Measurement-induced non-commutativity in adaptive fermionic linear optics

Quantum Physics [Submitted on 26 Mar 2026] Measurement-induced non-commutativity in adaptive fermionic linear optics Chenfeng Cao, Yifan Tang, Jens Eisert Fermionic linear optics (FLO) with Gaussian resources is efficiently classically simulable. We show that this is no longer the case for such quantum circuits for fermions with internal degrees of freedom, equipped with mid-circuit number monitoring and classical feedforward. In our architecture, the measurement record routes the selected blocks into a fixed-order Bell-fusion pairing geometry. On the level of classical description, this implies realizing a situation in which the permutation sum no longer collapses to a single determinant or Pfaffian. Each post-selected branch expands as a signed sum of path-ordered products of typically non-commuting dressed blocks, and branch amplitudes are matrix elements of the resulting non-commutative trace polynomials. Numerically, we observe Porter-Thomas statistics as the output distribution and a rapid growth of the minimal order-respecting matrix product operator bond dimension. These results thus establish mid-circuit measurement-induced non-commutativity as a route to sampling hardness for noninteracting fermions under reasonable complexity assumptions, without introducing coherent two-body interactions into the FLO evolution. Comments: 19 pages, 7 figures Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2603.24950 [quant-ph]   (or arXiv:2603.24950v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2603.24950 Focus to learn more Submission history From: Chenfeng Cao [view email] [v1] Thu, 26 Mar 2026 02:37:23 UTC (4,008 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-03 References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)