Quantifying Entanglement in Cluster States Built with Error-Prone Interactions

TL;DR

This paper investigates how slow two-qubit errors in different interaction models affect the fidelity of one-dimensional cluster states used in measurement-based quantum computing, proposing methods to characterize and correct these errors for scalable quantum networks.

Contribution

It introduces an experimentally viable fidelity measure for assessing the impact of slow interaction errors on cluster states and designs refocusing pulses to mitigate these errors.

Findings

Ising and XY interactions allow perfect teleportation despite large errors.

Maximum two-qubit error decreases as the inverse square root of cluster size.

Refocusing pulses can correct slow interaction errors, enabling larger cluster states.

Abstract

Measurement-based quantum computing is an alternative paradigm to the circuit-based model. This approach can be advantageous in certain scenarios, such as when read-out is fast and accurate, but two-qubit gates realized via inter-particle interactions are slow and can be parallelized to efficiently create a cluster state. However, understanding how two-qubit errors impact algorithm accuracy and developing experimentally viable approaches to characterize cluster-state fidelity are outstanding challenges. Here, we consider one-dimensional cluster states built from controlled phase, Ising, and XY interactions with slow two-qubit error in the interaction strength, consistent with error models of interactions found in a variety of qubit architectures. We detail an experimentally viable teleportation fidelity that offers a measure of the impact of these errors on the cluster state. Our fidelity calculations show that the error has a distinctly different impact depending on the underlying interaction used for the two-qubit entangling gate. In particular, the Ising and XY interactions can allow perfect teleportation through the cluster state even with large errors, but the controlled phase interaction does not. Nonetheless, we find that teleportation through cluster state chains of size $N$ has a maximum two-qubit error for teleportation along a quantum channel that decreases as $N^{-1/2}$. To enable construction of larger cluster states, we design lowest-order refocusing pulses for correcting these slow errors in the interaction strength. Our work generalizes to higher-dimensional cluster states and sets the stage for experiments to monitor the growth of entanglement in cluster states built from error-prone interactions.