Research on one long-studied path to topological quantum computing raises new questions

For decades, physicists have speculated that it may be possible to protect quantum computation “topologically” through the use of certain particles whose movements around each other form quantum “braids.” These braids would offer greater stability than is possible in other quantum computing approaches. Therefore, they could, at least partially, protect the computation from “the ubiquitous decoherence which is the bane of such computation,” as Yiruo Lin and Anthony Leggett put it.

A new paper by Lin and his former Ph.D. advisor Leggett raises questions about one of the leading candidate physical systems for such so-called “topological quantum computing” (TQC).

Specifically, they reconsidered the long-hypothesized suitability of subatomic particles called “Majorana fermions” as present in a class of superconductors known as "two-dimensional (p + ip) Fermi superfluids.”

While these systems have been considered a leading TQC candidate for two decades, Lin and Leggett now suspect that they have been misunderstood because of limitations of the formalism used to interpret them: the Bogoliubov–de Gennes mean-field equations.

“The analysis... in the literature has been through a method of approximation which has proved very successful in dealing with traditional problems,” explained Leggett. “Most of the papers on quantum computing using these systems have simply applied this technique. And for a long time, I’ve been worried, and other people have been worried too, about whether the fact that this method has worked so successfully for traditional problems... is adequate to guarantee that it’s going to also work for the much more delicate kinds of operation that you’re going to have to carry out when you do quantum computing.”

In short, previous studies have assumed that the number of electrons in these Majorana fermion systems doesn’t need to be strictly conserved. Lin and Leggett suspect that this assumption is wrong, and that previous conclusions about these systems may thus be invalid.

However, the paper emphasizes that the authors haven’t yet definitively concluded that these systems must be abandoned. Further, because other TQC candidate systems—and other, more abstract forms of braiding—are unaffected by the concern, it isn’t a disaster for TQC if the authors are right.

Leggett laughed, “We don’t believe, as it were, that we’ve knocked out topological quantum computing!”

The paper, “Some questions concerning Majorana fermions in 2D (p + ip) Fermi superfluids,” was written by invitation for the inaugural issue of Springer’s new Quantum Frontiers journal. It can be found at https://doi.org/10.1007/s44214-022-00006-w.

Leggett is the John D. and Catherine T. MacArthur Chair Emeritus of Physics at UIUC. Lin completed his Ph.D. at UIUC in 2017 and is now at Texas A&M University.