BPBO: Blindness-Preserving Brickwork Optimization by Certified Region Resynthesis

Abstract

Universal blind quantum computation (UBQC) hides a client's computation by using a computation-independent BFK09 brickwork graph and encoding the computation in measurement angles, which limits the use of graph-changing optimizations. We study blindness-preserving brickwork optimization (BPBO): certified local resynthesis of BFK09-compatible brickwork patterns below the blinding layer. BPBO detects one-, two-, and three-wire regions; for each candidate region it either proves a semantic floor or supplies an executable witness, and it accepts a replacement only after its branch-frame, output-frame, and blinding behavior have been checked. The optimized outputs remain standard brickwork patterns and are evaluated with a logical qubit-recycled UBQC execution stack that runs arbitrary-length patterns using n x 2 active logical qubits. The layer evidence includes a one-wire H-count floor, a two-wire CNOT-cost floor, a three-wire parity-ledger floor, a clean three-cell CCZ witness whose optimality claim is scoped to the CNOT+T phase-gadget family, and an endpoint-target three-cell CCX/Toffoli application witness; the fixed middle-target CCX case is retained as a four-cell fallback. The security statement is a compatibility result: BPBO preserves UBQC blindness at the declared optimized dimensions and remains compatible with inherited verification guarantees under explicit test-round conditions, without introducing a new trap-soundness theorem. On Bell/CX, Grover-2, endpoint-Toffoli, and Grover-3 evaluation cases, BPBO demonstrates certified local reductions; in the largest case, Grover-3, the materialized pattern is reduced from 3 x 725 to 3 x 98 while preserving the expected marked-state statistics up to sampling noise.