Learning quantum graph states with product measurements

Abstract

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 $n\gg d$ and $N=O(d\log (1/\epsilon )+d^2\log n),$ this algorithm correctly learns the graph state with probability at least $1-\epsilon$. From channel coding theory, we find that for arbitrary joint measurements on graph states, any learning algorithm achieving this accuracy requires at least $\Omega (\log (1/\epsilon )+d\log n)$ copies when $d=o(\sqrt{n})$. We also supply bounds on $N$ when every graph state encounters identical and independent depolarizing errors on each qubit.

arXiv commentaccepted to IEEE ISIT

References in corpus (13)

• Measurement-based quantum computation with cluster states
• Predicting Many Properties of a Quantum System from Very Few Measurements
• Multi-party entanglement in graph states
• The Quantum Chernoff Bound
• Quantum error-correcting codes associated with graphs
• Multiparticle entanglement purification for graph states
• Sample-optimal tomography of quantum states
• Local unitary versus local Clifford equivalence of stabilizer states
• Local unitary versus local Clifford equivalence of stabilizer and graph states
• Online Learning of Quantum States
• Fast graph operations in quantum computation
• The Learnability of Quantum States
• Quantum algorithms for learning a hidden graph and beyond

Cited by in corpus (2)

• Robust projective measurements through measuring code-inspired observables
• Agnostic Tomography of Stabilizer Product States