{"work":{"id":"724b8c4b-8d57-4114-899f-4e448d2f8f33","openalex_id":null,"doi":null,"arxiv_id":"1403.2975","raw_key":null,"title":"Optimal ancilla-free Clifford+T approximation of z-rotations","authors":null,"authors_text":"N","year":2014,"venue":"quant-ph","abstract":"We consider the problem of approximating arbitrary single-qubit z-rotations by ancilla-free Clifford+T circuits, up to given epsilon. We present a fast new probabilistic algorithm for solving this problem optimally, i.e., for finding the shortest possible circuit whatsoever for the given problem instance. The algorithm requires a factoring oracle (such as a quantum computer). Even in the absence of a factoring oracle, the algorithm is still near-optimal under a mild number-theoretic hypothesis. In this case, the algorithm finds a solution of T-count m + O(log(log(1/epsilon))), where m is the T-count of the second-to-optimal solution. In the typical case, this yields circuit approximations of T-count 3log_2(1/epsilon) + O(log(log(1/epsilon))). Our algorithm is efficient in practice, and provably efficient under the above-mentioned number-theoretic hypothesis, in the sense that its expected runtime is O(polylog(1/epsilon)).","external_url":"https://arxiv.org/abs/1403.2975","cited_by_count":null,"metadata_source":"pith","metadata_fetched_at":"2026-05-24T04:56:00.249382+00:00","pith_arxiv_id":"1403.2975","created_at":"2026-05-09T06:15:39.314870+00:00","updated_at":"2026-06-05T21:23:00.469572+00:00","title_quality_ok":true,"display_title":"Optimal ancilla-free Clifford+T approximation of z-rotations","render_title":"Optimal ancilla-free Clifford+T approximation of z-rotations"},"hub":{"state":{"work_id":"724b8c4b-8d57-4114-899f-4e448d2f8f33","tier":"hub","tier_reason":"10+ Pith inbound or 1,000+ external citations","pith_inbound_count":20,"external_cited_by_count":null,"distinct_field_count":2,"first_pith_cited_at":"2024-01-29T01:28:42+00:00","last_pith_cited_at":"2026-05-13T19:03:18+00:00","author_build_status":"not_needed","summary_status":"needed","contexts_status":"needed","graph_status":"needed","ask_index_status":"not_needed","reader_status":"not_needed","recognition_status":"not_needed","updated_at":"2026-06-06T10:00:47.084067+00:00","tier_text":"hub"},"tier":"hub","role_counts":[{"context_role":"background","n":7},{"context_role":"method","n":2}],"polarity_counts":[{"context_polarity":"background","n":7},{"context_polarity":"use_method","n":2}],"runs":{},"summary":{},"graph":{},"authors":[]}}