Quantum process tomography (QPT) is the gold standard for fully characterizing quantum processes, yet it is resource intensive. In this work, we shift our focus from global to local quantum processes, which are beneficial for practical scenarios, such as distributed quantum computing and quantum networks. We term these local processes as reduced quantum processes and present a comprehensive theory to describe them. To experimentally characterize all $k$-reduced quantum processes of an $n$-qubit quantum process, we introduce our primary method, quantum process overlapping tomography (QPOT), and compare it with two alternative approaches: ancilla QPT and parallel QPT. Suppose the target quantum process involves $T$ local interactions, each acting on $l_i$ qubits, with the total number of affected qubits satisfying $l:=\sum _{i=1}^T{l}_i\le n$. The experimental configurations required for each method are as follows: QPOT requires $2^l\times e^{\mathcal{O}(k)}\times \log (n)$ experimental configurations. Ancilla QPT requires $e^{\mathcal{O}(k)}\times \log (2n)$ experimental configurations but additionally demands $n$ ancilla qubits and the preparation of maximally entangled states. Parallel QPT requires approximately $\sum _{i=1}^{n^k}{2}^{m_i}\times {12}^k$ experimental configurations, where $m_i$ denotes the number of qubits interacting with the $i\mathrm{th}$ reduced quantum process. Among these methods, QPOT exhibits superior efficiency and broader applicability. The efficacy of our methods is confirmed through experimental demonstrations conducted on IBM hardware, aligning well with our theory.

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• Quantum algorithms & computation
• Quantum channels
• Quantum circuits
• Quantum information processing
• Quantum information theory
• Quantum tomography