8

I have heard about the diamond norm, and from what I understood it is a "nice" tool to quantify quality of quantum gates in the NISQ era. I would like to know a little more before going in detail in the litterature.

My question are the following:

Why is it considered as a good tool to quantify quality of quantum gates? Why this tool and not another one?

What are the nice properties this tool has? I have seen in Is the diamond norm subadditive under composition? that it is subbaditive which make the tool useful to bound the diamond norm of a full algorithm given the diamond norm of each gate. Are there other some useful properties? I guess this question will be related somehow to the previous one. I tried to find this information in literature, but unfortunately all papers I read just give the definition and the diamond norm and a way to compute it numerically.

Nick Decroos
  • 252
  • 1
  • 4
Marco Fellous-Asiani
  • 1,514
  • 2
  • 13
  • 33
  • 2
    Mark Wilde's textbook might be a good resource to look up these properties. There is a chapter called 'Distance Measures' which discusses this norm. You can access a free pdf at this link : https://arxiv.org/abs/1106.1445 – Purva Thakre Dec 27 '19 at 20:17
  • 3
    It is natural in the same way you want CP maps, not just positive maps: You want your map also to work - or your gate quality also be good - if you act on part of a larger quantum system. – Norbert Schuch Dec 28 '19 at 00:39
  • 1
    @PurvaThakre thank you for the link, it is really a nice reference ! – Marco Fellous-Asiani Jan 01 '20 at 19:55
  • @NorbertSchuch allright, I see what you mean. Thanks. – Marco Fellous-Asiani Jan 01 '20 at 19:56

0 Answers0