Valence-bond states for quantum computation

By Frank Verstraete, J. I. Cirac. 2003

243 citations recorded by the source corpus.

We propose a way of universal quantum computation by doing joint measurements on distributed singlets. We show how these joint measurements become local measurements when the singlets are interpreted as the virtual components of a large valence-bond state. This proves the equivalence of the cluster-state-based quantum computational model and the teleportation-based model, and we discuss several features and possible extensions. We show that all stabilizer states have a very simple interpretation in terms of valence-bond solids, which allows to understand their entanglement properties in a transparent way.

Subfields: Artificial Intelligence

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Citations in the corpus

A literature survey of low‐rank tensor approximation techniques (2013, neutral): “Well-known examples include the so called projected entangled-pair states (PEPS) [260, 261] and the multiscale entanglement renormalization ansatz (MERA) [264].”
Computations in quantum tensor networks (2012, background): “…Product States ( mps ) [21, 22] of Density Matrix Renormalization Groups ( dmrg ) [23, 24], but also projected entangled pair states ( peps ) [25, 26], weighted graph states ( wgs ) [27], Multi-scale Entanglement Renormalization Approaches ( mera ) [28], string-bond states ( sbs ) [29] as…”
Linear optical quantum computing with photonic qubits (2005, background): “Verstraete and Cirac (2004) demonstrated how the teleportation-based computing scheme of Gottesman and Chuang could be related to clusters.”
Hand-waving and interpretive dance: an introductory course on tensor networks (2016, background): “Despite this, physically relevant states often possess additional structure not found in arbitrary states, and as such do not exhibit this pathological complexity, allowing them to be efficiently described and studied.”
Quantum measurements without sums (2006, background): “(7)This operation δ : H ⊗H → H has appeared in the quantum informatics literature under the name fusion, providing a means for constructing cluster states [5, 33].”
Quantum spin liquid states (2016, background): “These wavefunctions are presently known as projected entangled pair states (PEPSs) (Verstraete and Cirac, 2004a,b).”
Interacting quantum observables: categorical algebra and diagrammatics (2009, methodology): “Alternatively, the cluster state can be prepared by applying a Hadamard gate to one part of a Bell pair to obtain states of the form |8〉 = |0+〉 + |1−〉, and then ‘fusing’ these entangled pairs [76].”