Affiliation:
1. Computer Science and Artificial Intelligence Laboratory, Massachusetts Institute of Technology32-G638, Cambridge, MA 02139-4307, USA
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 one can do exponentially better in a statistical setting. In particular, to predict the outcomes of
most
measurements drawn from an arbitrary probability distribution, one needs only a number of sample measurements that grows linearly with
n
. This theorem has the conceptual implication that quantum states, despite being exponentially long vectors, are nevertheless ‘reasonable’ in a learning theory sense. The theorem also 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.
Subject
General Physics and Astronomy,General Engineering,General Mathematics
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