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

TL;DR

This paper introduces a novel, efficient framework for designing time-optimal, selective dynamical decoupling sequences in quantum computing, leveraging graph coloring and coding theory to target specific interactions while reducing protocol length.

Contribution

It presents a general, scalable method combining graph coloring and classical coding theory to construct tailored dynamical decoupling sequences for quantum systems.

Findings

Successfully suppresses residual interactions in superconducting qubits

Enables Hamiltonian engineering for quantum simulation

Reduces sequence length compared to traditional methods

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.