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Machine learning quantum states in the NISQ era
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We review the development of generative modeling techniques in machine learning for the purpose of reconstructing real, noisy, many-qubit quantum states. Motivated by its interpretability and utility, we discuss in detail the theory of the restricted Boltzmann machine. We demonstrate its practical use for state reconstruction, starting from a classical thermal distribution of Ising spins, then moving systematically through increasingly complex pure and mixed quantum states. Intended for use on experimental noisy intermediate-scale quantum (NISQ) devices, we review recent efforts in reconstruction of a cold atom wavefunction. Finally, we discuss the outlook for future experimental state reconstruction using machine learning, in the NISQ era and beyond.
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The learnability scaling of quantum states: restricted Boltzmann machines
To reproduce the ground-state energy of a one-dimensional transverse-field Ising chain near its critical point, a restricted Boltzmann machine needs a number of weights that grows as the square of the number of qubits...
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