Quantum spin models for measurement-based quantum computation

Abstract

To cite this article: Tzu-Chieh Wei (2018) Quantum spin models for measurement-based quantum computationABSTRACT Measurement-based quantum computation is different from other approaches for quantum computation, in that everything needs to be done is only local measurement on a certain entangled state. It thus uses entanglement as the resource that drives computation. We give a pedagogical treatment on the basics, and then review some selected developments beyond graph states, including Affleck-Kennedy-Lieb-Tasaki states and more recent 2D symmetry-protected topological states. We point out some open questions along the way. ARTICLE HISTORY

AKLT models on decorated square lattices are gapped

“…Unexpectedly, 2D AKLT states have recently emerged as resource for univeral quantum computation in the framework of the measurement-based quantum computation (MBQC) [9][10][11][12]. The spin-3/2 AKLT state on the honeycomb lattice was first shown to provide the appropriate entanglement structure for universal QC [13,14], a result subsequently generalized to other trivalent lattices [15].…”

Many-body quantum magic

“…[61,62] for introductions) and in particular widely considered as candidate many-body resource states for MBQC (see e.g. [22] for a review). It is realized that certain classes of nontrivial SPT phases in ≥ 2D must contain magic that is "robust" in a sense [36], indicating that on top of entanglement, magic may be a characteristic feature that underlies the physics of such systems.…”

“…For example, a direct question following the above discussions is whether magic can be used to diagnose whether the phase is universal for Pauli MBQC, or more generally certain notions of quantum "computational phase transitions". In particular, noting that the above studied Miller-Miyake and Levin-Gu models are known to be universal on the Union Jack lattice but likely not universal on the triangular lattice [22,60], we wonder if more refined analysis on the scaling factors and robustness properties of magic associated with different lattices helps understand how many-body magic is connected to MBQC power. On the other hand, magic determines the cost of many standard methods for preparing and simulating the systems and could plausibly be connected to related problems like the notorious sign problem in various forms (see e.g.…”

“…the cost of probing or simulating them and their computational power. Important relevant topics include, among others, the computational universality in measurementbased quantum computing (MBQC) [20][21][22][23], sign problems for Monte Carlo methods (see e.g. [24][25][26]), etc.…”

Quantum computation by teleportation and symmetry

“…In general, the world of two-dimensional systems with TOP, SET, SPT, and other orders is largely unexplored for MBQC. The class of valence-bond solid states with weak SPT order has been thoroughly investigated [28,70,71] in recent years. The family of hypergraph states with strong SPT order has also been shown to be good resource states [47,79].…”