Symmetry constraints on temporal order in measurement-based quantum computation

@article{Raussendorf2016SymmetryCO,
  title={Symmetry constraints on temporal order in measurement-based quantum computation},
  author={Robert Raussendorf and Pradeep Kiran Sarvepalli and Tzu-Chieh Wei and Poya Haghnegahdar},
  journal={Inf. Comput.},
  year={2016},
  volume={250},
  pages={115-138}
}
We discuss the interdependence of resource state, measurement setting and temporal order in measurement-based quantum computation. The possible temporal orders of measurement events are constrained by the principle that the randomness inherent in quantum measurement should not affect the outcome of the computation. We provide a classification for all temporal relations among measurement events compatible with a given initial stabilizer state and measurement setting, in terms of a matroid… 
View PDF on arXiv
3 Citations
Highly Influential Citations
1
Background Citations
3
Methods Citations
2

Figures from this paper

3 Citations

Measurement-Based Quantum Computation

  • T. Wei
  • Physics, Computer Science
    Oxford Research Encyclopedia of Physics
  • 2021
The measurement-based approach offers a potential alternative to the standard circuit approach to realize a practical quantum computer and provides useful connections to the emergence of time ordering, computational complexity and classical spin models, blind quantum computation, etc.

Putting paradoxes to work: contextuality in measurement-based quantum computation

We describe a joint cohomological framework for measurement-based quantum computation (MBQC) and the corresponding contextuality proofs. The central object in this framework is an element [ β Ψ ] in…

Entanglement, Flow and Classical Simulatability in Measurement Based Quantum Computation

This paper shows how gFlow can be used to directly give a bound on the classical simulation of an MBQC, and establishes a link between entanglement and the existence of gFlow for a graph state, as well as relating the gFlow to upper bound on how efficiently a computation can be simulated classically.

References

SHOWING 1-10 OF 40 REFERENCES

Quantum state reduction for universal measurement based computation.

It is shown that most of the resource states currently known can be reduced to the cluster state, the first known universal resource state, via adaptive local measurements at a constant cost.

Classical simulation versus universality in measurement-based quantum computation

It is shown that the Schmidt-rank width, a measure recently introduced to assess universality of resource states, plays a crucial role in also this context and is related to the optimal description of states in terms of tree tensor networks.

Computation by measurements: A unifying picture

The ability to perform a universal set of quantum operations based solely on static resources and measurements presents us with a striking viewpoint for thinking about quantum computation and its…

Universal resources for measurement-based quantum computation.

It is proved that graph states associated with 2D lattices such as the hexagonal and triangular lattice are universal, and the first example of a universal nongraph state is obtained.

Effective Quantum Time Travel

The quantum teleportation protocol can be used to probabilistically simulate a quantum circuit with backward-in-time connections and to realize encrypted measurements of future states for which the decryption key becomes available only after the state is created.

Generalized flow and determinism in measurement-based quantum computation

We extend the notion of quantum information flow defined by Danos and Kashefi (2006 Phys. Rev. A 74 052310) for the one-way model (Raussendorf and Briegel 2001 Phys. Rev. Lett. 86 910) and present a…

Closed timelike curves in measurement-based quantum computation

Many results have been recently obtained regarding the power of hypothetical closed timelike curves (CTCs) in quantum computation. Here we show that the one-way model of measurement-based quantum…

Measurement-based quantum computation on cluster states

We give a detailed account of the one-way quantum computer, a scheme of quantum computation that consists entirely of one-qubit measurements on a particular class of entangled states, the cluster…

The 2D AKLT state is a universal quantum computational resource

Quantum computation promises exponential speedup over classical computation by exploiting the quantum mechanical nature of physical processes [1]. In addition to the standard circuit models,…

Measurement-based quantum computation

Quantum computation offers a promising new kind of information processing, where the non-classical features of quantum mechanics are harnessed and exploited. A number of models of quantum computation…