Questions tagged [universal-gate-sets]
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8 questions
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Is $SO(2)$ with any entangling gate universal?
Let $E \in SU(2^k)$ be any entangling gate (for some $k \geq 2)$. Then my question is simply whether or not it is known that $SO(2) \cup \{ E \}$ is universal for $\mathsf{BQP}$?
Clearly it seems that ...
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Why are IBM's basis gates not linearly independent?
IBM lists the basis gates for its Heron processor as $CZ,RZ(\theta),SX,X,I$. For clarity, these are the Controlled-Z, Z-rotation, sqrt(Pauli-X), Pauli-X, and identity gates respectively.
My ...
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Is it possible to exactly compile Toffoli using H and CSWAP gates and ancilla qubits?
Question:
Given controlled-SWAP (CSWAP) and Hadamard (H) gates, is it possible to exactly compile the Toffoli (CCX) gate?
Note that I'm not looking for an encoded Toffoli gate. The answer should ...
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Is it possible to approximately compile Toffoli using H and CSWAP?
Question:
Given all controlled-SWAP (CSWAP) and Hadamard (H) gates on 3 qubits, is it possible to approximately compile the Toffoli (CCX) gate?
Discussion
From basic simulations, it appears that all $\...
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Is $\{CNOT, CZ, T\}$ a universal gate set?
If one would like to drop the Hadamard from the usual $\{CNOT, H, T\}$ gate set, what is a suitable replacement? It seems like $CZ$ might work here but I don't really know how to prove or disprove it.
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Alternative gate sets for universal Clifford computation?
The standard universal set of gates for Clifford computation is CNOT, H and S. Are there other options, in particular, gate sets that don't use the S gate?
If yes, what are some examples?
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Universality of adding gate to Cliffords without inverses
In this answer it is explained how adding any non-Clifford gate $G$ to the Clifford gate set gives a universal gate set. However, that defines the gate set as the group generated by $G$ and the ...
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Circumventing the Eastin-Knill theorem by means of Shor's fault tolerant Toffoli gate
I have been reading about the Eastin-Knill theorem, which states that no quantum error correction code can can transversely implement a universal gate set. In this context, for example, the surface ...
