Discord in relation to resource states for measurement-based quantum computation

Abstract

We consider the issue of what should count as a resource for measurement-based quantum computation (MBQC). While a state that supports universal quantum computation clearly should be considered a resource, universality should not be necessary given the existence of interesting, but less computationally-powerful, classes of MBQCs. Here, we propose minimal criteria for a state to be considered a resource state for MBQC. Using these criteria, we explain why discord-free states cannot be resources for MBQC, contrary to recent claims [Hoban et al., arXiv:1304]. Independently of our criteria, we also show that the arguments of Hoban et al., if correct, would imply that Shor's algorithm (for example) can be implemented by measuring discord-free states.

Entanglement and deterministic quantum computing with one qubit

“…Our approach is to study the space of quantum states that can be generated during the computational process, and in particular study the correlations within these states. This approach follows earlier works on the circuit model [20,21], DQC1 [22][23][24][25][26][27], measurement based quantum computing [28], and other models [10]. As in these works, we do not take error correction into account.…”

Measurement-Based Classical Computation

“…In other aspects the two models are strikingly different. In response to an earlier pre-print of this present work, Rieffel and Wiseman [20] introduced criteria which divides sets of MBQC instances into superficially and inherently measurement based. Using their criteria, all instances of MBCC would be superficially measurement based.…”

“…Can we identify further instances of MBCC whose efficient classical simulation would lead to hierarchy collapse, or which provide other evidence of non-classical computation? Rieffel and Wiseman [20] suggest a comparison with the output distribution of Shor's order finding algorithm. It is very likely that the algorithm cannot be efficiently simulated by a classical computing device.…”