Universal compilation for quantum state tomography

Quantum state tomography is essential for quantum computing and quantum information technology. Recent progress in quantum technologies opened a new paradigm in quantum state tomography, such as using quantum computers. However, even under the quantum algorithms aid, the quantum state tomography requires a heavy growth of the number of measurements.

Recently, quantum compiling, a circuit-based approach that compiles a trainable unitary into a target unitary, provides a fascinating playground in quantum computing. 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 various gradient-based optimizations and evaluate the performance of trainable unitary topologies for getting high efficiency. The results are comparable with the shadow tomography method - a similar fashion in the field, and reveal the crucial role of the circuit depth in robust fidelity. Our work expresses the universal compilation algorithm's adequate capacity to maximize quantum state tomography's efficiency. Further, it promises applications in quantum metrology, quantum sensing, and various quantum computing tasks in the Noisy intermediate-scale quantum era.