Simulation of Two-Qubit Grover Algorithm in MBQC with Universal Blind Quantum Computation

Simulating the Universal Blind Quantum Computation (UBQC) protocol on gate-based platforms requires updating each measurement basis from earlier outcomes within the same execution. Existing Measurement-Based Quantum Computation (MBQC) simulation tools typically handle this feed-forward outside a single executable quantum program, so they do not natively expose the fixed-graph measurement-by-measurement update order studied here. We address this gap by implementing the flow-based Pauli corrections and a simulation-level UBQC angle-update rule as in-circuit dynamic-circuit primitives in Qiskit. Applied to two-qubit Grover's algorithm on a custom $2\times 9$ flow of 18 qubits, the resulting program achieves deterministic success under both plain MBQC and the UBQC layer. Under the depolarizing-noise setting considered here, the angle-blinding layer remains close to plain MBQC, with only a modest additional gap relative to the dominant MBQC-over-circuit overhead. To show that the construction is not tied only to this Grover-specific pattern, we also verify a $G_{2,5}$ brickwork-state fragment with representative universal-gate primitives under the same client/server blinding view. Structural blindness for a full algorithmic brickwork resource remains future work, but within this scope the construction provides a concrete dynamic-circuit route toward fixed-graph, privacy-preserving delegated-quantum-computing simulation at the protocol-update level.