Hidden qubit cluster states

TL;DR

This paper reveals that continuous-variable and hybrid cluster states contain hidden qubit cluster states within their logical subsystems, explaining their effectiveness in measurement-based quantum computing.

Contribution

It introduces a subsystem decomposition approach to uncover hidden qubit structures in CV, GKP, and hybrid cluster states, providing new insights into their utility.

Findings

Hidden qubit cluster states are embedded in logical subsystems of CV and GKP states.

Graphical description illustrates entanglement between logical and gauge modes.

Results extend to finitely squeezed states, informing resource efficiency.

Abstract

Continuous-variable cluster states (CVCSs) can be supplemented with Gottesman-Kitaev-Preskill (GKP) states to form a hybrid cluster state with the power to execute universal, fault-tolerant quantum computing in a measurement-based fashion. As the resource states that comprise a hybrid cluster state are of a very different nature, a natural question arises: Why do GKP states interface so well with CVCSs? To answer this question, we apply the recently introduced subsystem decomposition of a bosonic mode, which divides a mode into logical and gauge-mode subsystems, to three types of cluster state: CVCSs, GKP cluster states, and hybrid CV-GKP cluster states. We find that each of these contains a "hidden" qubit cluster state across their logical subsystems, which lies at the heart of their utility for measurement-based quantum computing. To complement the analytical approach, we introduce a simple graphical description of these CV-mode cluster states that depicts precisely how the hidden qubit cluster states are entangled with the gauge modes, and we outline how these results would extend to the case of finitely squeezed states. This work provides important insight that is both conceptually satisfying and helps to address important practical issues like when a simpler resource (such as a Gaussian state) can stand in for a more complex one (like a GKP state), leading to more efficient use of the resources available for CV quantum computing.