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 an exponential number of measurements to be performed and hence is impractical when the system's size grows large. In this paper, 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 in reverse. In this manner, the state tomography problem is converted to a state-to-state transfer problem. To solve the latter problem, we use a closed-loop-learning control approach. Our scheme is experimentally tested using techniques of four-qubit nuclear magnetic resonance. The experimental results indicate that the proposed tomographic scheme can handle a broad class of states, including entangled states in the field of quantum information, as well as dynamical states of quantum many-body systems common to condensed-matter physics.