Symmetry-protected gates of Majorana qubits in a high-$T_c$ higher-order topological superconductor platform

Abstract

We propose a platform for braiding Majorana non-Abelian anyons based on a heterostructure between a dd-wave high-T_cTc superconductor and a quantum spin-Hall insulator. It has been recently shown that such a setup for a quantum spin-Hall insulator leads to a pair of Majorana zero modes at each corner of the sample, and thus can be regarded as a higher-order topological superconductor. We show that upon applying a Zeeman field in the region, these Majorana modes split in space and can be manipulated for braiding processes by tuning the field and pairing phase. We show that such a setup can achieve full braiding, exchanging, and arbitrary phase gates (including the \pi/8π/8 magic gates) of the Majorana zero modes, all of which are robust and protected by symmetries. As many of the ingredients of our proposed platform have been realized in recent experiments, our results provide a new route toward universal topological quantum computation.

Higher-order topological phases in crystalline and non-crystalline systems: a review

“…Several works have studied higher-order symmetry-protected topological phases in interacting fermion or boson systems which exhibit gapless corner or hinge modes [494][495][496][497][498][499][500][501][502][503][504][505][506][507][508][509][510][511]. Besides HOTIs and semimetals we have discussed, higher-order topological superconductors have also gained much attention for the Majorana modes at corners or hinges, which provide alternative platforms to realize non-Abelian braiding for topological quantum computation in the future [512][513][514][515][516][517][518].…”

Majorana corner states in an attractive quantum spin Hall insulator with opposite in-plane Zeeman energy at two sublattice sites

“…Higher-order topological (HOT) superconductors and superfluids have attracted great attentions in recent years due to their novel exhibitions of topology on the lowerdimensional boundaries including corners and hinges and potential applications in topological quantum computations [59][60][61][62][63][64]. In contrast to conventional (firstorder) topological superconductors (SCs) and superfluids (SFs), rth (r ≥ 2)-order SCs and SFs in d dimensions manifest (d − r)D (d − r-dimensional) topologically protected Majorana boundary states.…”

Majorana corner states in an attractive quantum spin Hall insulator with opposite in-plane Zeeman energy at two sublattice sites

“…Higher-order topological (HOT) superconductors (SCs) and superfluids (SFs) have attracted great attentions in recent years due to their novel exhibitions of topology on the lowerdimensional boundaries including corners and hinges and potential applications in topological quantum computations [61][62][63][64][65][66][67][68]. In contrast to conventional first-order topological SCs and SFs, rth (r ⩾ 2)-order SCs and SFs in d dimensions manifest (d − r)D (d − r-dimensional) topologically protected Majorana boundary states.…”