Special Computer Science/Discrete Mathematics Seminar I

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 the number of qubits n. By contrast, traditional quantum state tomography requires a number of measurements that grows exponentially with n. Besides possible applications in experimental physics, this learning theorem has two implications for quantum computing: first, the use of trusted classical advice to verify untrusted quantum advice, and second, a new simulation of quantum one-way protocols. Even if one can "learn" a quantum state using a linear number of measurements, one might need an exponential amount of computation. As time permits, I'll discuss a result on how one might exploit that fact to copy-protect quantum software.