{"paper":{"title":"Optimal and improved gate decompositions for accelerated classical simulation of near-Gaussian fermionic circuits","arxiv_id":"2603.18869","primary_cat":"quant-ph","submitted_at":"2026-03-19T13:13:41+00:00","version_compiled":"v2"},"notice":"Every quoted sentence is the authors' text from the arXiv listing abstract. Labels and probabilities are the outputs of classifier-1.13.0 on the question bank abstract-p1-20260923, exactly as returned. No sentence in this record was written by a language model.","schema":"pith.compiled-record/v0","status":"compiled","abstract":{"source":"arXiv listing abstract v2","sentences":[{"i":0,"p":1.0,"id":"s0","own":false,"role":"background","text":"Fermionic Gaussian circuits can be simulated efficiently on a classical computer, but become universal when supplemented with non-Gaussian operations.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.05,"main_claim_p":0.04,"quantitative":false,"quantitative_p":0.25,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.0,"background":1.0,"limitation":0.0,"future_work":0.0,"contribution":0.0,"interpretation":0.0}},{"i":1,"p":0.99,"id":"s1","own":false,"role":"background","text":"Similar to stabilizer circuits augmented with non-stabilizer resources, these non-Gaussian circuits can be simulated classically using rank- or extent-based methods.","hedge":{"p":0.98,"label":"asserted"},"own_p":0.05,"main_claim_p":0.03,"quantitative":false,"quantitative_p":0.44,"role_probabilities":{"gap":0.0,"method":0.01,"result":0.0,"background":0.99,"limitation":0.0,"future_work":0.0,"contribution":0.0,"interpretation":0.0}},{"i":2,"p":0.97,"id":"s2","own":false,"role":"background","text":"These methods decompose non-Gaussian states or operations into Gaussian ones, with runtimes that scale polynomially with measures of non-Gaussianity such as the rank and the extent -- quantities that typically grow exponentially with the number of non-Gaussian resources.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.06,"main_claim_p":0.05,"quantitative":true,"quantitative_p":0.7,"role_probabilities":{"gap":0.0,"method":0.03,"result":0.0,"background":0.97,"limitation":0.0,"future_work":0.0,"contribution":0.0,"interpretation":0.0}},{"i":3,"p":0.7,"id":"s3","own":false,"role":"gap","text":"Current fermionic rank- and extent-based simulators have mostly been limited to Gaussian circuits with magic-state injection.","hedge":{"p":0.98,"label":"asserted"},"own_p":0.04,"main_claim_p":0.02,"quantitative":false,"quantitative_p":0.13,"role_probabilities":{"gap":0.7,"method":0.0,"result":0.0,"background":0.26,"limitation":0.04,"future_work":0.0,"contribution":0.0,"interpretation":0.0}},{"i":4,"p":1.0,"id":"s4","own":false,"role":"gap","text":"Extending them to mixed states and non-unitary channels has been hindered by the lack of known extent-optimized decompositions for physically relevant gates and noisy channels.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.05,"main_claim_p":0.03,"quantitative":false,"quantitative_p":0.11,"role_probabilities":{"gap":1.0,"method":0.0,"result":0.0,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.0,"interpretation":0.0}},{"i":5,"p":0.92,"id":"s5","own":false,"role":"contribution","text":"In this work, we address this gap.","hedge":{"p":0.79,"label":"asserted"},"own_p":0.35,"main_claim_p":0.03,"quantitative":false,"quantitative_p":0.02,"role_probabilities":{"gap":0.06,"method":0.0,"result":0.0,"background":0.02,"limitation":0.0,"future_work":0.0,"contribution":0.92,"interpretation":0.0}},{"i":6,"p":0.93,"id":"s6","own":true,"role":"contribution","text":"First, we derive analytic decompositions for key non-Gaussian gates and channels, including decompositions for arbitrary two-qubit fermionic gates which are provably optimal for diagonal gates or those acting on Jordan-Wigner-adjacent qubit pairs.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.98,"main_claim_p":0.19,"quantitative":false,"quantitative_p":0.33,"role_probabilities":{"gap":0.0,"method":0.05,"result":0.02,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.93,"interpretation":0.0}},{"i":7,"p":0.94,"id":"s7","own":true,"role":"result","text":"Second, we show that stochastic Pauli noise can reduce the effective extent of non-Gaussian rotation gates, but that fermionic magic is substantially more robust to such noise than stabilizer magic.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.92,"main_claim_p":0.13,"quantitative":true,"quantitative_p":0.93,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.94,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.06,"interpretation":0.0}},{"i":8,"p":0.81,"id":"s8","own":true,"role":"contribution","text":"Finally, we demonstrate how these decompositions can accelerate classical sampling from the output distribution of a quantum circuit.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.94,"main_claim_p":0.23,"quantitative":false,"quantitative_p":0.05,"role_probabilities":{"gap":0.0,"method":0.01,"result":0.18,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.81,"interpretation":0.0}},{"i":9,"p":0.57,"id":"s9","own":true,"role":"method","text":"This involves a generalization of existing sparsification methods, previously limited to convex-unitary channels, to circuits involving intermediate measurements and feed-forward.","hedge":{"p":0.99,"label":"asserted"},"own_p":0.8,"main_claim_p":0.06,"quantitative":false,"quantitative_p":0.1,"role_probabilities":{"gap":0.0,"method":0.57,"result":0.0,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.43,"interpretation":0.0}},{"i":10,"p":0.88,"id":"s10","own":true,"role":"result","text":"Our decompositions also yield speedups for emulating noisy Pauli rotations with quasiprobability simulators in the large-angle/arbitrary-strength-noise and small-angle/low-noise parameter regimes.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.9,"main_claim_p":0.12,"quantitative":false,"quantitative_p":0.4,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.88,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.12,"interpretation":0.0}}]},"compiled":{"main_claim":{"p":0.9,"text":"Finally, we demonstrate how these decompositions can 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