  Current and imminent quantum hardware lacks reliability and applicability due
to noise and limited qubit counts. Quantum circuit cutting -- a technique
dividing large quantum circuits into smaller subcircuits with sizes appropriate
for the limited quantum resource at hand -- is used to mitigate these problems.
However, classical postprocessing involved in circuit cutting generally grows
exponentially with the number of cuts and quantum counts. This article
introduces the notion of approximate circuit reconstruction. Using a
sampling-based method like Markov Chain Monte Carlo (MCMC), we
probabilistically select bit strings of high probability upon reconstruction.
This avoids excessive calculations when reconstructing the full probability
distribution. Our results show that such a sampling-based postprocessing method
holds great potential for fast and reliable circuit reconstruction in the NISQ
era and beyond.
