The learnability of quantum states

Scott Aaronson
2007 Proceedings of the Royal Society A  
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
more » ... on protocols, and second, the use of trusted classical advice to verify untrusted quantum advice.
doi:10.1098/rspa.2007.0113 fatcat:l5lmp5zdizap7ml5j5jvgtr7qe