Perfect chiral circulation, the sequential transfer of a quantum state around a closed loop with unit fidelity, has been achieved in specific few-site systems, yet the universal physical conditions underlying this phenomenon remain unclear. We prove that discrete translational invariance and an equidistant energy spectrum together constitute the necessary and sufficient conditions for perfect chiral circulation. With this criterion established, an exact closed-form Hamiltonian valid for arbitrary $N$-site rings naturally follows. In the minimal three-site ring, we demonstrate two physically distinct realizations: Floquet engineering of a driven open chain that restores translational invariance by equalizing the couplings and correlated doublon dynamics in an anyon-Hubbard model where fractional statistics intrinsically provide the synthetic flux that renders the spectrum equidistant. Our results establish unified physical criteria for perfect chiral circulation, with potential applications in diverse platforms such as superconducting circuits, cold atoms, classical electrical circuits, and photonic synthetic dimensions, and further extend this framework beyond spatial transport by incorporating internal degrees of freedom such as spin.

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• Cold atoms & matter waves
• Quantum control
• Transport phenomena
• Floquet systems
• Quantum rings
• Hubbard model