Skip to main content
Share Your Experience: Take the 2024 Developer Survey
6 votes
Accepted

Universal Gate Set, Magic States, and costliness of the T gate

The T state $Z^{1/4}|+\rangle$ has four core advantages over most other states: You can physically inject T states at pretty high fidelity. It has a reasonably cheap distillation circuit, as far as ...
Craig Gidney's user avatar
  • 37.8k
4 votes

Can every unitary be approximated by gates from the Clifford Hierarchy?

This is too long for a comment but not an answer. First we must define some notion of closeness of unitaries. Other metrics should be fine, but operator norm seems like a good one. Now I think your ...
Jonas Anderson's user avatar
3 votes

Universal Gate Set, Magic States, and costliness of the T gate

Imagine you're interested in implementing a gate $$ P_k=\left(\begin{array}{cc} 1 & 0 \\ 0 & e^{i\pi/2^k} \end{array}\right), $$ so $Z=P_0$, $S=P_1$ and $T=P_2$. Now imagine that you're going ...
DaftWullie's user avatar
  • 58.8k
1 vote

Universal Gate Set, Magic States, and costliness of the T gate

To shorten Craig's answer, T is a single qubit gate, diagonal in the Z basis, and still a relatively simple, easy-to-understand rotation. H for example is not a rotation. For your last question - the ...
Yaron Jarach's user avatar

Only top scored, non community-wiki answers of a minimum length are eligible