  Measurement-based quantum computing (MBQC) is a model of quantum computing
that proceeds by sequential measurements of individual spins in an entangled
resource state. However, it remains a challenge to produce efficiently such
resource states. Would it be possible to generate these states by simply
cooling a quantum many-body system to its ground state? Cluster states, the
canonical resource states for MBQC, do not occur naturally as unique ground
states of physical systems. This inherent hurdle has led to a significant
effort to identify alternative resource states that appear as ground states in
spin lattices. Recently, some interesting candidates have been identified with
various valence-bond-solid (VBS) states. In this review, we provide a
pedagogical introduction to recent progress regarding MBQC with VBS states as
possible resource states. This study has led to an interesting
interdisciplinary research area at the interface of quantum information science
and condensed matter physics.
