For questions about the set of quantum gates that form a set of gates from which another gate can be produced; this set is analogous the classical set of universal gates (either a NOR gate or a NAND gate can produce any other gate). This tag, however, is not to be used for the classical set of universal gates; those questions are probably more appropriate on Computer Science SE.
Questions tagged [universal-gates]
140 questions
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Are these gate sets proven to be not universal?
I was reading the paper An introduction to measurement based quantum computation (Josza, 2005) and on page 13 they say the following:
Theorem: Any gate array using gates from the set $\{CX,R_x(\theta) \text{ all } θ\}$ or from the set…
Ethan Davies
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Does Aharanov's proof of the universality of CCNOT+Hadamard carry over to CSWAP+Hadamard?
In an old paper from 2003, D. Aharanov simplified Shi's proof that CCNOT (or Toffoli) gates + Hadamard gates together form a computationally universal gate set for quantum computing. The CCNOT gate is well-known to be computationally universal for…
Mark Spinelli
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Is a gate set being capable of producing any state starting from the zero state a sufficient condition for universality?
In this answer: https://quantumcomputing.stackexchange.com/a/5896/19951 to a question asking how to prove (or disprove) universality, it is stated that a universal gate set "has to be capable of producing any state starting from the all zeros…
jamman2000
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Is there any universal gate set with an efficient word problem?
On N qubits, take a set of operators that form a universal gate set. Further, assume this gate set is given with a finite presentation of the group it generates and this group has a decideable and efficient word problem. The word problem is taken…
user442920
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Is $R_x$, $R_y$, $R_z$, and $CNOT$ a Universal gate set?
The book "Introduction to Spintronics" 2nd edition says on page 542 that an arbitrary single qubit rotation and a CNOT comprises a universal gate set. Is this true?
If so, why isn't this the gate set implemented in commercial quantum computing…
Malcolm Regan
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Toffoli and Hadamard: simulating quantum calculation with integer numbers?
I see that Toffoli and Hadamard gates are "universal for quantum calculation". This paper by Aharonov says that this universality has a slightly wider meaning than usual. This is clear from the fact that Toffoli and Hadamard gates are represented by…
Doriano Brogioli
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What is XPRS basic gate on IBM 'peekskill' system?
I have checked IBM 'peekskill' system and it has basic gates defined as:
CX, ID, RZ, SX, X, XPRS.
It is the only one IBM system that has XPRS gate on its list.
Does anyone knows what kind of gate XPRS is?
Other 'peekskill' system properties:
27…
Mariusz
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