Reversible computing has emerged as promising technology having its applications in quantum computing, nanotechnology and optical computing. This paper presents design and analysis of reversible ripple, prefix and prefix ripple hybrid adders. Firstly an analysis and comparison of all the existing reversible ripple carry adders is presented. The reversible ripple carry adders are characterized by high quantum depth, low quantum cost and/or low garbage outputs and ancilla inputs bits. Secondly design methodology for reversible prefix adders is presented. The reversible prefix adders are characterized by low quantum depth, high quantum cost and/or high garbage outputs and ancilla inputs bits. Finally design of the proposed reversible prefix-ripple hybrid adders is presented and comparison of the different parameters of reversible ripple, prefix and prefix-ripple hybrid adders is illustrated.Reversible computing has emerged as promising technology having its applications in quantum computing, nanotechnology and optical computing. This paper presents design and analysis of reversible ripple, prefix and prefix ripple hybrid adders. Firstly an analysis and comparison of all the existing reversible ripple carry adders is presented. The reversible ripple carry adders are characterized by high quantum depth, low quantum cost and/or low garbage outputs and ancilla inputs bits. Secondly design methodology for reversible prefix adders is presented. The reversible prefix adders are characterized by low quantum depth, high quantum cost and/or high garbage outputs and ancilla inputs bits. Finally design of the proposed reversible prefix-ripple hybrid adders is presented and comparison of the different parameters of reversible ripple, prefix and prefix-ripple hybrid adders is illustrated.

IEEE Computer Society Annual Symposium on VLSIAug 1, 20126 citations

Reducing Depth of Quantum Adder using Ling Structure

Siyi Wang, Anupam Chattopadhyay

Improving the performance of quantum adder is an important technical challenge with major impact on the implementation of efficient, large-scale quantum computing. Continuing along this research direction, we propose a novel parallel-prefix quantum adder based on Ling expansion. We systematically explored classical structures for parallel-prefix adders assessing their suitability to be realized in quantum domain. Furthermore, Ling adder enforces Logical OR and large fan-out, which require innovative solutions. We addressed these challenges to realize the quantum Ling adder, which results in a T-depth of only $O\left( {\log \frac{n}{2}} \right)$ . This represents a substantial improvement over the previous quantum adders based on parallel prefix structure, which require O(log n) T-depth. We present extensive theoretical and simulation-based studies to establish our claims.Improving the performance of quantum adder is an important technical challenge with major impact on the implementation of efficient, large-scale quantum computing. Continuing along this research direction, we propose a novel parallel-prefix quantum adder based on Ling expansion. We systematically explored classical structures for parallel-prefix adders assessing their suitability to be realized in quantum domain. Furthermore, Ling adder enforces Logical OR and large fan-out, which require innovative solutions. We addressed these challenges to realize the quantum Ling adder, which results in a T-depth of only $O\left( {\log \frac{n}{2}} \right)$. This represents a substantial improvement over the previous quantum adders based on parallel prefix structure, which require O(log n) T-depth. We present extensive theoretical and simulation-based studies to establish our claims.

IFIP/IEEE International Conference on Very Large Scale IntegrationOct 16, 202314 citations

Formal Verification of Quantum Ancilla Safety

Jiqi Li, Jingyi Mei, Wang Fang +1 more

Ensuring ancilla safety is a critical correctness requirement for quantum compilation, since ancilla qubits are routinely introduced to implement complex operations with fewer gates and reduced depth. However, formally verifying this property is computationally hard due to state-space explosion in the number of qubits, particularly for dirty ancillae, which carry unknown initial states and must be restored after use. We propose an end-to-end verification-and-repair framework that rigorously addresses both clean and dirty ancilla safety. Our core contribution is a two-step reduction strategy: we first prove that verifying an $m$ -qubit dirty ancilla register decomposes into $2m$ independent clean ancilla safety checks; subsequently, we reduce each clean ancilla safety instance to an algebraic commutativity check against Pauli- $Z$ and Pauli- $X$ operators. This approach yields an efficient and naturally parallel verifier and enables actionable diagnosis by classifying violations into logic errors and phase errors. Leveraging this diagnosis, we further design lightweight repair routines that append local single-qubit rotations to eliminate a broad class of local ancilla faults. We implement the full pipeline in a prototype tool using a dual-backend architecture combining decision diagrams and weighted model counting, and validate it on diverse circuits ranging from arithmetic benchmarks to Grover's algorithm. Our experiments demonstrate scalability to thousands of qubits and show that the proposed repairs effectively improve ancilla safety while preserving circuit functionality.Ensuring ancilla safety is a critical correctness requirement for quantum compilation, since ancilla qubits are routinely introduced to implement complex operations with fewer gates and reduced depth. However, formally verifying this property is computationally hard due to state-space explosion in the number of qubits, particularly for dirty ancillae, which carry unknown initial states and must be restored after use. We propose an end-to-end verification-and-repair framework that rigorously addresses both clean and dirty ancilla safety. Our core contribution is a two-step reduction strategy: we first prove that verifying an $m$-qubit dirty ancilla register decomposes into $2m$ independent clean ancilla safety checks; subsequently, we reduce each clean ancilla safety instance to an algebraic commutativity check against Pauli-$Z$ and Pauli-$X$ operators. This approach yields an efficient and naturally parallel verifier and enables actionable diagnosis by classifying violations into logic errors and phase errors. Leveraging this diagnosis, we further design lightweight repair routines that append local single-qubit rotations to eliminate a broad class of local ancilla faults. We implement the full pipeline in a prototype tool using a dual-backend architecture combining decision diagrams and weighted model counting, and validate it on diverse circuits ranging from arithmetic benchmarks to Grover's algorithm. Our experiments demonstrate scalability to thousands of qubits and show that the proposed repairs effectively improve ancilla safety while preserving circuit functionality.

quant-pharXiv:2608.13099Lecture notes in computer scienceAug 14, 20260 citations

O\left( {\log \frac{n}{2}} \right)

. This represents a substantial improvement over the previous quantum adders based on parallel prefix structure, which require O(log n) T-depth. We present extensive theoretical and simulation-based studies to establish our claims.

m

-qubit dirty ancilla register decomposes into

2m

independent clean ancilla safety checks; subsequently, we reduce each clean ancilla safety instance to an algebraic commutativity check against Pauli-

Z

and Pauli-

X

operators. This approach yields an efficient and naturally parallel verifier and enables actionable diagnosis by classifying violations into logic errors and phase errors. Leveraging this diagnosis, we further design lightweight repair routines that append local single-qubit rotations to eliminate a broad class of local ancilla faults. We implement the full pipeline in a prototype tool using a dual-backend architecture combining decision diagrams and weighted model counting, and validate it on diverse circuits ranging from arithmetic benchmarks to Grover's algorithm. Our experiments demonstrate scalability to thousands of qubits and show that the proposed repairs effectively improve ancilla safety while preserving circuit functionality.