A Quantum Phase-based Comparator
Abstract
Quantum comparators decide the order of two operands. They rely on reversible logic acting on basis-encoded integers, so their width grows with the precision. We introduce the Quantum Phase-based Comparator (QPC), which compares two values carried in relative phases instead. The circuit places the two phases, entered with opposite signs, between a pair of Hadamard gates, and a fixed offset centers the interference, so that the probability of measuring zero falls below one half exactly when the first phase is the smaller. We give two implementations. With hard-coded values, the two values are written into the parameters of two phase gates, and the comparison costs one qubit and five gates. With the register-driven cascade, the values are drawn from two t-qubit registers through binary-weighted controlled-phase gates, at a cost of one qubit beyond the registers and depth linear in t; since the cascade induces each phase linearly from the register content, one circuit handles a superposition of operand pairs. The readout yields a biased coin rather than a definite bit, and we quantify the shots that a decision takes at a given phase separation. Scaling both phases by an integer widens the decision margin at no cost in width or depth, and an adaptive doubling schedule turns this amplification into a shot count logarithmic in the inverse separation.
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BibTeX
@misc{berti2026quantum,
title = {{A Quantum Phase-based Comparator}},
author = {Alessandro Berti and Alessandro Poggiali},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.25262},
eprint = {2609.25262},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.25262},
note = {CC BY-NC-SA 4.0},
}
RIS
TY - UNPB
TI - A Quantum Phase-based Comparator
AU - Alessandro Berti
AU - Alessandro Poggiali
PY - 2026
DA - 2026/09/21
PB - arXiv
DO - 10.48550/arxiv.2609.25262
UR - https://arxiv.org/abs/2609.25262
AB - Quantum comparators decide the order of two operands. They rely on reversible logic acting on basis-encoded integers, so their width grows with the precision. We introduce the Quantum Phase-based Comparator (QPC), which compares two values carried in relative phases instead. The circuit places the two phases, entered with opposite signs, between a pair of Hadamard gates, and a fixed offset centers the interference, so that the probability of measuring zero falls below one half exactly when the first phase is the smaller. We give two implementations. With hard-coded values, the two values are written into the parameters of two phase gates, and the comparison costs one qubit and five gates. With the register-driven cascade, the values are drawn from two t-qubit registers through binary-weighted controlled-phase gates, at a cost of one qubit beyond the registers and depth linear in t; since the cascade induces each phase linearly from the register content, one circuit handles a superposition of operand pairs. The readout yields a biased coin rather than a definite bit, and we quantify the shots that a decision takes at a given phase separation. Scaling both phases by an integer widens the decision margin at no cost in width or depth, and an adaptive doubling schedule turns this amplification into a shot count logarithmic in the inverse separation.
ER -