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arXiv:2602.05343 · Physical Review Letters

High-order dynamical decoupling in the weak-coupling regime

Leeseok Kim, Milad Marvian

quant-phSubmitted Feb 5, 2026• Announced Feb 6, 2026• 0 citations
v1 · Feb 5, 2026v2 · Sep 14, 2026
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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.

DOI
10.1103/bvkl-8pq2

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We introduce a high-order dynamical decoupling (DD) scheme for arbitrary system-bath interactions in the weak-coupling regime. Given any decoupling group G\mathcal GG that averages the interaction to zero, our construction yields pulse sequences whose length scales as O(∣G∣K)\mathcal{O}(|\mathcal G| K)O(∣G∣K), while canceling all error terms linear in the system-bath coupling strength up to order KKK in the total evolution time. As a corollary, for an nnn-qubit system with kkk-local system-bath interactions, we obtain an O(nk−1K)\mathcal{O}(n^{k-1}K)O(nk−1K)-pulse sequence, a significant improvement over existing schemes with O(exp⁡(n))\mathcal{O}(\exp(n))O(exp(n)) pulses (for k=O(1)k=\mathcal{O}(1)k=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.
Dynamical decoupling (DD) is perhaps the simplest and least resource-intensive error-suppression strategy for improving quantum computer performance. Here we report on a large-scale survey of the performance of 60 different DD sequences from ten families, including basic as well as advanced sequences with high-order error cancelation properties and built-in robustness. The survey is performed using three different superconducting-qubit IBMQ devices, with the goal of assessing the relative performance of the different sequences in the setting of arbitrary quantum state preservation. We find that the high-order universally robust (UR) and quadratic DD (QDD) sequences generally outperform all other sequences across devices and pulse-interval settings. Surprisingly, we find that DD performance for basic sequences such as the Carr-Purcell-Meiboom-Gill and XY4 sequences can be made to nearly match that of UR and QDD sequences by optimizing the pulse interval, with the optimal interval being substantially larger than the minimum interval possible on each device.
Dynamical decoupling (DD) emerges as a promising tool to suppress decoherence of quantum systems by eliminating the system-environment coupling. We investigate its power in combating pure dephasing of a qubit under random classical noise. Interestingly, the decoherence rate can be viewed as the interplay between noise spectrum and a controllable filter function. More specifically, the filter function is determined by the DD sequence we employed. Here we take Uhrig DD (UDD) as a benchmark sequence to illustrate the filtering process. We find that UDD sequence works as a perfect dynamical filter for low-frequency noise. For spectrum with hard cutoff, UDD increases the performance order by order with linearly increased number of pulses. However, for noise spectrum with soft cutoff, the required pulse number grows exponentially.
We analyze numerically the performance of the near-optimal quadratic dynamical decoupling (QDD) single-qubit decoherence errors suppression method [J. West et al., Phys. Rev. Lett. 104, 130501 (2010)]. The QDD sequence is formed by nesting two optimal Uhrig dynamical decoupling sequences for two orthogonal axes, comprising N1{N}_{1}N1​ and N2{N}_{2}N2​ pulses, respectively. Varying these numbers, we study the decoherence suppression properties of QDD directly by isolating the errors associated with each system basis operator present in the system-bath interaction Hamiltonian. Each individual error scales with the lowest order of the Dyson series, therefore immediately yielding the order of decoherence suppression. We show that the error suppression properties of QDD are dependent upon the parities of N1{N}_{1}N1​ and N2{N}_{2}N2​, and near-optimal performance is achieved for general single-qubit interactions when N1=N2{N}_{1}={N}_{2}N1​=N2​.
We prove the universality of the generalized QDDN1N2{}_{{N}_{1}{N}_{2}}N1​N2​​ (quadratic dynamical decoupling) pulse sequence for near-optimal suppression of general single-qubit decoherence. Earlier work showed numerically that this dynamical decoupling sequence, which consists of an inner Uhrig DD (UDD) and outer UDD sequence using N1{N}_{1}N1​ and N2{N}_{2}N2​ pulses, respectively, can eliminate decoherence to O(TN)O({T}^{N})O(TN) using O(N2)O({N}^{2})O(N2) unequally spaced ``ideal'' (zero-width) pulses, where TTT is the total evolution time and N=N1=N2N={N}_{1}={N}_{2}N=N1​=N2​. A proof of the universality of QDD has been given for even N1{N}_{1}N1​. Here we give a general universality proof of QDD for arbitrary N1{N}_{1}N1​ and N2{N}_{2}N2​. As in earlier proofs, our result holds for arbitrary bounded environments. Furthermore, we explore the single-axis (polarization) error suppression abilities of the inner and outer UDD sequences. We analyze both the single-axis QDD performance and how the overall performance of QDD depends on the single-axis errors. We identify various performance effects related to the parities and relative magnitudes of N1{N}_{1}N1​ and N2{N}_{2}N2​. We prove that using QDDN1N2{}_{{N}_{1}{N}_{2}}N1​N2​​ decoherence can always be eliminated to O(TminN1,N2)O({T}^{\mathrm{min}{{N}_{1},{N}_{2}}})O(TminN1​,N2​).
The Uhrig dynamical decoupling sequence achieves high-order decoupling of a single system qubit from its dephasing bath through the use of bang-bang Pauli pulses at appropriately timed intervals. High-order decoupling of single and multiple qubit systems from baths causing both dephasing and relaxation can also be achieved through the nested application of Uhrig sequences, again using single-qubit Pauli pulses. For the three-qubit decoherence free subsystem (DFS) and related subsystem encodings, Pauli pulses are not naturally available operations; instead, exchange interactions provide all required encoded operations. Here we demonstrate that exchange interactions alone can achieve high-order decoupling against general noise in the three-qubit DFS. We present decoupling sequences for a three-qubit DFS coupled to classical and quantum baths and evaluate the performance of the sequences through numerical simulations.
Dynamical decoupling can be used to preserve arbitrary quantum states despite undesired interactions with the environment, using control Hamiltonians affecting the system only. We present a system-independent analysis of dynamical decoupling based on leading order decoupling error estimates, valid for bounded-strength environments. Using as a key tool a renormalization transformation of the effective system-bath coupling Hamiltonian, we delineate the reliability domain of dynamical decoupling used for quantum state preservation, in a general setting for a single qubit. We specifically analyze and compare two deterministic dynamical decoupling schemes---periodic and concatenated---and distinguish between two limiting cases of fast versus slow environments. We prove that concatenated decoupling outperforms periodic decoupling over a wide range of parameters. These results are obtained for both ``ideal'' (zero-width) and realistic (finite-width) pulses This work extends and generalizes our earlier work [Phys. Rev. Lett. 95, 180501 (2005)].