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Measurement-induced non-commutativity in adaptive fermionic linear optics

arXiv Quantum Physics
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⚡ Quantum Brief
Researchers Chenfeng Cao, Yifan Tang, and Jens Eisert demonstrate that adaptive fermionic linear optics (FLO) with mid-circuit measurements and classical feedforward can achieve sampling hardness, overcoming prior classical simulability limits. The team shows that adding internal degrees of freedom to noninteracting fermions—paired with number monitoring—disrupts the classical efficiency of FLO, forcing non-commutative operations that resist deterministic simulation. Their architecture uses measurement records to route quantum blocks into fixed-order Bell-fusion pairings, causing permutation sums to expand into complex, non-commuting trace polynomials rather than simple determinants or Pfaffians. Numerical results reveal Porter-Thomas output distributions and exponential growth in matrix product operator bond dimensions, signaling quantum advantage without introducing two-body interactions. This work establishes mid-circuit measurements as a viable path to hardness in fermionic systems, challenging classical algorithms under standard complexity assumptions.
Measurement-induced non-commutativity in adaptive fermionic linear optics

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Quantum Physics arXiv:2603.24950 (quant-ph) [Submitted on 26 Mar 2026] Title:Measurement-induced non-commutativity in adaptive fermionic linear optics Authors:Chenfeng Cao, Yifan Tang, Jens Eisert View a PDF of the paper titled Measurement-induced non-commutativity in adaptive fermionic linear optics, by Chenfeng Cao and 2 other authors View PDF HTML (experimental) Abstract: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: 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 arXiv-issued DOI via DataCite (pending registration) Submission history From: Chenfeng Cao [view email] [v1] Thu, 26 Mar 2026 02:37:23 UTC (4,008 KB) Full-text links: Access Paper: View a PDF of the paper titled Measurement-induced non-commutativity in adaptive fermionic linear optics, by Chenfeng Cao and 2 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-03 References & Citations INSPIRE HEP NASA ADSGoogle Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: 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 Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) Links to Code Toggle Papers with Code (What is Papers with Code?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos Demos Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower (What are Influence Flowers?) Core recommender toggle CORE Recommender (What is CORE?) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs. Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)

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Source: arXiv Quantum Physics