices. The second, motivated by the Gottesman-Knill theorem's result that deviation from stabilizer states ("magic") is necessary for a problem to exhibit quantum advantage, details results with implications for the Standard Model in general that the 3 flavor ultradense neutrino systems with the highest, most-persistent magic are those that start with neutrinos in all 3 flavors.
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.
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.
The quantum simulation of fermionic gauge field theories is one of the anticipated uses of quantum computers in the noisy intermediate-scale quantum (NISQ) era. Recently work has been done to simulate properties of the fermionic Z2 gauge field theory in (1+1)D and the pure gauge theory in (2+1)D. In this work, we investigate various options for simulating the fermionic Z2 gauge field theory in (2+1)D. To simulate the theory on a NISQ device it is vital to minimize both the number of qubits used and the circuit depth. In this work we propose ways to optimize both criteria for simulating time dynamics. In particular, we develop a new way to simulate this theory on a quantum computer, with minimal qubit requirements. We provide a quantum circuit for simulating a single first-order Trotter step that minimizes the number of 2-qubit gates needed and gives comparable results to methods requiring more qubits. Furthermore, we investigate variational Trotterization approaches that allow us to further decrease the circuit depth.
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.
It is well known that the neutrino flavor in extreme astrophysical environments changes under the effect of three contributions: the vacuum oscillation, the interaction with the surrounding matter, and the collective oscillations due to interactions between different neutrinos. The latter adds a nonlinear contribution to the equations of motion, making the description of their dynamics complex. In this work we study various strategies to simulate the coherent collective oscillations of a system of N neutrinos in the two-flavor approximation using quantum computation. This was achieved by using a pair-neutrino decomposition designed to account for the fact that the flavor Hamiltonian, in the presence of the neutrino-neutrino term, presents an all-to-all interaction that makes the implementation of the evolution dependent on the qubit topology. We analyze the Trotter error caused by the decomposition demonstrating that the complexity of the implementation of time evolution scales polynomially with the number of neutrinos and that the noise from near-term quantum device simulation can be reduced by optimizing the quantum circuit decomposition and exploiting a full-qubit connectivity. We find that the gate complexity using second order Trotter-Suzuki formulas scales better with system size than with other decomposition methods such as quantum signal processing. We finally present the application and the results of our algorithm on a real quantum device based on trapped-ion qubits.
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.