We consider the propagation of electrons in a lattice with an anisotropic dispersion in the x -y plane (lattice constant a), such that it supports open orbits along the x axis in an out-of-plane... Show moreWe consider the propagation of electrons in a lattice with an anisotropic dispersion in the x -y plane (lattice constant a), such that it supports open orbits along the x axis in an out-of-plane magnetic field B. We show that a point source excites a "breathing mode," a state that periodically spreads out and refocuses after having propagated over a distance . pound = (eaB/h)-1 in the x direction. Unlike known magnetic focusing effects, governed by the classical cyclotron radius, this is an intrinsically quantum mechanical effect with a focal length oc h over bar. Show less
Because Majorana zero modes store quantum information nonlocally, they are protected from noise, and have been proposed as a building block for a quantum computer. We show how to use the same... Show moreBecause Majorana zero modes store quantum information nonlocally, they are protected from noise, and have been proposed as a building block for a quantum computer. We show how to use the same protection from noise to implement universal fermionic quantum computation. Our architecture requires only two Majorana modes to encode a fermionic quantum degree of freedom, compared to alternative implementations which require a minimum of four Majorana modes for a spin quantum degree of freedom. The fermionic degrees of freedom support both unitary coupled cluster variational quantum eigensolver and quantum phase estimation algorithms, proposed for quantum chemistry simulations. Because we avoid the Jordan-Wigner transformation, our scheme has a lower overhead for implementing both of these algorithms, allowing for simulation of the Trotterized Hubbard Hamiltonian in O(1) time per unitary step. We finally demonstrate magic state distillation in our fermionic architecture, giving a universal set of topologically protected fermionic quantum gates. Show less
