Noise-Induced Topology in Chiral Quantum Walks

Abstract

Noise typically destroys quantum coherence and washes out transport phenomena that rely on interference. Chiral quantum walks are a case in point: a particle hopping on a lattice threaded by a magnetic flux can spread asymmetrically due to interference between paths, an asymmetry that noise is expected to erase. Remarkably, we find that the most ubiquitous noise -- random fluctuations of on-site energies (dephasing) -- instead renders this asymmetry topologically robust. The density profile develops a skewness that grows in time while its center stays fixed, and in a finite chain the late-time relaxation modes pile up at one edge: a skin effect lacking the drift of conventional non-Hermitian skin effects. With multiple sites per unit cell, the dephasing strength alone can cause a topological phase transition, reversing the asymmetry. On a flux ladder with noisy rung hopping, the noise causes a drift of rung coherences, a quantum ratchet with no classical counterpart. Underlying these effects, the noise-averaged dynamics is an interacting (generically non-integrable) Lindbladian that remains analytically tractable. The modes governing late-time relaxation are bound states of the noise-induced interaction and form a band with a point gap, absent both without noise and under postselection, whose winding number fixes the direction of the asymmetry. These effects are within reach of several experimental platforms, including synthetic lattices, superconducting qubits, and optical lattices.