Quantum computation by local measurement

Abstract

Quantum computation is a novel way of information processing which allows, for certain classes of problems, exponential speedups over classical computation. Various models of quantum computation exist, such as the adiabatic, circuit and measurement-based models. They have been proven equivalent in their computational power, but operate very differently. As such, they may be suitable for realization in different physical systems, and also offer different perspectives on open questions such as the precise origin of the quantum speedup. Here, we give an introduction to the one-way quantum computer, a scheme of measurement-based quantum computation. In this model, the computation is driven by local measurements on a carefully chosen, highly entangled state. We discuss various aspects of this computational scheme, such as the role of entanglement and quantum correlations. We also give examples for ground states of simple Hamiltonians which enable universal quantum computation by local measurements.

36 pages, single column, 6 figures, not published version (as restricted by the journal), please refer to ARCMP for the final published version

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Cited by in corpus (35)

• One-Dimensional Symmetry Protected Topological Phases and their Transitions
• Universal quantum computation using fractal symmetry-protected cluster phases
• The 2D AKLT state on the honeycomb lattice is a universal resource for quantum computation
• Generation of arbitrary all-photonic graph states from quantum emitters
• Spectral gaps of AKLT Hamiltonians using Tensor Network methods
• Universal measurement-based quantum computation with spin-2 Affleck-Kennedy-Lieb-Tasaki states
• Symmetry-protected topologically ordered states for universal quantum computation
• Hybrid valence-bond states for universal quantum computation
• Quantum spin systems for measurement-based quantum computation
• Universal measurement-based quantum computation in two-dimensional SPT phases
• Ground states of 1D symmetry-protected topological phases and their utility as resource states for quantum computation
• Universal measurement-based quantum computation in a one-dimensional architecture enabled by dual-unitary circuits
• The complexity of simulating constant-depth BosonSampling
• Universal quantum computing using $({\mathbb{Z}}_d{)}^3$ symmetry-protected topologically ordered states
• Quantum computational universality of spin-3/2 Affleck-Kennedy-Lieb-Tasaki states beyond the honeycomb lattice
• AKLT models on decorated square lattices are gapped
• Compilation of algorithm-specific graph states for quantum circuits
• Exactly solvable many-body dynamics from space-time duality
• Entanglement dynamics and phase transitions of the Floquet cluster spin chain
• Contextuality and bundle diagrams
• Measurement-based quantum simulation of Abelian lattice gauge theories
• Physical Realization of Measurement Based Quantum Computation
• Interacting quantum walk on a graph
• Criteria of minimum squeezing for quantum cluster state generation
• Transitions in the quantum computational power
• Pivoting through the chiral-clock family
• Generation of genuine all-way entanglement in defect-nuclear spin systems through dynamical decoupling sequences
• Response to defects in multi- and bipartite entanglement of isotropic quantum spin networks
• Quantum computation by teleportation and symmetry
• Measurement-based quantum machine learning
• Entanglement in Quantum Systems Based on Directed Graphs
• A Unified Framework for Quantum Supervised Learning
• The genuinely multipartite nonlocality of graph states is model-dependent
• Entanglement transition in a cluster spin chain coupled with free spins
• Creating long-range entangled Majorana pairs: from spin-1/2 twisted Kitaev to generalized XY chains