Measurement-Based Quantum Computing With Valence-Bond-Solids

Abstract

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.

Hybrid valence-bond states for universal quantum computation

“…Studying various aspects of this model also offers new perspectives and insights, such as improvement of the resource overhead in linear-optics quantum computation [6,7], utilization of topological protection [8], renormalization and holographic principles [7,9,10], exploration of quantum computational phases of matter [11][12][13][14], and the relation to symmetries [15] and contextuality [16]. There are still several aspects of MBQC to be understood, such as complete characterization of universal resource states and whether they can arise as unique ground states of gapped two-body interacting Hamiltonians [17][18][19][20].…”

Cluster state generation in one-dimensional Kitaev honeycomb model via shortcut to adiabaticity

“…There exists an alternative paradigm, where the desired quantum gate operations are obtained through single-particle projective measurements on some highly entangled resource states or cluster states [6]. This is known as the measurementbased quantum computation (MBQC) [7][8][9]. The caveat is that one needs to prepare highly entangled states before the MBQC algorithm begins.…”

Universal measurement-based quantum computation in two-dimensional symmetry-protected topological phases

“…In contrast, the paradigm of the measurementbased quantum computation (MBQC) [15][16][17], with the teleportation-based schemes [18] and the one-way quantum computer [15,16,[19][20][21] as the prominent examples, offers an alternative framework, in which local measurement alone achieves the same power of computation as other models, provided that a prior sufficiently entangled state is given. One of the challenges in MBQC is to identify these entangled states, namely, the universal resource states that enable the success of driving universal quantum computation.…”