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Universal compilation is a training process that compiles a trainable unitaryinto a target unitary and it serves vast potential applications from quantumdynamic simulations to optimal circuits with deep-compressing, devicebenchmarking, quantum error mitigation, and so on. Here, we propose a universalcompilation-based variational algorithm for the preparation and tomography ofquantum states in low-depth quantum circuits. We apply the Fubini-Studydistance to be a trainable cost function under various gradient-basedoptimizers, including the quantum natural gradient approach. We evaluate theperformance of various unitary topologies and the trainability of differentoptimizers for getting high efficiency. In practice, we address differentcircuit ansatzes in quantum state preparation, including the linear andgraph-based ansatzes for preparing different entanglement target states such asrepresentative GHZ and W states. We also discuss the effect of the circuitdepth, barren plateau, readout noise in the model, and the error mitigationsolution. We next evaluate the reconstructing efficiency in quantum statetomography via various popular circuit ansatzes and reveal the crucial role ofthe circuit depth in the robust fidelity. The results are comparable with theshadow tomography method, a similar fashion in the field. Our work expressesthe adequate capacity of the universal compilation-based variational algorithmto maximize the efficiency in the quantum state preparation and tomography.Further, it promises applications in quantum metrology and sensing and isapplicable in the near-term quantum computers for verification of the circuitsfidelity and various quantum computing tasks.

Universal compilation for quantum state preparation and tomography