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Quantum Bit String Comparators (QBSC) operate on two sequences of n-qubits,enabling the determination of their relationships, such as equality, greaterthan, or less than. This is analogous to the way conditional statements areused in programming languages. Consequently, QBSCs play a crucial role invarious algorithms that can be executed or adapted for quantum computers. Thedevelopment of efficient and generalized comparators for any $n$-qubit lengthhas long posed a challenge, as they have a high-cost footprint and lead toquantum delays. Comparators that are efficient are associated with inputs offixed length. As a result, comparators without a generalized circuit cannot beemployed at a higher level, though they are well-suited for problems withlimited size requirements. In this paper, we introduce a generalized design forthe comparison of two $n$-qubit logic states using just two ancillary bits. Thedesign is examined on the basis of qubit requirements, ancillary bit usage,quantum cost, quantum delay, gate operations, and circuit complexity, and istested comprehensively on various input lengths. The work allows for sufficientflexibility in the design of quantum algorithms, which can accelerate quantumalgorithm development.

A Generalized Space-Efficient Algorithm for Quantum Bit String Comparators