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Is the Solovay-Kitaev theorem relevant for modern hardware?

I think you'll find that most hardware, at the hardware level, gives you arbitrary single qubit rotations. So, in that sense, it is true that Solovay-Kitaev is not directly applicable to current ...
• 59.9k
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How does approximating gates via universal gates scale with the length of the computation?

Throughout this answer, the norm of a matrix $A$, $\left\lVert A\right\rVert$ will be taken to be the spectral norm of $A$ (that is, the largest singular value of $A$). The solovay-Kitaev theorem ...
• 3,716
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Approximating unitary matrices

You have picked two particularly simple matrices to implement. The first operation (G) is just the square root of X gate (up to global phase): In your gate set, this is $R_X(\pi/2)$. The second ...
• 39.6k

Sampling random circuits vs Solovay-Kitaev compiler

The Solovay-Kitaev algorithm is not practical. It is very useful theoretically because it proves that once you have a "dense" set of quantum gates (i.e. a set with which you can approximate any other ...
• 5,027

Approximating unitary matrices

When a two qubit gate $W$ can be expressed (up to a global phase) in the computational basis by a matrix with entirely real entries, i.e., $W \in O(4)$, then there is general construction of ...
• 2,575
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Status of software packages for quantum compiling

For Qiskit, there are two tools you can check out. The two qubit kak tool does exactly what you want for 2 qubits. If you give it a two qubit unitary, it gives you a list of gates to realize this, ...
• 11.3k
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How can I find a Clifford+T approximation of an arbitrary one qubit gate in Qiskit?

On the Qiskit front, a Solovay-Kitaev algorithm implementation is on its way https://github.com/Qiskit/qiskit-terra/pull/5657. If you want to use or have a look to this ...
• 5,819
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Basic approximation in Solovay-Kitaev algorithm

I don't pretend that this is optimal in the sense of minimal number of applications, but here's one method that comes from the universality proof... The unitary that you want to implement can be ...
• 59.9k
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Why is phase gate a member of universal gate set?

You might want a small set of gates, but it doesn't necessarily mean that you want the smallest set possible. When you talk about a fault-tolerant quantum computer, what you really want to do is ...
• 59.9k
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In Solovay-Kitaev's algorithm, where does the rotation relation $\sin(\theta / 2) = 2 \sin^2(\phi/2)\sqrt{1 - \sin^4(\phi/2)}$ come from?

This simply comes from equation an arbitrary rotation $R_{n}(\theta)$ with the rotation $$U=R_X(\phi)R_Y(\phi)R_X(-\phi)R_Y(-\phi).$$ The way that I did this calculation, just to verify this claim, ...
• 59.9k

Approximating unitary matrices

Neither of these gates require approximate sequences. You can implement them exactly with your specified gate sets with no great effort. Up to a global phase (which should be irrelevant), G is simply ...
• 59.9k