Learning an unknown n-qubit quantum state is a fundamental challenge in quantum computing theory and practice. Information-theoretically, it is well-known that tomography requires exponential in n many copies of an unknown state in order to estimate it upto small trace distance. But a natural question is, are there models of learning where fewer copies suffice and are there interesting classes of states that can be learned with fewer copies? In this talk, I will give a brief overview of learning Boolean functions, structured quantum states, and alternate learning models where efficient learning is possible.
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