Color it, Code it, Cancel it: k-local dynamical decoupling from classical additive codes

Abstract

Dynamical decoupling is a central technique in quantum computing for actively suppressing decoherence and systematic imperfections through sequences of single-qubit operations. Conventional sequences typically aim to completely freeze system dynamics, often resulting in long protocols whose length scales exponentially with system size. In this work, we introduce a general framework for constructing time-optimal, selectively-tailored sequences that remove only specific local interactions. By combining techniques from graph coloring and classical coding theory, our approach enables compact and hardware-tailored sequences across diverse qubit platforms, efficiently canceling undesired Hamiltonian terms while preserving target interactions. This opens up broad applications in quantum computing and simulation. At the core of our method is a mapping between dynamical decoupling sequence design and error-detecting codes, which allows us to leverage powerful coding-theoretic tools to construct customized sequences. To overcome exponential overheads, we exploit symmetries in colored interaction hypergraphs, extending graph-coloring strategies to arbitrary many-body Hamiltonians. We demonstrate the effectiveness of our framework through concrete examples, including compact sequences that suppress residual ZZ and ZZZ interactions in superconducting qubits and Heisenberg exchange coupling in spin qubits. We also show how it enables Hamiltonian engineering by simulating the anisotropic Kitaev honeycomb model using only isotropic Heisenberg interactions.

Figures (10)

• Figure 1: Canceling local interactions by dynamical decoupling. Our framework permits an efficient and selective suppression of local interactions. For example, by applying tailored DD sequences to a device with dense connectivity (top), we can separate the system into non-interacting clusters, preserving only certain interactions within each cluster (middle), or completely freezing the system's dynamics (bottom). Our framework also applies to general interactions graphs going beyond nearest neighbor and is not restricted to instantaneous control pulses.
• Figure 2: Framework for constructing efficient dynamical decoupling sequences. (a) Flowchart of our approach. Starting from an interaction hypergraph, we color it, generate a symmetric variant, and construct its quotient. Additive codes are then used to produce efficient universal sequences, which are tailored to suppress specific Hamiltonian terms. (b) Example of each step in the protocol. We start from a simple 7-qubit loop (step 1) and we color it assuming a nearest-neighbor interaction model (step 2). We then construct a color-preserving symmetric hypergraph connecting all different colors (step 3), which allows us to simplify the DD problem by just considering the corresponding quotient hypergraph (step 4). The DD sequence is then constructed by using additive codes, forming a universal decoupling group that suppresses arbitrary two-local interactions (step 5). We then tailor the sequence for specific qubit architectures (step 6).
• Figure 3: Colored bilinear array graph. (a) Interaction hypergraph $I_{\rm Dev}$ of $7$ physical qubits with two-local interactions arranged in a bilinear array, along with the minimal color partition $C[I_{\rm Dev}]$. (b) Expanded hypergraph $I_{\rm Dev}^{'}$ constructed from $I_{\rm Dev}$ and $C[I_{\rm Dev}]$.
• Figure 4: Dynamical decoupling from orthogonal arrays. (a) The quotient hypergraph $I_{\rm Dev}^{'}/C[I_{\rm Dev}]$ formed by collapsing all physical qubits of the same color in $I_{\rm Dev}^{'}$ into a single equivalence class. (b) The orthogonal array $\text{OA}(L=16,\chi_I=3,S=4,k=2)$ which generates a universal DD sequence for two-local Hamiltonian defined by the quotient hypergraph $I_{\rm Dev}^{'}/C[I_{\rm Dev}]$. Each column is colored according to the associated color class $c_i$.
• Figure 5: Colored graphs of common superconducting qubit architectures. We assume a noise model where each qubit experiences both longitudinal coherence errors ($Z$ errors) and transversal coherence errors ($X$ and $Y$ errors), along with residual $ZZ$ interactions between nearest- and next-nearest-neighbors, and $ZZZ$ interactions among any three consecutive qubits. The colorings also apply when residual $ZZ$ interactions extend to next-nearest neighbors. (a) Heavy-hex lattice with $\chi_I = 6$ colors. (b) Square lattice with $\chi_I = 6$ colors. (c) The resulting quotient hypergraph is identical for both architectures.

Theorems & Definitions (1)

• Theorem 4.1