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3 votes

What's the best way to approximate a unitary $N\times N$ gate by a quantum circuit?

I'm not sure where you are getting an exponential number of steps. Let $\mathcal{G}$ be a finite set of generators for $SU(N)$ that is closed under inverses. The Solovay-Kitaev theorem says that for ...
Condo's user avatar
  • 2,048
3 votes
Accepted

Quantum compilation algorithm with respect to other Shatten $p$-norm

Yes, you get the same behavior. This is because all norms on finite dimensional spaces are equivalent. That means that for every $p$ there exist constants $c_p, d_p > 0$ such that $$ d_p \|X\|_p \...
Rammus's user avatar
  • 5,863
2 votes

Gate synthesis with parametrised precision

The "method accepting an arbitrary gate" is a tricky part". There are methods with some set of gates that you might have to later translate with a further transpiler pass. For the ...
luciano's user avatar
  • 5,803
2 votes

Seeking Programming Projects and Tools for Quantum Gate Decomposition Implementations

First off, the question itself is disparate. You need some version of the Solovay-Kitaev theorem for optimizing a sub-circuit that acts on a single qubit, and you can also use it for two or three ...
Greg Kuperberg's user avatar
1 vote

Approximate decomposition of general $n$-qubit unitary to universal gate set

Your statement of the theorem is slightly inaccurate. However, this inaccuracy is actually very important, and perhaps this is what creates confusion. Briefly, the Solovay-Kitaev (SK) theorem and ...
MonteNero's user avatar
  • 2,666
1 vote

What's the best way to approximate a unitary $N\times N$ gate by a quantum circuit?

A line of research might be, if you have a way to write your unitary as $U = e^{A}$ for some complex matrix $A$. Then you can use the Lie-Trotter or Suzuki-Trotter decomposition to approximate your ...
baptistechev's user avatar
1 vote

Seeking Programming Projects and Tools for Quantum Gate Decomposition Implementations

It has been a long time (>4 years) since the last time I looked at this code, but I implemented a working version of the Solovay-Kitaev algorithm back then. You will be able to find it in https://...
Adrien Suau's user avatar
  • 4,987
1 vote

Seeking Programming Projects and Tools for Quantum Gate Decomposition Implementations

This certainly depends on what one is attempting to do, ie the algorithm or unitary that one is attempting to implement, and the target basis state (along with understanding precision thresholds and ...
raeth's user avatar
  • 51
1 vote

How can I find a Clifford+T approximation of an arbitrary one qubit gate in Qiskit?

You should transpile first to cx and u3, so it will deal with 2Q gates ...
Ron Cohen's user avatar
  • 1,482

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