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Real-time dynamics of Plaquette Models using NISQ Hardware

Emilie Huffman, Miguel García Vera, Debasish Banerjee

Published Sep 30, 2021• 9 citations
OpenAlex

Abstract

Practical quantum computing holds clear promise in addressing problems not generally tractable with classical simulation techniques, and some key physically interesting applications are those of real-time dynamics in strongly coupled lattice gauge theories. In this article, we benchmark real-time dynamics of $\mathbb{Z}_2$ and $U(1)$ gauge invariant plaquette models using superconducting-qubit based quantum IBM Q computers. We design quantum circuits for models of increasing complexity and measure physical observables such as the return probability to the initial state, and locally conserved charges. Even though the quantum hardware suffers from decoherence, we demonstrate the use of error mitigation techniques, such as circuit folding methods implemented via the Mitiq package, and show what they can achieve within the quantum volume restrictions for the IBM Q quantum computers. Our study provides insight into the choice of quantum hardware topologies, construction of circuits, and the utility of error mitigation methods to devise large-scale quantum computation strategies for lattice gauge theories.

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Practical quantum computing holds clear promise in addressing problems not generally tractable with classical simulation techniques, and some key physically interesting applications are those of real-time dynamics in strongly coupled lattice gauge theories. In this article, we benchmark real-time dynamics of Z2\mathbb{Z}_2Z2​ and U(1)U(1)U(1) gauge invariant plaquette models using superconducting-qubit based quantum IBM Q computers. We design quantum circuits for models of increasing complexity and measure physical observables such as the return probability to the initial state, and locally conserved charges. Even though the quantum hardware suffers from decoherence, we demonstrate the use of error mitigation techniques, such as circuit folding methods implemented via the Mitiq package, and show what they can achieve within the quantum volume restrictions for the IBM Q quantum computers. Our study provides insight into the choice of quantum hardware topologies, construction of circuits, and the utility of error mitigation methods to devise large-scale quantum computation strategies for lattice gauge theories.
Practical quantum computing holds clear promise in addressing problems not generally tractable with classical simulation techniques, and some key physically interesting applications are those of real-time dynamics in strongly coupled lattice gauge theories. In this article, we benchmark the real-time dynamics of Z2{\mathbb{Z}}_{2}Z2​ and U(1)U(1)U(1) gauge-invariant plaquette models using noisy intermediate-scale quantum (NISQ) hardware, specifically the superconducting-qubit-based quantum IBM Q computers. We design quantum circuits for models of increasing complexity and measure physical observables such as the return probability to the initial state and locally conserved charges. NISQ hardware suffers from significant decoherence and a corresponding difficulty to interpret the results. We demonstrate the use of hardware-agnostic error mitigation techniques, such as circuit folding methods implemented via the Mitiq package, and we show what they can achieve within the quantum volume restrictions for the hardware. Our study provides insight into the choice of Hamiltonians, the construction of circuits, and the utility of error mitigation methods to devise large-scale quantum computation strategies for lattice gauge theories.
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 10−310^{-3}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 λφ4λφ^4λφ4 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 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.
Lattice gauge theories in varying dimensions, lattice volumes, and truncations offer a rich family of targets for Hamiltonian simulation on quantum devices. In return, formulating quantum simulations can provide new ways of thinking about the quantum structure of gauge theories. In this work, we consider pure S U ( 3 ) gauge theory in two and three spatial dimensions in a streamlined version of the electric basis. We use a formulation of the theory that balances locality of the Hamiltonian and size of the gauge-invariant state space, and we classically pre-compute dictionaries of plaquette operator matrix elements for use in circuit construction. We build circuits for simulating time evolution on arbitrary lattice volumes, spanning circuits suitable for Noisy Intermediate-Scale Quantum era hardware to future fault-tolerant devices. Relative to spin models, time evolution in lattice gauge theories involves more complex local unitaries, and the Hilbert space of all quantum registers may have large unphysical subspaces. Based on these features, we develop general, volume-scalable tools for optimizing circuit depth, including pruning and fusion algorithms for collections of large multicontrolled unitaries. We describe scalings of quantum resources needed to simulate larger circuits and some directions for future algorithmic development.
Quantum simulations of many-body systems offer novel methods for probing the dynamics of the Standard Model and its constituent gauge theories. Extracting low-energy predictions from such simulations rely on formulating systematically-improvable representations of lattice gauge theory Hamiltonians that are efficient at all values of the gauge coupling. One such candidate representation for SU(2) is the fully gauge-fixed Hamiltonian defined in the mixed basis. This work focuses on the quantum simulation of the smallest non-trivial system: two plaquettes with open boundary conditions. A mapping of the continuous gauge field degrees of freedom to qubit-based representations is developed. It is found that as few as three qubits per plaquette is sufficient to reach per-mille level precision on predictions for observables. Two distinct algorithms for implementing time evolution in the mixed basis are developed and analyzed in terms of quantum resource estimates. One algorithm has favorable scaling in circuit depth for large numbers of qubits, while the other is more practical when qubit count is limited. The latter algorithm is used in the measurement of a real-time observable on IBM's Heron superconducting quantum processor, ibm_fez. The quantum results match classical predictions at the percent-level. This work lays out a path forward for two- and three-dimensional simulations of larger systems, as well as demonstrating the viability of mixed-basis formulations for studying the properties of SU(2) gauge theories at all values of the gauge coupling.