Rotational Abstractions for Verification of Quantum Fourier Transform Circuits

TL;DR

This paper introduces a scalable formal verification method for Quantum Fourier Transform circuits that reduces the problem to bit-vector logic, enabling verification of circuits with up to 10,000 qubits and 50 million gates.

Contribution

The paper presents a novel abstraction-based verification approach for QFT circuits that significantly improves scalability compared to previous methods.

Findings

Verified QFT circuits with up to 10,000 qubits

Successfully handled 50 million quantum gates

Achieved a major scalability breakthrough in quantum circuit verification

Abstract

With the race to build large-scale quantum computers and efforts to exploit quantum algorithms for efficient problem solving in science and engineering disciplines, the requirement to have efficient and scalable verification methods are of vital importance. We propose a novel formal verification method that is targeted at Quantum Fourier Transform (QFT) circuits. QFT is a fundamental quantum algorithm that forms the basis of many quantum computing applications. The verification method employs abstractions of quantum gates used in QFT that leads to a reduction of the verification problem from Hilbert space to the quantifier free logic of bit-vectors. Very efficient decision procedures are available to reason about bit-vectors. Therefore, our method is able to scale up to the verification of QFT circuits with 10,000 qubits and 50 million quantum gates, providing a meteoric advance in the size of QFT circuits thus far verified using formal verification methods.