Formal Verification of Quantum Ancilla Safety

Quantum compilers routinely introduce temporary working space called ancilla qubits to implement complex operations with fewer gates and reduced circuit depth. These ancillae are broadly classified into clean ancillae (initialized to a known zero state) and dirty ancillae (which carry unknown, potentially entangled initial states and must be restored after use). Ensuring ancilla safety—meaning the circuit restores each ancilla to its pre-use state and leaves no residual correlation with the working register—is a critical correctness requirement. However, verifying this property is computationally hard due to state-space explosion, especially for dirty ancillae under universal quantum gates.

The authors propose a fully automated, backend-agnostic framework that reduces global ancilla safety verification to local algebraic checks. The reduction strategy proceeds in two main steps. First, the authors prove that verifying an m-qubit dirty ancilla register decomposes into 2m independent clean ancilla safety checks on two fixed, linearly independent and non-orthogonal single-qubit states (specifically, the eigenstates of Pauli-Z and Pauli-X). Second, each clean ancilla safety instance is reduced to an algebraic commutativity check against Pauli-Z and Pauli-X operators.

This algebraic formulation transforms a global state-space problem into independent operator-level checks, enabling parallel verification and actionable diagnostics. By observing commutativity violations, the verifier classifies faults into logic errors and phase errors. Guided by these diagnostic categories, the framework synthesizes lightweight repair routines that append local single-qubit rotations to eliminate common local ancilla faults while preserving circuit functionality.