# Tag Info

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 ...
• 36.7k

### Are these gate sets proven to be not universal?

I think the authors haven't tried to prove it, hence the formulation. In fact, it is simple to see that $CX$ and $R_z(\theta)$ is not universal as both gates map computational basis states to ...
• 4,987

### Does the Quantum Fourier Transform require universality?

Yes, the QFT requires universality. No, there isn't a non-universal gate set that implements the QFT. Just having the QFT as an operation is already computationally universal, because it can generate ...
• 36.7k

### How to translate between continuous variable model and discrete model?

Here is a partial answer. In general, the connection between continuous and discrete variables gets pretty complicated... However, if you restrict yourself to Gaussian unitaries on the CV side, and ...

### 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 ...
• 58k

### Which single-qubit mixed states work for magic state distillation?

I've not kept sufficiently up to date with the most recent literature, however, here are some partial results: Along certain axes of the Bloch sphere, the divide between the octahedron and the ...
• 58k
Accepted

### How to transpile a quantum circuit using the $\{H,T,CNOT\}$ universal set of gates?

Solovay-Kitaev algorithm is implemented in SolovayKitaev class. You can use it by transpiling your circuit using ...
• 10.1k
Accepted

### Calculating the classical OR gate in a 3 qubit (+1 ancillary qubit) circuit

There are two errors in your code: You only initialize the first two bits, the last bit of the input is unused. Thus, you should replace: ...
• 6,162
Accepted

### Decomposition of rotational matrix using {$H, T$} only

There are (asymptotically) far more efficient ways of performing the calculation than using the Solovay-Kitaev algorithm. I like the package provided here, assuming your rotation can easily be related ...
• 58k
Accepted

1 vote

### Are these gate sets proven to be not universal?

There is another way to see that CNOT+ $R_Y(\theta)$ is universal while CNOT+ $R_X(\theta)$ or CNOT+ $R_Z(\theta)$ is not. The general mathematical result says that one has to satisfy Theorem 3.1 of ...
• 241
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 ...
• 714
1 vote

### Calculating the classical OR gate in a 3 qubit (+1 ancillary qubit) circuit

Maybe I'm not answering the root of your question. I would like to point out that Qiskit has a boolean expression synthesiser that automatically does that: ...
• 5,763

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