Observation of Robust and Coherent Non-Abelian Hadron Dynamics on Noisy Quantum Processors

Abstract

The real-time evolution of strongly interacting matter remains a frontier of fundamental physics, as classical simulations are hampered by exponential Hilbert space growth and entanglement-driven bottlenecks in tensor networks. This study reports the quantum simulation of hadron dynamics within a $(1+1)$-dimensional SU(2) lattice gauge theory using a 156-qubit IBM superconducting processor. Leveraging a hardware-efficient Loop-String-Hadron (LSH) encoding, we simulate the dynamics of the physical degrees of freedom on a $60$-site lattice in the weak-coupling regime, as a crucial step toward the continuum limit. We successfully observe the light-cone propagation of a confined meson and internal oscillations indicative of early-time hadronic breathing modes. Notably, these high-fidelity results were obtained directly from the quantum data via a differential measurement protocol, together with measurement error mitigation, demonstrating a robust pathway for large-scale simulations even on noisy hardware. To validate the results, we benchmarked the quantum algorithm and outcome from the quantum processor against state-of-the-art approximated classical algorithms using CPU -- based on tensor network methods and Pauli propagation method, respectively. Furthermore, we provide a quantitative comparison demonstrating that as the system approaches the weak-coupling or the continuum limit, the quantum processor maintains a consistent structural robustness where classical tensor networks and Pauli propagation methods encounter an onset of exponential complexity or symmetry violations as an artifact of approximation in the algorithm. These results establish a scalable pathway for simulating non-Abelian dynamics on near-term quantum hardware and mark a critical step toward achieving a practical quantum advantage in high-energy physics.

Figures (13)

• Figure 1: Encoding physical degrees of freedom to qubits. The local fermion number is defined on the staggered lattice as $n_f(r)= n_i(r)+n_o(r)$ for even sites and $n_f(r)= 2-[n_i(r)+n_o(r)]$ for odd sites. At any site, $n_f=2$ denotes the presence of a Baryon, $n_f=1$ denotes the presence of the end of a meson or a longer string, and $n_f=0$ denotes the vacuum for fermions. In the left panel, the qubit layout is given. Using the Qiskit Transpiler, the least noisy 120 qubit chain is obtained, which is denoted in black on the hardware layout. This allows one to perform a simulation for a 60-site lattice.
• Figure 2: Schematic of quantum evolution on a 4-site lattice. The diagram illustrates the buildup of entanglement and particle number fluctuations over 3 Trotter steps under the LSH Hamiltonian. The system is initialized at $t=0$ in a zero-entanglement product state containing two baryons (total fermion number $N_f=4$). At $t=1$, the evolution transitions the system to a single meson state ($N_f=2$). Subsequent steps ($t=2, 3$) generate increasingly complex superpositions of states with varying particle numbers ($N_f \in \{2, 4, 6\}$), governed by the interplay of the electric ($H_E$) and mass ($H_M$) Hamiltonian terms. This fluctuation of total particle number is a hallmark of relativistic quantum field theory. Each basis state is represented as $\otimes_{r} |n_i,n_o\rangle_r$ and mapped directly to qubit registers. The values of $n_f$ across the lattice at all time steps are measured to construct the experimental heatmaps presented in this work. The branching of the wavefunction depicted here highlights the rapid growth of entanglement, rendering the full 120-qubit simulation classically intractable.
• Figure 3: Real Time Propagation of SU(2) Hadron: validation of the ansatz, algorithm, and impelmentation on hardware. The top panel displays a cartoon representation of the initial states; (a) The strong coupling vacuum for a staggered lattice, and (b) A meson is placed at the middle of the lattice on top of the strong coupling vacuum. The fermion/antifermion number $n_f=0$ at all sites except at two middle sites of (b), which are both singly occupied and are characterized by $n_f=1$. The lower panels shows the light-cone propagation of a meson ($t$ vs. lattice site $r$) placed at the center of the lattice at $t=0$. The fermion density $n_f$ for the time evolution of the state (a) subtracted from (b) in the same, is plotted for 20 time steps. Space-time evolution of particle density $n_f$ on a 60-site lattice is compared using three different approaches: (i) Quantum simulation on IBM Boston using only measurement error mitigation. , (ii) Tensor network calculation using the MPS and MPO constructed for the full LSH Hamiltonian and using 2-site TDVP algorithm. (ii) Pauli Propagation method applied for the classical simulation of the quantum circuit. The dynamics on the left half of the figure (lattice sites $0-29$) are from one calculation, while the right half of the plot shows another. The visible agreement confirms the validity of the experimental result as simulation of the full LSH. Moreover, the MPS calculation is performed for the full LSH Hamiltonian and uses the TDVP algorithm to avoid Trotterization error. The Quantum simulation is performed using the weak-coupling approximated LSH and first-order Trotterization. The visible match between the left and right sides of the plot validates both approximations in the scaled-up experiment. In the inset of each plot, the clock time taken for each method is compared (for MPS, projected time with exponential scaling is shown). Our QPU time for a fixed budget of $10k$ shots per trotter step, was a constant 20 seconds per trotter step; the same for the Pauli Propagation method increased linearly on a CPU and for the tensor network method increased exponentially (the last few steps were constant as the bond dimension was kept constant). The relative deviation in average fermion density is compared in the bottom panel.
• Figure 4: Comparing robustness of quantum simulation versus classical simulation towards $x\rightarrow \infty$. Top row: The dynamics of average fermion density is plotted with time. For $x=50$, MPS and PPM agree exactly, QPU shows deviation but follow the trend. For $x=100$, MPS and PPM start to separate out after 5th Trotter steps, QPU deviates but follows the trend. For $x=200$, post 10th Trotter step, MPS and PPM do not follow the same trend, QPU follows PPM, with deviation. Middle row: The conservation of global charges are tracked for all simulation. Overall it stays conserved in all the methods. As presented in the insets, QPU shows a small deviation, for all $x$ values. MPS preserves the global constraints by construction mathew2025tensor. PPM shows small deviation, and it increases with increasing $x$. Bottom row: The entanglement entropy, obtained via TN calculation, shows linear growth for $x=50$, saturates to a plateau for $x=100$, while the allowed bond dimension fails to handle entanglement growth for $x=200$ case, and in effect the MPS simulation fails to capture physics anymore. The drop in entanglement is an artifact of finite bond dimension, rather than being a physical phenomenon.
• Figure 5: Proof of concept. Particle number for a lattice of 8 sites as calculated from qubit expectation values at each Trotter step using Qiskit simulator, compared with the exact diagonalization result for the full LSH Hamiltonian, which is free from any Trotterization error and approximation error. Parameters in the quantum circuit are chosen to reproduce the intended regime of the theory with $x=100$ and $m/g=1$. The initial state is chosen to be the strong coupling vacuum, which is a computational basis state.