Quantum process tomography is a fundamental tool for characterizing unknown quantum operations in quantum computing, communication, and metrology. For a general quantum channel on a d-dimensional Hilbert space, the number of independent real parameters scales as O(d⁴), leading to rapidly increasing measurement resources. If the process is unitary, only d²-1 independent real parameters remain after removing the global phase. Existing adaptive schemes have reduced the required number of independent measurement data for unitary quantum process tomography to d² + d-1, but a gap still remains from the parameter-counting reference lower bound d²-1.
We propose an adaptive quantum process tomography scheme for unitary processes to approach this bound. The method is formulated in the framework of entanglement-assisted quantum process tomography. By applying the unknown unitary operation to one subsystem of a maximally entangled state, the process characterization is converted into the reconstruction of the corresponding Choi pure state. In the ideal noiseless model, each measured projection probability is regarded as one independent datum, and all historical probabilities constrain a candidate unitary set.
The key innovation is the direct adaptive optimization of probe states. Instead of selecting the next probe state from a predetermined finite set, we search for it in the experimentally accessible probe-state space induced by unitary operations. For each candidate probe state, the range of the predicted projection probabilities over the current candidate set is used as a distinguishability measure. The probe state with the largest probability range is selected, so that the next measurement can amplify the difference among the remaining candidates and effciently shrink the feasible set.
Numerical simulations for different dimensions, target unitary processes, and random initial conditions show that the proposed strategy steadily improves the reconstruction fidelity. Within the tested dimensions and accuracy thresholds, stable high-fidelity reconstruction can be achieved with about d² independent measurement data, close to d²-1. Statistical comparisons around d²-1, d², and d² + 1 indicate that d² provides more stable high-precision reconstruction in the tested cases. A representative d = 8 result also supports the convergence trend in a higher-dimensional case. This work provides a structurally clear and numerically supported adaptive approach for effcient unitary quantum process tomography near the minimal-data regime, while finite-sample and noisy scenarios remain for future study.