Publication
Physical Review Applied 24, 044091 (2025), selected as an Editors’ Suggestion. Published on 29 October 2025.
Research Question
How can all target reduced density matrices be reconstructed with the fewest experimentally feasible parallel measurement settings, while retaining flexibility across system sizes and interaction topologies?
Optimal QOT Framework
We map quantum overlapping tomography to a minimum clique-cover problem. A binary linear program finds optimal measurement schedules, while a fast greedy iterative algorithm provides near-optimal solutions for larger systems. The same framework also supports nearest-neighbor and mixed-locality reduced density matrices.
Figure 1 - Parallel Pauli measurements recover overlapping reduced density matrices; the qubit-wise commuting matrix turns schedule design into a coverage optimization problem.
Figure 2 - Comparison with earlier QOT constructions for six to ten qubits and locality lengths from two to four.
Experimental Validation
The method was tested on two complementary platforms. Four-qubit nuclear magnetic resonance experiments reconstructed two-qubit reduced density matrices and classified nine entanglement families. Noisy superconducting processors prepared four-, six-, and nine-qubit GHZ states to evaluate measurement-sample efficiency at increasing scale.
Key Results
- Optimal QOT reduced the four-qubit measurement schedule from 15 observables to 9 and cut experimental time by approximately 40% relative to the original protocol.
- Reconstructed two-qubit reduced density matrices achieved average fidelities of approximately 99.1% for both the original and optimized schedules.
- A deep neural network classified nine four-qubit entanglement families with 95.9% accuracy in simulation and 94.7% accuracy on experimental data, without full state tomography.
- For four-, six-, and nine-qubit GHZ experiments, the original QOT required 26%, 49%, and 62% more samples, respectively, to reach comparable reconstruction quality.
Figure 3 - Reconstruction fidelity versus measurement count and neural-network classification across nine four-qubit entanglement families.
Figure 4 - Sample-cost comparison for four-, six-, and nine-qubit GHZ-state experiments.
My Contributions
- Combined optimal overlapping tomography with a deep neural network to learn nine classes of four-qubit entanglement from partial measurement data.
- Enabled entanglement-family recognition without full quantum state tomography.
- Achieved 95.9% classification accuracy on numerical simulations and 94.7% on real experimental data.
Significance
The framework makes partial tomography more efficient, scalable, and adaptable to realistic quantum-hardware constraints. It supports state characterization, local-observable estimation, Hamiltonian learning, and machine-learning-assisted analysis across multiple processor technologies.