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### 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 ...
• 2,048
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 \...
• 5,863

### 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 ...
• 5,803

### 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 ...
• 1,436
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 ...
• 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 ...
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://...
• 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 ...
• 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 ...
• 1,482

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