High-order dynamical decoupling in the weak-coupling regime

TL;DR

This paper presents a high-order dynamical decoupling scheme that efficiently suppresses system-bath interactions in quantum systems, significantly reducing pulse sequences needed compared to previous methods, especially for multi-qubit systems.

Contribution

The authors develop a novel high-order DD construction that scales polynomially with system size, outperforming existing exponential-scaling schemes, and extend it to time-dependent noise suppression.

Findings

Pulse sequences scale as O(|G| K), reducing complexity.

Sequences outperform Quadratic DD in weak-coupling regime.

Construction is asymptotically optimal and verified numerically.

Abstract

We introduce a high-order dynamical decoupling (DD) scheme for arbitrary system-bath interactions in the weak-coupling regime. Given any decoupling group $\mathcal G$ that averages the interaction to zero, our construction yields pulse sequences whose length scales as $\mathcal{O}(|\mathcal G| K)$, while canceling all error terms linear in the system-bath coupling strength up to order $K$ in the total evolution time. As a corollary, for an $n$-qubit system with $k$-local system-bath interactions, we obtain an $\mathcal{O}(n^{k-1}K)$-pulse sequence, a significant improvement over existing schemes with $\mathcal{O}(\exp(n))$ pulses (for $k=\mathcal{O}(1)$). The construction is obtained via a mapping to the continuous necklace-splitting problem, which asks how to cut a multi-colored interval into pieces that give each party the same share of every color. We provide explicit pulse sequences for suppressing general single-qubit decoherence, prove that the pulse count is asymptotically optimal, and verify the predicted error scaling in numerical simulations. For the same number of pulses, we observe that our sequences outperform the state-of-the-art Quadratic DD in the weak-coupling regime. We also note that the same construction extends to suppress slow, time-dependent Hamiltonian noise.