Digital Quantum Simulation of Dynamics in Interacting Fields

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Overview

Research area: Quantum simulation of quantum field theories — specifically lattice gauge theory (SU(2)) and scalar field theory (λφ⁴) — implemented on present-day superconducting quantum hardware.

Technical level: Advanced. The dissertation assumes graduate-level familiarity with lattice gauge theory, Hamiltonian formulations of field theories, Trotterization, and quantum error mitigation. The introduction does provide background on these topics, but the core results sit in the non-perturbative QCD / quantum-computing-algorithm literature.

Scope (one sentence): This dissertation develops scalable quantum-circuit formulations for SU(2) lattice gauge theory and scalar field theory, introduces a physics-aware truncation scheme, and validates each proposal on IBM quantum processors against classical benchmarks.

What This Paper Is About

Systems such as the quark-gluon plasma — which filled the early universe and is recreated at the Large Hadron Collider — are strongly interacting and far from equilibrium, and their real-time evolution lies in the non-perturbative regime of QCD where classical Monte Carlo methods hit a sign problem. Quantum computers can in principle store and evolve such states directly, but today's noisy intermediate-scale quantum (NISQ) hardware has limited qubit counts and circuit depths. The dissertation's goal is to build efficient, hardware-ready formulations and algorithms for these dynamics, so that both current demonstrations and future scaling toward experimentally relevant QCD simulations become possible.

Key Contributions

1. A scalable framework for energy loss and hadronization in 1+1-dimensional SU(2) lattice gauge theory. The setup simulates a heavy quark traversing a lattice of light quarks; classical lattice QCD methods are translated into physics-informed quantum circuits that prepare the interacting ground state, and the evolution is executed on IBM's ibm_pittsburgh, with charge distribution and energy loss measured on hardware.

2. A mixed-basis quantum simulation of the fully gauge-fixed SU(2) Hamiltonian. This formulation is expected to remain efficient at all gauge couplings, and the continuous gauge fields can be digitized with as few as three qubits per plaquette while reproducing low-energy observables at 10⁻³ precision.

3. Sequency Hierarchy Truncation (SeqHT), a physics-aware truncation method. SeqHT exploits the hierarchy in the contributions of basis operators (the Walsh basis, whose "sequency" labels are the digital analog of frequency) to discard subdominant terms. Demonstrated on adiabatic preparation of the λφ⁴ ground state on ibm_sherbrooke, it reduces circuit depth by ∼30% and suppresses hardware noise in the extracted observables.

4. Hardware validation of every proposed simulation, with results reported to be in agreement with classical benchmarks.

Main Findings

• Hardware agreement with classical benchmarks: All proposed simulations were run on quantum hardware and the results were consistent with classical benchmarks, per the dissertation abstract.
• Energy loss and hadronization are simulable on current devices: In the 1+1-dimensional SU(2) study, observables including charge distribution and energy loss were measured on ibm_pittsburgh after preparing the interacting ground state with physics-informed circuits.
• Compact digitization of gauge fields: The mixed-basis, fully gauge-fixed SU(2) formulation reproduces low-energy observables at 10⁻³ precision using as few as three qubits per plaquette.
• Truncation reduces depth measurably: SeqHT cut circuit depth by approximately 30% in the λφ⁴ ground-state preparation on ibm_sherbrooke, which also suppressed hardware noise in the extracted observables.
• Low-energy states are dominated by low-sequency terms: The field-basis decomposition of scalar-field operators into tensor products of identity and Z operators (the Walsh basis) shows that low-energy wavefunctions concentrate in low-sequency terms — the structure SeqHT exploits.
• Resource overhead, not physics, is the bottleneck: The dissertation identifies resource overhead as the limiting factor for reaching larger systems on present-day hardware, motivating truncation methods that preserve the relevant observables.

Methodology in Plain English

The work follows the standard three-stage recipe for digital quantum simulation, with each stage adapted to the physics at hand.

State preparation. Rather than preparing arbitrary states (which costs exponentially many gates), the dissertation prepares ground states using adiabatic state preparation — starting in the easily prepared ground state of a simple Hamiltonian and slowly deforming it into the target Hamiltonian — and variational methods such as VQE and its adaptive variants. Notably, for the system sizes relevant here, both the optimization and the evolution were run on classical computers, because noise on current hardware prevents the energy measurements from resolving well enough for a classical optimizer to converge.

Time evolution. Real-time evolution is implemented by Trotterization: the Hamiltonian is split into groups of commuting Pauli operators, each of which can be applied directly as a circuit, and the error from the non-commuting pieces is controlled by taking more, smaller time steps. The dissertation notes that first-order Trotter error scales as O(t²/n) and second-order as O(t³/n²), and that higher-order schemes do not necessarily help because their commutator prefactors can be larger.

Measurement. Since measurement is projective, expectation values are reconstructed from many shots, with shot noise scaling as 1/√N, using basis rotations before computational-basis (Pauli-Z) readout.

Error handling. Error suppression (e.g., dynamical decoupling on idle qubits), error mitigation (Pauli twirling, readout error mitigation, operator decoherence renormalization, zero-noise extrapolation), and—for the longer term—quantum error correction are distinguished and discussed.

Truncation. SeqHT ranks basis operators by how much they contribute and keeps only the dominant ones, reducing circuit depth while preserving the observables of interest.

The background also frames why quantum hardware is needed at all: both entanglement and quantum magic (non-stabilizerness) grow in real-time dynamics, defeating tensor-network and stabilizer-simulable approaches respectively.

Why This Matters

Impact on research. The dissertation provides concrete, hardware-tested circuit constructions for lattice gauge theory and scalar field theory, plus a general-purpose truncation tool. It argues that preparing and validating algorithms now means the methods will be in hand when capable hardware arrives — a hedge against the current mismatch between NISQ devices and experimentally relevant QCD.

Real-world applications:

• Quark-gluon plasma physics: modeling energy loss and hadronization of quarks traversing strongly interacting matter, the physics probed in heavy-ion collisions at the Large Hadron Collider.
• Early-universe cosmology: the quark epoch shortly after the Big Bang, when the universe was filled with quark-gluon plasma.
• Astrophysics: neutrinos in extreme astrophysical environments and matter in the interior of neutron stars, both cited as non-equilibrium strongly correlated systems.
• Event-generator improvement: real-time observables such as energy loss and hadronization are currently accessible only through phenomenological models whose parameters are tuned to data and whose uncertainties cannot be systematically reduced; first-principles simulation would address that gap.

Industry relevance. All hardware demonstrations use IBM Quantum superconducting processors (ibm_pittsburgh, ibm_sherbrooke) and IBM's Qiskit programming environment, making the results directly relevant to near-term quantum-computing vendors and to the error-mitigation and circuit-compilation toolchains they build. The ∼30% circuit-depth reduction from SeqHT is the kind of resource saving that translates into practical advantage on noisy machines.

Future Directions

• Scaling to larger lattices and higher dimensions. The dissertation is explicit that resource overhead limits progress to larger systems on present-day hardware; extending the 1+1-dimensional SU(2) energy-loss study and the mixed-basis formulation beyond current sizes is the obvious next step.
• Applying SeqHT beyond the scalar case. SeqHT is demonstrated on λφ⁴ ground-state preparation and motivated by systems with a hierarchy of length scales; extending it to gauge-theory Hamiltonians is a natural open question.
• Approaching the continuum limit. The mixed-basis formulation is argued to remain efficient at all gauge couplings, which raises the question of how far continuum extrapolation (lattice spacing to zero) can be pushed with these digitizations.
• Co-designing with fault tolerance. The dissertation argues that quantum simulations will need to incorporate error correction through co-design efforts rather than waiting for general-purpose logical qubits, and that incorporating gauge redundancies and symmetries as error-correcting codes is an active direction.

Target Audience

Graduate students and researchers in lattice QCD, nuclear and high-energy physics, and quantum information science who are building or evaluating quantum algorithms for field theories. It is most valuable to readers who want a template for translating a classical lattice formulation into hardware-executable circuits, and to quantum-computing practitioners interested in realistic physics workloads and resource-reduction techniques such as SeqHT. Readers without a lattice gauge theory background will find the introductory chapter useful but the results sections demanding.

Note: the supplied content is a truncated version of the dissertation (abstract, acknowledgements, and Chapter 1), so chapter-level details such as specific lattice sizes, qubit counts per simulation, shot counts, and error-mitigation settings are not reported here.

Authors’ abstract

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 $λφ^4$ 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.