Cutting a Wire with Non-Maximally Entangled States

Distributed quantum computing supports combining the computational power of multiple quantum devices to overcome the limitations of individual devices. Circuit cutting techniques enable the distribution of quantum computations via classical communication. These techniques involve partitioning a quantum circuit into smaller subcircuits, each containing fewer qubits. The original circuit's outcome can be replicated by executing these sub circuits on separate devices and combining their results. However, the number of circuit executions required to achieve a fixed result accuracy with circuit cutting grows exponentially with the number of cuts, posing significant costs. In contrast, quantum teleportation allows the distribution of quantum computations without an exponential increase in circuit executions. Nevertheless, each teleportation requires a pre-shared pair of maximally entangled qubits for transmitting a quantum state, and non-maximally entangled qubits cannot be used for this purpose. Addressing this, our work explores utilizing non-maximally entangled qubit pairs in wire cutting, a specific form of circuit cutting, to mitigate the associated costs. The cost of this cutting procedure reduces with the increasing degree of entanglement in the pre-shared qubit pairs. We derive the optimal sampling overhead in this context and present a wire cutting technique employing pure non-maximally entangled states that achieves this optimal sampling overhead. Hence, this offers a continuum between existing wire cutting and quantum teleportation.