Toward Scalable Characterization of NISQ era Quantum Processor via Hierarchical Tomography

In this work, we propose a hierarchical quantum state tomography method designed to dramatically reduce the measurement and computational complexities required for the characterization of large-scale quantum systems. Our method incrementally reconstructs the quantum state layer by layer, beginning with individual qubits and incrementally incorporating pairwise and higher-order interactions. This method exploits the sparse connectivity of current quantum systems, enabling a tunable trade-off between resource requirements and the accuracy of state reconstruction. If we relax the requirement for highly accurate reconstruction of arbitrary quantum states, the measurement and computational complexities can be reduced to polynomials. We compare the performance of hierarchical tomography with three tomography methods across three different types of random quantum states: separable, two-body correlated, and non-separable states. We demonstrate that hierarchical tomography consistently achieves higher fidelity than other tomography methods for most quantum states and is less sensitive to readout errors.