Learning quantum graph states with product measurements

@article{Ouyang2022LearningQG,
  title={Learning quantum graph states with product measurements},
  author={Yingkai Ouyang and Marco Tomamichel},
  journal={2022 IEEE International Symposium on Information Theory (ISIT)},
  year={2022},
  pages={2963-2968}
}
We consider the problem of learning N identical copies of an unknown n-qubit quantum graph state with product measurements. These graph states have corresponding graphs where every vertex has exactly d neighboring vertices. Here, we detail an explicit algorithm that uses product measurements on multiple identical copies of such graph states to learn them. When n ≫ d and N = O(d log(1/ϵ) + d2 log n), this algorithm correctly learns the graph state with probability at least 1 – ϵ. From channel… 
[PDF] Semantic Reader

References

SHOWING 1-10 OF 23 REFERENCES
Online learning of quantum states
TLDR
This paper shows how to output hypothesis states that incur at most excess loss over the best possible state on the first T measurements, and gives three different ways to prove the results—using convex optimization, quantum postselection, and sequential fat-shattering dimension—which have different advantages in terms of parameters and portability.
Shadow tomography of quantum states
  • S. Aaronson
  • Computer Science
    Electron. Colloquium Comput. Complex.
  • 2017
TLDR
Surprisingly, this work gives a procedure that solves the problem of shadow tomography by measuring only O( ε−5·log4 M·logD) copies, which means, for example, that the authors can learn the behavior of an arbitrary n-qubit state, on *all* accepting/rejecting circuits of some fixed polynomial size, by measuringonly nO( 1) copies of the state.
Quantum Algorithms for Learning a Hidden Graph
TLDR
This work studies the problem of learning an unknown graph provided via an oracle using a quantum algorithm, and gives quantum algorithms in the graph state model whose complexity is similar to the parity query model.
The learnability of quantum states
  • S. Aaronson
  • Physics
    Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
  • 2007
TLDR
This theorem has the conceptual implication that quantum states, despite being exponentially long vectors, are nevertheless ‘reasonable’ in a learning theory sense and has two applications to quantum computing: first, a new simulation of quantum one-way communication protocols and second, the use of trusted classical advice to verify untrusted quantum advice.
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…
Fast graph operations in quantum computation
TLDR
This work shows that this correspondence between certain entangled states and graphs can be harnessed in the reverse direction to yield a graph data structure, which allows for more efficient manipulation and comparison of graphs than any possible classical structure.
Multiparticle entanglement purification for graph states.
We introduce a class of multiparticle entanglement purification protocols that allow us to distill a large class of entangled states. These include cluster states, Greenberger-Horne-Zeilinger states,…
Learning Quantum Circuits of Some T Gates
TLDR
The results greatly extend the previously known facts that stabilizer states can be efficiently identified based on the stabilizer formalism.
Predicting many properties of a quantum system from very few measurements
TLDR
An efficient method for constructing an approximate classical description of a quantum state using very few measurements of the state is proposed, called a ‘classical shadow’, which can be used to predict many different properties.
Quantum error-correcting codes associated with graphs
TLDR
It is proved necessary and sufficient conditions for the graph such that the resulting code corrects a certain number of errors, which allows a simple verification of the one-error correcting property of codes of length 5 in any dimension.
...
...