Joint Wire Cutting with Non-Maximally Entangled States

Distributed quantum computing leverages multiple quantum devices collectively to perform computations exceeding each device's capabilities. A currently studied technique to enable this distributed approach is wire cutting, which decomposes a quantum circuit into smaller subcircuits by cutting connecting wires. These subcircuits can be executed on distributed devices, and their results are then classically combined to reconstruct the original computation's result. However, wire cutting requires additional circuit executions to preserve result accuracy, with their number growing exponentially with each cut. Thus, minimizing this sampling overhead is crucial for reducing execution time. Employing shared non-maximally entangled (NME) states between distributed devices reduces this overhead for single wire cuts, approaching ideal teleportation with maximally entangled states. Extending this approach to jointly cutting multiple wires using NME states remained unexplored. This study addresses this gap by investigating the use of NME states for joint wire cuts, aiming to reduce the sampling overhead further. The three main contributions include (i) determining the minimal sampling overhead for this scenario, (ii) analyzing the overhead when using composite NME states constructed from smaller NME states, and (iii) introducing a wire cutting technique that achieves the optimal sampling overhead with pure NME states, advancing toward wire cutting with arbitrary NME states.