Quantum Pure State Tomography via Variational Hybrid Quantum-Classical Method

To obtain a complete description of a quantum system, one usually employs standard quantum state tomography, which however requires exponential number of measurements to perform and hence is impractical when the system's size grows large. In this work, we introduce a self-learning tomographic scheme based on the variational hybrid quantum-classical method. The key part of the scheme is a learning procedure, in which we learn a control sequence capable of driving the unknown target state coherently to a simple fiducial state, so that the target state can be directly reconstructed by applying the control sequence reversely. In this manner, the state tomography problem is converted to a state-to-state transfer problem. To solve the latter problem, we use the closed-loop learning control approach. Our scheme is further experimentally tested using techniques of a 4-qubit nuclear magnetic resonance. {Experimental results indicate that the proposed tomographic scheme can handle a broad class of states including entangled states in quantum information, as well as dynamical states of quantum many-body systems common to condensed matter physics.