{"paper":{"title":"Linear-Time T-Gate Optimization via Random Abstraction","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"A linear-time randomized algorithm optimizes T gates by propagating constant-width bitstrings to approximate reachable quantum states.","cross_cats":["quant-ph"],"primary_cat":"cs.PL","authors_text":"Aws Albarghouthi","submitted_at":"2026-05-13T15:54:13Z","abstract_excerpt":"Quantum computers promise exponential speedups for problems in cryptography, chemistry, and optimization. Realizing this promise requires fault tolerance: physical qubits are noisy, so logical qubits must be encoded redundantly across many physical ones using quantum error-correcting codes. In most practical fault-tolerance schemes, T gates cannot be implemented transversally and instead require costly magic-state distillation protocols involving a complex set of operations. As a result, T-gate count can dominate the resource budget of large-scale quantum computations, making T-count minimizat"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We give a linear-time randomized algorithm for phase folding, based on a novel randomized static analysis. Our static analysis soundly approximates the set of reachable quantum states with an arbitrarily high probability. Our key insight is a static analysis that does not track symbolic expressions, but propagates constant-width bitstrings down the circuit.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The randomized bitstring propagation soundly approximates the reachable quantum states with arbitrarily high probability for the purpose of phase folding.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"A randomized linear-time phase-folding algorithm using constant-width bitstring abstraction optimizes T-count in quantum circuits orders of magnitude faster than prior tools while achieving comparable reductions.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"A linear-time randomized algorithm optimizes T gates by propagating constant-width bitstrings to approximate reachable quantum states.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"57db9aff058b6d81723cf42e4a24709f765e9c285b5bf623a781241e1fb4d45b"},"source":{"id":"2605.13929","kind":"arxiv","version":1},"verdict":{"id":"3fc02628-c62f-4d40-9ab2-23d5842b5ef5","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-15T02:50:05.767028Z","strongest_claim":"We give a linear-time randomized algorithm for phase folding, based on a novel randomized static analysis. Our static analysis soundly approximates the set of reachable quantum states with an arbitrarily high probability. Our key insight is a static analysis that does not track symbolic expressions, but propagates constant-width bitstrings down the circuit.","one_line_summary":"A randomized linear-time phase-folding algorithm using constant-width bitstring abstraction optimizes T-count in quantum circuits orders of magnitude faster than prior tools while achieving comparable reductions.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The randomized bitstring propagation soundly approximates the reachable quantum states with arbitrarily high probability for the purpose of phase folding.","pith_extraction_headline":"A linear-time randomized algorithm optimizes T gates by propagating constant-width bitstrings to approximate reachable quantum states."},"references":{"count":43,"sample":[{"doi":"10.4204/eptcs.287.1","year":2018,"title":"In: Selinger, P., Chiribella, G","work_id":"af9b3619-04d2-4750-af11-64bdda3f82b4","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"10.1145/3704873","year":2025,"title":"Matthew Amy and Joseph Lunderville. 2025. Linear and non-linear relational analyses for quantum program optimization.Proceedings of the ACM on Programming Languages9, POPL, Article 37 (2025), 1072–110","work_id":"52497a86-2ca3-415d-884a-5974d10b68af","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"10.1109/tcad.2014.2341953","year":2014,"title":"Matthew Amy, Dmitri Maslov, and Michele Mosca. 2014. Polynomial-time T-depth optimization of Clifford+T circuits via matroid partitioning.IEEE Transactions on Computer-Aided Design of Integrated Circu","work_id":"93a365ce-af16-4b36-bfe5-997e1b8cc48b","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"10.1109/tit.2019.2906374","year":2019,"title":"T-count optimization and reed–muller codes.IEEE Transactions on Information Theory, 65(8):4771–4784","work_id":"851f60fa-2d87-458e-b610-3dc8741e091f","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"10.22331/q-2023-11-20-1185","year":2023,"title":"Benjamin Bichsel, Anouk Paradis, Maximilian Baader, and Martin Vechev. 2023. Abstraqt: Analysis of Quantum Circuits via Abstract Stabilizer Simulation.Quantum7 (2023), 1185. doi:10.22331/q-2023-11-20-","work_id":"baca74ee-3f94-4be2-b937-dba070a57dde","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":43,"snapshot_sha256":"5fe084a9ff3c15a3d8a176e0283930c2e56d5e3401915ed701852cabb7e9ca56","internal_anchors":4},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}