Source-linked AI summary
Observation of hadron scattering in a lattice gauge theory on a quantum computer
Julian Schuhmacher, Guo-Xian Su, Jesse J. Osborne, Anthony Gandon, Jad C. Halimeh, Ivano Tavernelli
TL;DR
Hardware-induced noise distorts quantum-circuit output distributions and can bias observables. The paper applies distribution error mitigation, including marginal DEM, and reports agreement between mitigated observables and MPS reference values, while noting mitigation trade-offs and tuning limitations.
Problem
Hardware-induced noise changes measured output distributions, motivating mitigation of bias in diagonal and local observables.
Method
The paper uses Clifford-based distribution error mitigation and adapts it to marginal distributions for estimating local diagonal observables.
Results
Mitigated local and diagonal observables show remarkable agreement with MPS reference values even for large Trotter step sizes and long evolution times.
Takeaways & Limitations
Marginal DEM provides a reduced-subspace approach for mitigating local observables on the studied linear-topology circuits.
Takeaways & Limitations
The mitigation depends on empirically tuned hyperparameters, whose effects on the learned Pauli noise channel require more rigorous study.
Abstract
from arXiv · showhide
Scattering experiments are at the heart of high-energy physics (HEP), breaking matter down to its fundamental constituents, probing its formation, and providing deep insight into the inner workings of nature. In the current huge drive to forge quantum computers into complementary venues that are ideally suited to capture snapshots of far-from-equilibrium HEP dynamics, a major goal is to utilize these devices for scattering experiments. A major obstacle in this endeavor has been the hardware overhead required to access the late-time post-collision dynamics while implementing the underlying gauge symmetry. Here, we report on the first quantum simulation of scattering in a lattice gauge theory (LGT), performed on \texttt{IBM}'s \texttt{ibm\_marrakesh} quantum computer. Specifically, we quantum-simulate the collision dynamics of electrons and positrons as well as mesons in a $\mathrm{U}(1)$ LGT representing $1+1$D quantum electrodynamics (QED), uncovering rich post-collision dynamics that we can precisely tune with a topological $Θ$-term and the fermionic mass. By monitoring the time evolution of the scattering processes, we are able to distinguish between two main regimes in the wake of the collision. The first is characterized by the delocalization of particles when the topological $Θ$-term is weak, while the second regime shows localized particles with a clear signature when the $Θ$-term is nontrivial. Furthermore, we show that by quenching to a small mass at the collision point, inelastic scattering occurs with a large production of matter reminiscent of quantum many-body scarring. Our work provides a major step forward in the utility of quantum computers for investigating the real-time quantum dynamics of HEP collisions.
METHODS
The study implements U(1) lattice-gauge-theory dynamics on IBM’s ibm_marrakesh device, using MPS references and error-mitigation procedures to evaluate scattering circuits.
- Hardware and simulations: Classical reference values came from MPS simulations of the applied quantum circuits.This reference approach matches the implemented circuits rather than ideal continuous-time evolution.
- Hardware and simulations: Experiments ran on IBM’s ibm_marrakesh device, with active qubits selected using readout and two-qubit gate fidelities.Benchmarking preceded the experiments, and device properties were monitored over time.
- Hardware and simulations: The experiments used dynamical decoupling and Pauli twirling, with 500 randomizations and 100 measurements per randomization.Together these settings produced 50,000 measurements per estimated expectation value.
- Measured observables: Particle occupation numbers were defined using background-subtracted local magnetizations derived from mitigated on-site observables.The construction compares particle-plus-vacuum and vacuum initial-state occupations.
- Error mitigation: Distribution Error Mitigation estimates hardware noise with a companion circuit and applies the learned channel model to physics-circuit distributions.The implementation uses marginal post-processing adapted to the study’s system sizes.
- Error mitigation: The reported mitigated observables agree remarkably well with MPS references despite large Trotter steps and long evolution times.The mitigation method assumes a first-order Clifford approximation of the physics circuit’s full noise channel.
ERROR MITIGATION
The paper develops marginal Distribution Error Mitigation to reduce the scaling cost of correcting noisy probability distributions and applies it to local diagonal observables.
- DEM and mDEM: Distribution Error Mitigation corrects Pauli-channel effects on quantum-circuit output probability distributions using Clifford-based noise characterization.The method is adapted here for improved scaling when estimating local diagonal observables.
- Noise model: The ideal and noisy output distributions are related through a hardware-induced completely positive and trace-preserving noise channel.The noisy distribution is obtained from the noisy state produced by circuit execution.
- DEM and mDEM: DEM approximates the noise channel with a Clifford-derived channel whose ideal output distribution can be sampled classically.The approximation is taken to lowest order in Clifford perturbation theory.
- Noise model: The noise map is represented by a block-circulant stochastic matrix that can be characterized through its first column and efficiently diagonalized with a Walsh-Hadamard transform.This structure enables learning the channel from the noise-characterization circuit.
- DEM and mDEM: The learned channel parameters are used to mitigate the noisy distribution of the desired non-Clifford quantum state.Element-wise division and inverse Fast-Walsh-Hadamard transforms enter the channel reconstruction.
- Uncertainty and stability: Regularization improves numerical stability, while bootstrap resampling estimates the statistical uncertainty of mitigated magnetizations.The bootstrap procedure repeatedly resamples measured distributions before evaluating local observables.
- DEM and mDEM: Marginal DEM restricts mitigation to local qubit subsets, reducing the original 2^n-vector scaling for on-site observables.For each site, the method uses a segment of neighboring qubits characterized by regularization and neighborhood-size hyperparameters.
- Uncertainty and stability: The hyperparameters are tuned against MPS results, with empirically effective ranges of ϵ ∈[0.01, 0.1] and n_C ∈[4, 9].The paper states that the effect of these hyperparameters on the learned noise channel requires more rigorous future study.
SCATTERING EXPERIMENTS
The supplementary scattering materials document measured and mitigated electric-flux data and report the applied circuit sizes for representative Trotter-step counts.
- Supplementary scattering data: Supplementary figures compare measured and mitigated electric-flux evolution for wave-packet, vacuum, and background-subtracted configurations.Mitigation hyperparameters and bootstrap-derived error bars are also reported.
- Supplementary scattering data: Table S1 reports the sizes of the applied quantum circuits for selected numbers of Trotter steps.The table provides a circuit-resource reference for representative simulation depths.