Superposition-Based Abstractions for Quantum Data Encoding Verification

Abstract

Many quantum algorithms operate on classical data, by first encoding classical data into the quantum domain using quantum data encoding circuits. To be effective for large data sets, encoding circuits that operate on large data sets are required. However, as the size of the data sets increases, the encoding circuits quickly become large, complex and error prone. Errors in the encoding circuit will provide incorrect inputs to quantum algorithms, making them ineffective. To address this problem, a formal method is proposed for verification of encoding circuits. The key idea to address scalability is the use of abstractions that reduce the verification problem to bit-vector space. The major outcome of this work is that using this approach, the authors have been able to verify encoding circuits with up to 8191 qubits with very low memory (85 MB) and time (0.29s), demonstrating that the proposed approach can easily be employed to verify even much larger encoding circuits. The results are very significant because, traditional verification approaches that rely on modelling quantum circuits in Hilbert space have only demonstrated verification scalability up to 250 qubits. Also, this is the first approach to tackle the verification of quantum encoding circuits.