Corpus ID: 231861895

On the Hardness of PAC-learning stabilizer States with Noise

  title={On the Hardness of PAC-learning stabilizer States with Noise},
  author={Aravind Gollakota and Daniel Liang},
We consider the problem of learning stabilizer states with noise in the Probably Approximately Correct (PAC) framework of Aaronson [Aar07] for learning quantum states. In the noiseless setting, an algorithm for this problem was recently given by Rocchetto [Roc18], but the noisy case was left open. Motivated by approaches to noise tolerance from classical learning theory, we introduce the Statistical Query (SQ) model for PAC-learning quantum states, and prove that algorithms in this model are… Expand


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Shadow tomography of quantum states
  • S. Aaronson
  • Mathematics, Physics
  • Electron. Colloquium Comput. Complex.
  • 2017
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. Expand
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The connection theorem is proved, together with a quantum analog of the so-called private multiplicative weights algorithm of Hardt and Rothblum, to give a protocol to solve the problem of shadow tomography using order ( logm) 2 2 copies of ρ, compared to Aaronson’s previous bound of O(logm) 4( logd) . Expand