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The Learnability of Quantum States

Scott Aaronson
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Abstract

Traditional quantum state tomography requires a number of measurements that grows exponentially with the number of qubits n. But using ideas from computational learning theory, we show that "for most practical purposes" one can learn a state using a number of measurements that grows only linearly with n. Besides possible implications for experimental physics, our learning theorem 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.

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Scott Aaronson. 2007-03-04. The Learnability of Quantum States. https://doi.org/10.1098/rspa.2007.0113

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