Practical Noise Mitigation for Quantum Annealing via Dynamical Decoupling -- Towards Industry-Relevant Optimization using Trapped Ions

TL;DR

This work addresses the challenge of environmental noise in quantum annealing, focusing on local-field fluctuations in MAGIC-based trapped-ion systems. It introduces a dynamical decoupling strategy that interleaves global spin flips with a modified, constant-cost anneal to suppress noise without destabilizing the encoded optimization, and demonstrates this on minimal MOT and cutting stock QUBO instances. The key findings include that moderate DD rates (around 2–3 pulses per ms) recover fidelity toward the noiseless limit across realistic noise levels and spectra, and that fidelity follows a universal scaling with the product of noise amplitude and DD interval (or a generalized exponent for time-dependent noise). The results provide a practical, scalable route for near-term quantum annealing on trapped ions and offer insights applicable to other quantum-annealing platforms for robust hardware-aware optimization.

Abstract

Quantum annealing is a framework for solving combinatorial optimization problems. While it offers a promising path towards a practical application of quantum hardware, its performance in real-world devices is severely limited by environmental noise that can degrade solution quality. We investigate the suppression of local field noise in quantum annealing protocols through the periodic application of dynamical decoupling pulses implementing global spin flips. As test problems, we construct minimal Multiple Object Tracking QUBO instances requiring only five and nine qubits, as well as cutting stock instances of five and six qubits. To further place our results in a practical context, we consider a trapped-ion platform based on magnetic gradient-induced coupling as a reference architecture, using it to define experimentally realistic noise and coupling parameters. We show that external magnetic field fluctuations, typical in such setups, significantly degrade annealing fidelity, while moderate dynamical decoupling pulse rates, which are achievable in current experiments, restore performance to near-ideal levels. Our analytical and numerical results reveal a universal scaling behavior, with fidelity determined by a generalized parameter combining noise amplitude and dynamical decoupling pulse interval. While our analysis is grounded in the trapped-ion platform, the proposed noise mitigation strategy and resulting performance improvements are applicable to a broad range of quantum annealing implementations and establish a practical and scalable route for error mitigation in near-term devices.

Figures (6)

• Figure 1: Two frames of a video from andriluka2010monocularleal2015motchallenge with pedestrians walking in front of the camera. The color of the bounding boxes identifies the persons. Two frames with two detections each can be formulated as a QUBO problem with four binary variables.
• Figure 2: Probability of a changed ground state of the cost Hamiltonian for the quadratized minimal MOT problem (five qubits, see Eq. \ref{['eq:5qubit_MOT']}) as a function of the standard deviation of uncorrelated fluctuations in the two-body couplings $\sigma(\delta J_{ij}) / J$. Each point corresponds to the mean of $10\,000$ samples and has a variance of $\leq 2.5\cdot 10^{-5}$. The grey dashed line corresponds to a fit with an arctan function, starting at $\sigma (\delta J_{ij})) / J = 0.3$. Fit parameters: $a, b, c, d \approx 0.41, 2.59, 0.50, 0.22$.
• Figure 3: Probability of a changed ground state of the cost Hamiltonian for the quadratized minimal MOT problem (5 qubits, see Eq. \ref{['eq:5qubit_MOT']}) as a function of the standard deviation of the local field disorder $\delta h_i^z$ in units of $J$ for correlated (blue) and uncorrelated (red) disorder. The data points show the mean probabilities of a changed ground state for $10\,000$ simulations each (variance of $\leq 2.5\cdot 10^{-5}$), where $\delta h_i^z$ is sampled from a Gaussian distribution with zero mean. The grey dashed lines represent fits with the arctangent function $f(x) = a \arctan(b(x-c)) + d$, starting from $\delta h_i^z / J = 1$. For correlated disorder: $a, b, c, d \approx 0.74, 0.63, 0.39, -0.17$. For uncorrelated disorder: $a, b, c, d \approx 0.57, 0.81, 0.99, 0.10$.
• Figure 4: Fidelity of the final state, compared to the state encoding the problem solution, at the end of a quantum annealing sweep versus dynamical decoupling pulse rate, using the minimal MOT test problem with five qubits and an annealing time of $2.6/J$ (corresponding, for an energy scale of $J = 26$ Hz, to a sweep duration of $100$ms). Box plots compare results for correlated noise ($\delta h_i^z(t) = \delta h^z(t)$) using identical noise spectra with two Lorentzian frequency peaks at 50 Hz and 150 Hz but different amplitudes of 250 Hz (blue), 500 Hz (red), 750 Hz (green), and 1000 Hz (orange). The crosses in each boxplot give a comparison with the median value of annealing sweeps subject to constant disorder ($\delta h^z(t) = \delta h^z$) of the same respective amplitude. The horizontal dashed line shows the achievable fidelity of the ideal noiseless protocol ($\approx 0.84$). Data for each boxplot corresponds to 50 random independent noise realizations (see Appendix \ref{['app:methods']}). We observe that the achieved final fidelity converges to the noiseless case for a sufficient rate of dynamical decoupling pulses, with higher noise amplitudes requiring higher rates.
• Figure 5: Impact of noise peak frequency on dynamical-decoupling performance. As Fig. \ref{['fig:2peaks_all_corr']}, but using different noise spectra with a single Lorentzian peak centered at varying frequencies, all with the same amplitude of 750Hz. The solid line gives a comparison with the median value of annealing sweeps with constant disorder ($\delta h^z(t) = \delta h^z$) and the same amplitude of 750Hz. The horizontal dashed line shows the achievable fidelity of the ideal noiseless protocol. Data for each boxplot corresponds to 50 random independent noise realizations (see Appendix \ref{['app:methods']}). Similar to Fig. \ref{['fig:2peaks_all_corr']}, the final fidelity converges to the noiseless, case for sufficient rates of dynamical decoupling pulses. The required rates are only slightly dependent on the noise frequency.