  Quantum circuit cutting has emerged as a promising method for simulating
large quantum circuits using a collection of small quantum machines. Running
low-qubit "circuit fragments" not only overcomes the size limitation of
near-term hardware, but it also increases the fidelity of the simulation.
However, reconstructing measurement statistics requires computational resources
- both classical and quantum - that grow exponentially with the number of cuts.
In this manuscript, we introduce the concept of a golden cutting point, which
identifies unnecessary basis components during reconstruction and avoids
related down-stream computation. We propose a hypothesis-testing scheme for
identifying golden cutting points, and provide robustness results in the case
of the test failing with low probability. Lastly, we demonstrate the
applicability of our method on Qiskit's Aer simulator and observe a reduced
wall time from identifying and avoiding obsolete measurements.
