Tatsuhiko N. Ikeda

Quantum computers are believed to solve a class of computational problems that are based on modular arithmetic faster than classical computers. Among the arithmetic building blocks, comparison of integer pairs is a primitive. Here we report its demonstration in the Reimei quantum computer at RIKEN, whose trapped-ion architecture provides all-to-all qubit connectivity together with high gate fidelities. We observe high success probabilities for bit widths n = 3, 5, 7, and 9: Under a conventional output-only success criterion we obtain 95% at n=9; under a stricter criterion additionally requiring the ancilla to be correct, the success is 69% at n=9. These results demonstrate reliable quantum comparison at scales far beyond those previously achieved experimentally, not only for comparators but also in the broader context of quantum arithmetic circuits.

Prethermal discrete time crystals (DTCs) are a novel phase of periodically driven matter that exhibits robust subharmonic oscillations without requiring disorder. However, previous realizations of prethermal DTCs have relied on the presence of polarization, either spontaneous or induced. Here, we introduce a new class of prethermal DTCs termed ``unpolarized prethermal discrete time crystals'' (UPDTCs) that arise without any uniform/staggered polarization and propose an experiment to observe them in current trapped-ion quantum simulators. By studying a model of trapped ions using a quantum circuit simulator, we demonstrate that robust period-doubled dynamics can persist in the autocorrelation function of the staggered magnetization, even though its expectation value does not exhibit such dynamics. The period-doubled dynamics is not explained by the classical picture of flipping spins but by quantum fluctuations. We establish that UPDTCs are exponentially long-lived in the high-frequency driving regime, a hallmark of prethermalization. These results expand the known phenomenology and mechanism of prethermal time crystals and underscore the role of quantum effects in stabilizing novel nonequilibrium phases.