Doubly optimal parallel wire cutting without ancilla qubits

A restriction in the quality and quantity of available qubits presents a substantial obstacle to the application of near-term and early fault-tolerant quantum computers in practical tasks. To confront this challenge, some techniques for effectively augmenting the system size through classical processing have been proposed; one promising approach is quantum circuit cutting. The main idea of quantum circuit cutting is to decompose an original circuit into smaller sub-circuits and combine outputs from these sub-circuits to recover the original output. Although this approach enables us to simulate larger quantum circuits beyond physically available circuits, it needs classical overheads quantified by the two metrics: the sampling overhead in the number of measurements to reconstruct the original output, and the number of channels in the decomposition. Thus, it is crucial to devise a decomposition method that minimizes both of these metrics, thereby reducing the overall execution time. This paper studies the problem of decomposing the parallel $n$-qubit identity channel, i.e., $n$-parallel wire cutting, into a set of local operations and classical communication; then we give an optimal wire-cutting method comprised of channels based on mutually unbiased bases, that achieves minimal overheads in both the sampling overhead and the number of channels, without ancilla qubits. This is in stark contrast to the existing method that achieves the optimal sampling overhead yet with ancilla qubits. Moreover, we derive a tight lower bound of the number of channels in parallel wire cutting without ancilla systems and show that only our method achieves this lower bound among the existing methods. Notably, our method shows an exponential improvement in the number of channels, compared to the aforementioned ancilla-assisted method that achieves optimal sampling overhead.