Improved bounded-strength decoupling schemes for local Hamiltonians

TL;DR

This paper introduces new bounded-strength dynamical decoupling schemes for local quantum many-body Hamiltonians, utilizing combinatorial structures from error-correcting codes to achieve more efficient decoupling with improved scaling.

Contribution

It presents the concept of balanced-cycle orthogonal arrays and their construction from classical error-correcting codes, enabling more efficient decoupling schemes for local Hamiltonians.

Findings

Decoupling scheme length scales as O(n log n) for 2-local Hamiltonians.

Schemes for -local Hamiltonians scale as O(n^{-1} log n).

Improves over previous quadratic-scaling schemes.

Abstract

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 $O(n^{\ell-1} \log n)$.