A method of providing a topological quantum computing operation, comprising: providing a first quasiparticle and a second quasiparticle respectively localized at second and first ends of a first topological wire segment of a nanowire wherein the first topological wire segment is defined by a first chemical potential; providing a third quasiparticle and a fourth quasiparticle respectively localized at first and second ends of a second topological wire segment of the nanowire wherein the second topological wire segment is defined by a second chemical potential; forming a potential well in a nontopological phase region of the nanowire that extends between the first topological wire segment and the second topological wire segment; turning the nontopological phase region that extends between the second and the third quasiparticles into a topological phase region that extends between the second and the third quasiparticles while maintaining the potential well wherein forming the potential well in the nontopological phase region that extends between the second and the third quasiparticles and turning the nontopological phase region that extends between the second and the third quasiparticles into the topological phase region that extends between the second and the third quasiparticles comprises adjusting an array of gates to drive phase changes in the nanowire that comprises the nontopological phase regions and the first and second topological wire segments; fusing, in the potential well, the second and the third quasiparticles together in a manner that traps a fusion outcome quasiparticle resulting from the fusion of the second and the third quasiparticles in the potential well wherein the fusion outcome quasiparticle is a first fusion outcome quasiparticle; using a measuring device measuring the first fusion outcome quasiparticle; and using the array of gates: bringing the potential well having the first fusion outcome quasiparticle trapped therein and the second end of the first topological wire segment toward each other; and fusing the first quasiparticle and the first fusion outcome quasiparticle together to yield a second fusion outcome quasiparticle. providing a first quasiparticle and a second quasiparticle respectively localized at second and first ends of a first topological wire segment of a nanowire wherein the first topological wire segment is defined by a first chemical potential; providing a third quasiparticle and a fourth quasiparticle respectively localized at first and second ends of a second topological wire segment of the nanowire wherein the second topological wire segment is defined by a second chemical potential; forming a potential well in a nontopological phase region of the nanowire that extends between the first topological wire segment and the second topological wire segment; turning the nontopological phase region that extends between the second and the third quasiparticles into a topological phase region that extends between the second and the third quasiparticles while maintaining the potential well wherein forming the potential well in the nontopological phase region that extends between the second and the third quasiparticles and turning the nontopological phase region that extends between the second and the third quasiparticles into the topological phase region that extends between the second and the third quasiparticles comprises adjusting an array of gates to drive phase changes in the nanowire that comprises the nontopological phase regions and the first and second topological wire segments; fusing, in the potential well, the second and the third quasiparticles together in a manner that traps a fusion outcome quasiparticle resulting from the fusion of the second and the third quasiparticles in the potential well wherein the fusion outcome quasiparticle is a first fusion outcome quasiparticle; using a measuring device measuring the first fusion outcome quasiparticle; and using the array of gates: bringing the potential well having the first fusion outcome quasiparticle trapped therein and the second end of the first topological wire segment toward each other; and fusing the first quasiparticle and the first fusion outcome quasiparticle together to yield a second fusion outcome quasiparticle. bringing the potential well having the first fusion outcome quasiparticle trapped therein and the second end of the first topological wire segment toward each other; and fusing the first quasiparticle and the first fusion outcome quasiparticle together to yield a second fusion outcome quasiparticle.