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A way to apply every needed operation to the stored qubits without giving back the qubit savings is still missing in practice.","posed_since":"","precise":"For a constant-rate qLDPC family with distance d, give a fault-tolerant implementation of a universal logical gate set (all logical Clifford gates plus one non-Clifford gate on any chosen logical qubits) that uses O(n) ancilla qubits, has space-time cost per logical gate O(d polylog d), and has a threshold under circuit-level noise. Candidate ingredients include code surgery, code automorphisms and codes with transversal CCZ.","problem_ref":null,"references":"","settled_by":"An explicit gate scheme with stated overhead and a threshold proof or convincing circuit-level simulation at relevant sizes.","status_note":"Several 2024-2026 schemes cover parts of the gate set at moderate overhead.","title":"Low-overhead universal logical gates on constant-rate qLDPC 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