A Fundamental Bound for Robust Quantum Gate Control

TL;DR

This paper establishes a universal lower bound on the fidelity of quantum gates under uncertainties, providing a device-independent metric to assess and improve quantum control robustness across various quantum systems.

Contribution

It introduces a fundamental, dimensionless bound on quantum gate fidelity considering all bounded uncertainties, applicable to diverse quantum systems without assumptions on initial states or maps.

Findings

Derives a universal fidelity lower bound for quantum control under uncertainties.

Provides a device-independent metric for quantum hardware performance.

Applicable to qubits, qudits, and ancilla-assisted operations.

Abstract

We derive a universal performance limit for coherent quantum control in the presence of modeled and unmodeled uncertainties. For any target unitary $W$ that is implementable in the absence of error, we prove that the worst-case (and hence the average) gate fidelity obeys the lower bound $F \ge \Flb\bigl(\tf \Omeff\bigr)$, where $\tf$ is the gate duration and $\Omeff$ is a single frequency-like measure that aggregates \emph{all} bounded uncertainty sources, e.g., coherent control imperfections, unknown couplings, and residual environment interactions, without assuming an initially factorizable system-bath state or a completely positive map. The bound is obtained by combining an interaction-picture averaging method with a Bellman-Gronwall inequality and holds for any finite-norm Hamiltonian decomposition. Hence it applies equally to qubits, multi-level qudits, and ancilla-assisted operations. Because $\Flb$ depends only on the dimensionless product $\tf\Omeff$, it yields a device-independent metric that certifies whether a given hardware platform can, in principle, reach a specified fault-tolerance threshold, and also sets a quantitative target for robust-control synthesis and system identification.