  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 subcircuits 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.
