Quantum Computing Stack Exchange
Quantum Computing Stack Exchange

Questions tagged [universal-gate-sets]

9 questions
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1 answer

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 this ought to be true, in light of the standard…
Mary_Smith
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Can a universal gate set be constructed using only $|0\rangle$ state prep, global arbitrary 1-qubit gates, local CZ gates, and global Z measurements?

I'm exploring the possibilities of constructing a universal set of gates for quantum computation and was wondering about the following scenario: Is it possible to implement a universal set of gates using only: The ability to prepare all qubits in…
francois-marie
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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 $\text{CSWAP}$s and $H$s on 3 qubits generate an…
Jonas Anderson
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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. In general, is there a way to check if a gate…
John Doe
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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 code admits Clifford gates in a transversally,…
Josu Etxezarreta Martinez
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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?
Cairo
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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 Cliffords, and hence also contains the inverse of $G$.…
John
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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 understanding is that the native gate set should form a…
thespaceman
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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 implement Toffoli exactly on three physical qubits.…
Jonas Anderson
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