Robustness-Runtime Tradeoff for Quantum State Transfer

TL;DR

This paper introduces a measure of robustness for quantum state transfer protocols, analyzing their tolerance to initial state errors, and develops new protocols that optimize the tradeoff between speed and robustness.

Contribution

It defines the robustness of quantum state transfer, provides bounds using Schatten norms, and proposes new protocols balancing speed and error tolerance.

Findings

Robustness bounds are tightly linked to Schatten p-norms of operator commutators.

Partially state-dependent protocols can outperform existing bounds in certain regimes.

New protocols are introduced that interpolate between fully state-dependent and state-independent transfer.

Abstract

Quantum state transfer is the primitive of transporting an unknown state on one site of a lattice to another. Using power-law interactions, recent state transfer protocols achieve speedup by utilizing the intermediate ancilla sites. However, these protocols require the ancillas to be in a perfectly initialized state, which, due to noise or imperfect control, may not be the case. In this work we introduce the $\textit{robustness}$ of a state transfer protocol, which quantifies the protocol's tolerance to error in the initial ancilla state. In the Heisenberg picture, state transfer grows operators supported on the final site such that they no longer commute with all operators on the starting site. We prove that this robustness tightly bounds the Schatten $p$-norms of these commutators between initial and final-site operators. This generalizes the known cases of $p=\infty$ and $p=2$, which govern completely state-dependent and state-independent state transfer respectively, demonstrating that intermediate values of $p$ govern partially state-dependent state transfer. In conjunction with existing power-law light cones, our result gives new minimum runtimes for partially state-dependent protocols which, in certain regimes, are parametrically better than existing bounds. We introduce new robust state transfer protocols, charting the landscape between complete state-dependence and state-independence.