Experimental learning of quantum states
This addresses the challenge of scaling quantum state characterization for quantum information researchers, providing a foundational advance rather than an incremental improvement.
The paper tackles the problem of exponential scaling in quantum state tomography by experimentally demonstrating that quantum states can be learned with a linear number of measurements, achieving this in optical systems with up to 6 qubits.
The number of parameters describing a quantum state is well known to grow exponentially with the number of particles. This scaling clearly limits our ability to do tomography to systems with no more than a few qubits and has been used to argue against the universal validity of quantum mechanics itself. However, from a computational learning theory perspective, it can be shown that, in a probabilistic setting, quantum states can be approximately learned using only a linear number of measurements. Here we experimentally demonstrate this linear scaling in optical systems with up to 6 qubits. Our results highlight the power of computational learning theory to investigate quantum information, provide the first experimental demonstration that quantum states can be "probably approximately learned" with access to a number of copies of the state that scales linearly with the number of qubits, and pave the way to probing quantum states at new, larger scales.