Counter-intuitive yet efficient regimes for measurement based quantum computation on symmetry protected spin chains

TL;DR

This paper explores dense symmetry-breaking measurements in symmetry protected topological phases for measurement-based quantum computation, revealing that such an approach is both viable and resource-efficient, contrary to previous beliefs.

Contribution

It demonstrates that densely packed symmetry-breaking measurements can still enable effective quantum computation, challenging the conventional sparse measurement paradigm.

Findings

Dense measurements still enable computation

This approach is more resource-efficient

Contradicts previous assumptions about measurement spacing

Abstract

Quantum states picked from non-trivial symmetry protected topological (SPT) phases have computational power in measurement based quantum computation. This power is uniform across SPT phases, and is unlocked by measurements that break the symmetry. Except at special points in the phase, all computational schemes known to date place these symmetry-breaking measurements far apart, to avoid the correlations introduced by spurious, non-universal entanglement. In this work, we investigate the opposite regime of computation where the symmetry-breaking measurements are packed densely. We show that not only does the computation still function, but in fact, under reasonable physical assumptions, this is the most resource efficient mode.