[HN Gopher] Topological Superconductors
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Topological Superconductors
Author : Bang2Bay
Score : 45 points
Date : 2025-02-19 18:58 UTC (4 days ago)
(HTM) web link (pubs.acs.org)
(TXT) w3m dump (pubs.acs.org)
| perching_aix wrote:
| > TSCs offer a promising platform toward (nonuniversal)
| topological quantum computation
|
| Hold on, that sounds like quite an important limitation that
| hasn't been discussed widely before...
| scythe wrote:
| I've worked in quantum computing (many years ago...) and that
| statement surprises me as well. Not because it's a caveat, but
| because, last I checked, there isn't really any such thing as
| "nonuniversal" quantum computation; there are no well-defined
| complexity classes in between BQP and BPP (the latter is
| conjectured to = P). Either you have universal quantum gates,
| or you don't!
|
| The paper mentions this more specifically a few paragraphs in:
|
| >Majorana Fermions can emerge in a TSC (but not in a
| conventional metal) because a Majorana Fermion is its own
| antiparticle. [edit: I don't think this is quite right...
| Majorana fermions can emerge in a TSC because the spin-
| statistics theorem allows more freedom in two dimensions]
|
| >[...]
|
| >To achieve quantum computing, a Majorana Fermion normally
| needs to be bound to a defect (hence called MBS) with zero
| energy (hence also called MZM), which can contain nontrivial
| non-Abelian statistics.
|
| >[...]
|
| >Here, an MZM is a type of anyon termed Ising anyon, which
| contain non-Abelian statistics but by itself is not sufficient
| to carry out universal quantum computations. (3, 26)
|
| Now Ising anyons are something I actually studied in the
| context of topological error-correction, and my fuzzy memory
| says that some of these anyons can perform computations on
| qubits _but_ are limited to Clifford statistics and so do not
| provide a useful quantum speedup vs classical computers (in
| particular, this includes the synthetic anyons on the "Kitaev
| code" and the "color code" synthetic anyon models). But let's
| see what the references cited (3, 26) say. First reference (3):
|
| >Unfortunately, such qubit rotations are too restrictive to
| permit universal quantum computation; two additional processes
| are needed [12]. The first is a p/8 phase gate that introduces
| phase factors e+-ip/8 depending on the occupation number
| corresponding to a given pair of Majoranas. The second is the
| ability to read out the eigenvalue of the p
|
| Yes, this is exactly the "Clifford group statistics" problem.
| Incidentally, you don't need specifically the pi/8 gate; a
| couple of others will do (e.g. Toffoli's gate), but pi/8 is
| widely believed to be the simplest. When you are "stuck" with
| Clifford gates, you are able to perform "quantum computations"
| in the sense that you use qubits to do computing, but your
| complexity class is BPP.
|
| Now reference (26). This also mentions the Clifford problem (in
| a more detailed way) but expands:
|
| >Neither of these gates can be applied exactly, which means
| surrendering some of the protection we have worked so hard to
| obtain and we need some software error correction. However, it
| is not necessary for the pi / 8 phase gate or the two-qubit
| measurement to be extremely accurate in order for error
| correction to work. The former needs to be accurate to within
| 14% and the latter to within 38% (Bravyi, 2006). Thus the
| requisite quantum error correction protocols are not
| particularly stringent.
|
| So here the hope is that extremely high fidelities (the great
| promise of topological quantum computing) can be obtained for
| most of the computations, which reduces the required fidelity
| needed to obtain stable error-correction algorithms (the
| "threshold theorems") for the remaining operations that allow
| universal quantum computation.
|
| Whether this "rescues" the topological superconductor as a
| _practical_ platform for BQP-class computations is not
| immediately obvious to me, but I hope this gives an idea of
| what you get from a TSC and what you need to add to it in order
| to get a BQP-class quantum computer. For comparison, logic gate
| error tolerances required for quantum computers lacking any
| topologically protected subsystem to achieve stable computation
| are on the order of 0.1% or tighter.
| aghilmort wrote:
| thank you such a useful / insightful set of thoughts!
| vlmutolo wrote:
| I don't know for sure, but I'd bet that their construction can
| only implement "Clifford" gates, which are a subset of the
| gates needed for arbitrary quantum computation.
|
| This is a common situation. Lots of proposed quantum computing
| architectures are built to support only Clifford gates, and
| then they have a separate subsystem dedicated to implanting
| non-Clifford gates. The keyword to search here is "magic state
| distillation".
|
| More info here:
| https://quantumcomputing.stackexchange.com/questions/13629/w...
| derekmhewitt wrote:
| It's really cool that the full text of this paper is posted
| publicly like this, +1 for foss science. But it's also very dense
| and I'm not a physicist, can anyone ELI5 for us mere mortals?
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