Parity-Resolved Many-Body Kinetics of a Topological Qubit under Nonequilibrium Phonon Pulses

Abstract

Phonon bursts from ionizing radiation cause correlated errors in superconducting quantum processors. We study prescribed nonequilibrium phonon pulses in a Majorana qubit formed by two $2\,μ\mathrm{m}$ proximitized nanowires. Combining the lattice Lutchyn--Oreg model, microscopic electron--phonon coupling, and parity-resolved many-body dynamics, we track excitation, relaxation, and logical coherence. Without quasiparticle escape, recombination restores the initial Majorana occupations in about 130 ns, while phonons exchanged during excitation and recovery can retain logical-state information, leaving permanent coherence loss. For mirror-symmetric wires, the fractional coherence loss per wire is 0.75--1.0 times the excitation probability averaged over the two logical states, even at zero Majorana splitting; breaking mirror symmetry can suppress dephasing at small splitting. Factorized Boltzmann kinetics neglects quasiparticle correlations and overestimates residual parity flips. At equal deposited energy density, phonon spectra yield different excitation probabilities and coherence losses. Comparisons with Kitaev chains matched to the wire's gap and Majorana decay length reveal that low electron density suppresses excitation by energetic phonons, whereas hard-wall boundaries in a high-density control increase excitation efficiency by a factor of $5\times10^4$ relative to the wire for pulses centered at 1 meV. Magnetic-field and chemical-potential tuning yield different phonon sensitivities at the same bulk gap through changes in spin and electron--hole structure. Including hybrid states' semiconductor weights reduces near-threshold excitation rates fourfold when the tunnel coupling equals the parent superconducting gap. Our framework connects phonon spectra to leakage, poisoning, and coherence loss to guide Majorana-device design.

The paper asks how nonequilibrium phonon bursts affect leakage, parity poisoning, and coherence in a four-Majorana qubit formed by two proximitized semiconductor nanowires. It combines lattice Lutchyn–Oreg eigenstates, microscopic deformation-potential and piezoelectric transition rates, configuration-resolved Pauli kinetics, and selected many-body coherences. Prescribed phonon spectra are compared at equal excess energy density; matched Kitaev chains test electronic-structure dependence. For reference $2\,\mu\mathrm{m}$ wires with a $0.126$-meV bulk gap, correlated quasiparticles recombine with a mean post-pulse return time of approximately $130$ ns. Without quasiparticle exchange, parity conservation restores the initial Majorana occupation once the bulk empties. Factorized Boltzmann kinetics instead predicts spurious residual occupation approaching twice the weak-pulse excitation probability. Population recovery does not restore coherence: across seven spectra, permanent fractional coherence loss per wire is $0.75$–$1.00$ times the branch-averaged excitation probability. A reflection-symmetry argument gives orthogonal phonon profiles even at zero Majorana splitting; symmetry breaking permits partial coherence recovery below the excited-state linewidth. Excitation depends strongly on spectrum and wave functions, not just gap: near-threshold pulses are most efficient, while low density suppresses energetic-phonon absorption. Field and chemical-potential tuning to the same $25\,\mu\mathrm{eV}$ gap produce substantially different sensitivities. Semiconductor-weight normalization reduces near-threshold rates approximately fourfold when tunnel coupling equals the parent gap. The treatment assumes prescribed isotropic phonons and Born–Markov dynamics. Stated extensions include shell coupling and continuum transitions, realistic phonon transport and confinement, multiband/orbital effects, charging energy, shared-bath interwire correlations, back-action, and microscopic escape channels.