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, I'll show that "for most practical purposes" one can learn a quantum state using a number of measurements that grows only linearly with n.  Besides possible implications for experimental physics, this learning theorem has two applications to quantum computing: first, a new simulation of quantum protocols, and second, the use of trusted classical advice to verify untrusted quantum advice.