Quantum Uncomputation of Clean and Dirty Ancilla Qubits

2026-08-10

AI Summary

This work addresses a critical limitation in existing quantum circuit uncomputation methods, which support only clean ancilla qubits and cannot handle the more general case of dirty ancillas. The study establishes, for the first time, that deciding the existence of an uncomputation sequence is coNP-hard. To overcome this challenge, the authors propose a unified framework capable of handling both clean and dirty ancilla qubits, comprising two complementary approaches: a rewrite-based normalization algorithm (RwUn) and a template-based Store-Use pattern inference system (TpUn). Implemented as a prototype in Qiskit, the framework demonstrates strong empirical performance: RwUn achieves 100% coverage on benchmarks with complex dependencies, doubles the coverage on random classical circuits compared to prior methods, and attains approximately 50% coverage on random quantum circuits where existing techniques fail entirely.

Abstract

Automatic uncomputation aims to provide programming-language-level support to facilitate the correct and safe use of ancilla qubits in quantum computing, but efforts have only been made for clean ancillas, leaving dirty ancillas unexplored. We present a unified formalization of the uncomputation of both clean and dirty ancillas. For the first time, we prove that checking the existence of uncomputation is coNP-hard. We introduce two complementary synthesis-oriented existence-checking methods: a rewrite-based normalization algorithm (RwUn) and a template-based reasoning system (TpUn) that guarantees uncomputation through structured Store-Use patterns. We implement prototypes of both methods in Qiskit and Python. Compared to the state-of-the-art Reqomp~\cite{reqomp}, RwUn achieves 100% coverage on practical complex-dependency benchmarks, twice the coverage on random classical circuits, and about 50% coverage on random quantum circuits beyond the scope of existing methods, demonstrating broader applicability.

Problem

• quantum uncomputation
• ancilla qubits
• dirty ancillas
• clean ancillas
• coNP-hard

Innovation

• quantum uncomputation
• ancilla qubits
• coNP-hard
• rewrite-based normalization
• template-based reasoning