Matrix Models on Ion Traps - A Quantum Benchmarking Study
ORAL
Abstract
Matrix models are an important class of theories in high-energy and mathematical physics. They provide simplified but powerful frameworks for studying nonperturbative aspects of string theory, gauge/gravity duality, and the dynamics of strongly interacting quantum systems. Despite progress in classical calculational approaches, including Hamiltonian Monte Carlo and the quantum-mechanical bootstrap, these methods are largely limited to static, equilibrium properties. Simulation via quantum computers offers the ability to probe the real-time dynamics and out-of-equilibrium behavior, which remain intractable classically. Additionally, matrix models represent a unique class of quantum systems that pose fundamentally different simulation challenges compared to conventional spin models, making them valuable benchmarks for assessing quantum hardware capabilities.
We present the first experimental results of simulating matrix models on quantum computers. We focus on the simplest such model – a single SU(2) matrix in a quartic potential – and simulate its time evolution on a trapped-ion Quantinuum device. Our study addresses critical practical aspects of quantum simulation: analyzing the complexity of compiled circuits, characterizing gauge symmetry breaking due to Hilbert space truncation, quantifying device noise effects, and demonstrating error mitigation through zero-noise extrapolation. Using the Loschmidt echo as our primary observable, we benchmark quantum results against exact analytic solutions while systematically exploring the parameter space of evolution times, coupling strengths, and truncation levels. Through device-specific noisy simulations combined with error mitigation strategies, we establish concrete resource requirements and identify performance boundaries for current quantum hardware. This work provides essential benchmarking data for near-term quantum devices and lays the foundation for simulating more complex matrix models relevant to string theory and gauge/gravity duality, with future extensions targeting the BFSS and BMN models as quantum hardware capabilities advance.
We present the first experimental results of simulating matrix models on quantum computers. We focus on the simplest such model – a single SU(2) matrix in a quartic potential – and simulate its time evolution on a trapped-ion Quantinuum device. Our study addresses critical practical aspects of quantum simulation: analyzing the complexity of compiled circuits, characterizing gauge symmetry breaking due to Hilbert space truncation, quantifying device noise effects, and demonstrating error mitigation through zero-noise extrapolation. Using the Loschmidt echo as our primary observable, we benchmark quantum results against exact analytic solutions while systematically exploring the parameter space of evolution times, coupling strengths, and truncation levels. Through device-specific noisy simulations combined with error mitigation strategies, we establish concrete resource requirements and identify performance boundaries for current quantum hardware. This work provides essential benchmarking data for near-term quantum devices and lays the foundation for simulating more complex matrix models relevant to string theory and gauge/gravity duality, with future extensions targeting the BFSS and BMN models as quantum hardware capabilities advance.
*The authors acknowledge support from Oak Ridge National Laboratory for providing access to Quantinuum emulator and hardware credits used in this work.
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Presenters
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Gavin S Hartnett
- Q-CTRL Pty Ltd