A rigorous proof is presented that in particle-number-conserving Hamiltonians, single-particle quasiparticles always carry quantized charge and inertial mass identical to those of the original particles. It follows that Bogoliubov zero modes in vortex cores or at the edges of superconductors cannot be their own antiparticles capable of braiding quantum information. Thus, the actively pursued approach to quantum computing based on Majorana zero modes requires serious reconsideration. Additionally, we expose conceptual difficulties in preparing and controlling braidable quantum states via physical thermalization or slow external fields. These fundamental results should revive the long-standing search for a particle-number-conserving theory of superconductivity and superfluidity without the fictitious breaking of global U(1) symmetry.
Physicists have long sought particles that are their own antiparticles — Majorana fermions. They were supposed to be perfect 'mirror twins', immune to interference. Such states were suspected in superconductors — materials where current flows without resistance. It was thought that 'braiding' their trajectories would protect a quantum computer from errors.
However, a rigorous proof shatters this mirror. In a system with a fixed number of particles, any excitation carries the same charge as ordinary electrons. These states are not mysterious twins, but the same old electron blobs. Even the theory of superconductivity by Bardeen, Cooper, and Schrieffer was originally built on pairs, not on solitary 'twins'.
Now not only quantum computing is in question, but the very completeness of superconductivity theory. Perhaps a new approach must be sought that wouldn't violate particle number conservation. This is also important for understanding superconductivity inside neutron stars. And attempts to create Majorana modes by heating or magnetic fields are akin to hoping to assemble a puzzle by shaking the box — chaos destroys the delicate order.
🎯 The idea of using Majorana modes for quantum computing belongs to [scientist:Alexei Kitaev]Alexei Kitaev[/scientist] (2001). He showed how their 'braiding' could work as logical operations.