This paper provides the quantum analysis of new structures by Wu et al. and the Multi-Rotating Feistel Structure introduced by Albrecht et al. for Multi-Party Computation. For New Structure III, we provide the first 13-round quantum periodic distinguisher, enhancing the previous 12-round distinguisher. For New Structure IV, we find a 9-round quantum periodic distinguisher that achieves a 3-round improvement over the best-known previous results. Then, applying the Grover-meet-Simon algorithm, we improve the quantum key-recovery attack for New Structure IV with time complexity \(2^{\frac{(r-9)k}{2}}\) , surpassing previous work and traditional quantum brute force searches. Moreover, this paper discusses the quantum security of Multi-Rotating Feistel structure. For the recommended scheme by Albrecht et al., we achieve the first 7-round quantum periodic distinguisher, where the structure achieves full diffusion in only 6 rounds. For two variants, we also find the first quantum periodic distinguishers in any rounds and 9 rounds respectively.