Improved Bounded-Strength Decoupling Schemes for Local Hamiltonians

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We address the task of switching off the Hamiltonian of a system by removing all internal and system-environment couplings. We propose dynamical decoupling schemes, that use only bounded-strength controls, for quantum many-body systems with local system Hamiltonians and local environmental couplings. To do so, we introduce the combinatorial concept of balanced-cycle orthogonal arrays (BOAs) and show how to construct them from classical error-correcting codes. The derived decoupling schemes may be useful as a primitive for more complex schemes, e.g., for Hamiltonian simulation. For the case of $n$ qubits and a $2$-local Hamiltonian, the length of the resulting decoupling scheme scales as $O(n \log n)$, improving over the previously best-known schemes that scaled quadratically with $n$. More generally, using balanced-cycle orthogonal arrays constructed from families of BCH codes, we show that bounded-strength decoupling for any $\ell$-local Hamiltonian, where $\ell \geq 2$, can be achieved using decoupling schemes of length at most $O(n^{\ell-1} \log n)$.