Universal compilation for quantum state tomography

Universal compilation is a training process that compiles a trainable unitary into a target unitary. It has vast potential applications from depth-circuit compressing to device benchmarking and quantum error mitigation. Here we propose a universal compilation algorithm for quantum state tomography in low-depth quantum circuits. We apply the Fubini-Study distance as a trainable cost function and employ various gradient-based optimizations. We evaluate the performance of various trainable unitary topologies and the trainability of different optimizers for getting high efficiency and reveal the crucial role of the circuit depth in robust fidelity. The results are comparable with the shadow tomography method, a similar fashion in the field. Our work expresses the adequate capability of the universal compilation algorithm to maximize the efficiency in the quantum state tomography. Further, it promises applications in quantum metrology and sensing and is applicable in the near-term quantum computers for various quantum computing tasks.