38 research outputs found

    Efficient Learning of Non-Interacting Fermion Distributions

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    We give an efficient classical algorithm that recovers the distribution of a non-interacting fermion state over the computational basis. For a system of nn non-interacting fermions and mm modes, we show that O(m2n4log(m/δ)/ε4)O(m^2 n^4 \log(m/\delta)/ \varepsilon^4) samples and O(m4n4log(m/δ)/ε4)O(m^4 n^4 \log(m/\delta)/ \varepsilon^4) time are sufficient to learn the original distribution to total variation distance ε\varepsilon with probability 1δ1 - \delta. Our algorithm empirically estimates the one- and two-mode correlations and uses them to reconstruct a succinct description of the entire distribution efficiently.Comment: 7 page

    Learning the tensor network model of a quantum state using a few single-qubit measurements

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    The constantly increasing dimensionality of artificial quantum systems demands for highly efficient methods for their characterization and benchmarking. Conventional quantum tomography fails for larger systems due to the exponential growth of the required number of measurements. The conceptual solution for this dimensionality curse relies on a simple idea - a complete description of a quantum state is excessive and can be discarded in favor of experimentally accessible information about the system. The probably approximately correct (PAC) learning theory has been recently successfully applied to a problem of building accurate predictors for the measurement outcomes using a dataset which scales only linearly with the number of qubits. Here we present a constructive and numerically efficient protocol which learns a tensor network model of an unknown quantum system. We discuss the limitations and the scalability of the proposed method.Comment: 10 pages, 11 figure

    A survey on the complexity of learning quantum states

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    We survey various recent results that rigorously study the complexity of learning quantum states. These include progress on quantum tomography, learning physical quantum states, alternate learning models to tomography and learning classical functions encoded as quantum states. We highlight how these results are paving the way for a highly successful theory with a range of exciting open questions. To this end, we distill 25 open questions from these results.Comment: Invited article by Nature Review Physics. 39 pages, 6 figure

    Experimental learning of quantum states

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    The number of parameters describing a quantum state is well known to grow exponentially with the number of particles. This scaling limits our ability to characterize and simulate the evolution of arbitrary states to systems, with no more than a few qubits. However, from a computational learning theory perspective, it can be shown that quantum states can be approximately learned using a number of measurements growing linearly with the number of qubits. Here, we experimentally demonstrate this linear scaling in optical systems with up to 6 qubits. Our results highlight the power of the 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
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