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At its core, Quantum Mechanics is a theory developed to describe fundamental observations in the spectroscopy of solids and gases. Despite these practical roots, however, quantum theory is infamous for being highly counterintuitive, largely due to its intrinsically probabilistic nature. Neural networks have recently emerged as a powerful tool that can extract non-trivial correlations in vast datasets. They routinely outperform state-of-the-art techniques in language translation, medical diagnosis and image recognition. It remains to be seen if neural networks can be trained to predict stochastic quantum evolution without a priori specifying the rules of quantum theory. Here, we demonstrate that a recurrent neural network can be trained in real time to infer the individual quantum trajectories associated with the evolution of a superconducting qubit under unitary evolution, decoherence and continuous measurement from raw observations only. The network extracts the system Hamiltonian, measurement operators and physical parameters. It is also able to perform tomography of an unknown initial state without any prior calibration. This method has potential to greatly simplify and enhance tasks in quantum systems such as noise characterization, parameter estimation, feedback and optimization of quantum control.
Weak measurements of a superconducting qubit produce noisy voltage signals that are weakly correlated with the qubit state. To recover individual quantum trajectories from these noisy signals, traditional methods require slow qubit dynamics and subst
Phonon modes at microwave frequencies can be cooled to their quantum ground state using conventional cryogenic refrigeration, providing a convenient way to study and manipulate quantum states at the single phonon level. Phonons are of particular inte
Bidirectional conversion of electrical and optical signals lies at the foundation of the global internet. Such converters are employed at repeater stations to extend the reach of long-haul fiber optic communication systems and within data centers to
Demonstrating a quantum computational advantage will require high-fidelity control and readout of multi-qubit systems. As system size increases, multiplexed qubit readout becomes a practical necessity to limit the growth of resource overhead. Many co
We describe a possible implementation of the nanomechanical quantum superposition generation and detection scheme described in the preceding, companion paper [Armour A D and Blencowe M P 2008 New. J. Phys. Submitted]. The implementation is based on t