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]
156 questions
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What are magic states?
I wonder what are magic states, and a magic state gadget. While I'm reading a paper, these terms frequently appear.
김동민
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Explicit Conversion Between Universal Gate Sets
I'm interested in the conversion between different sets of universal gates. For example, it is known that each of the following sets is universal for quantum computation:
$\{T,H,\textrm{cNOT}\}$
$\{H,\textrm{c}S\}$, where $S=T^2$ and $S^2=Z$, and…
DaftWullie
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What is the mathematical justification for the "universality" of the universal set of quantum gates (CNOT, H, Z, X and π/8)?
In this answer I mentioned that the CNOT, H, X, Z and $\pi/8$ gates form a universal set of gates, which given in sufficient number of gates can get arbitrarily close to replicating any unitary quantum gate (I came to know about this fact from…
Sanchayan Dutta
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How are gates implemented in a continuous-variable quantum computer?
I've mostly worked with superconducting quantum computers I am not really familiar with the experimental details of photonic quantum computers that use photons to create continuous-variable cluster states such as the one that the Canadian startup…
Mark Fingerhuth
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How many two-qubit gates are required to implement a general N-qubit unitary?
Is there a known formula or a scaling behaviour for how many two-qubit gates are required to construct a general N-qubit unitary?
I suppose there are several cases to consider:
Exact representation of the gates
Approximate decompositions to a given…
as2457
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How does approximating gates via universal gates scale with the length of the computation?
I understand that there is a constructive proof that arbitrary gates can be approximated by a finite universal gate set, which is the Solovay–Kitaev Theorem.
However, the approximation introduces an error, which would spread and accumulate in a long…
M. Stern
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How to prove/disprove universality for a set of gates?
A universal set of gates are able to mimic the operation of any other gate type, given enough gates. For example, a universal set of quantum gates are the Hadamard ( $H$ ), the $\pi/8$ phase shift ( $T$ ), and the $\mathrm{CNOT}$ gate. How would one…
chuster
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Given a decomposition for a unitary $U$, how do you decompose the corresponding controlled unitary gate $C(U)$?
Suppose we have a circuit decomposition of a unitary $U$ using some universal gate set (for example CNOT-gates and single qubit unitaries). Is there a direct way to write down the circuit of the corresponding controlled unitary $C_U$ using the same…
M. Stern
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Does the Quantum Fourier Transform require universality?
Background:
In most setups of fault-tolerant quantum computation, universality is achieved using Clifford gates such as $(S, H, \text{CNOT})$ and the $T$-gate.
The Eastin-Knill theorem can be informally stated that it will be difficult (although…
Frederik Ravn Klausen
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Quantum XNOR Gate Construction
Tried asking here first, since a similar question had been asked on that site. Seems more relevant for this site however.
It is my current understanding that a quantum XOR gate is the CNOT gate. Is the quantum XNOR gate a CCNOT gate?
user820789
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Does anyone know the list of all known universal sets of quantum gates?
Does anyone know the list of all known universal sets of quantum gates? I know only two such sets: Cliffords + $T$ and rotations + CNOT.
Игорь Токарев
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Sampling random circuits vs Solovay-Kitaev compiler
Suppose I want to obtain a gate sequence representing a particular 1 qubit unitary matrix.
The gate set is represented by a discrete universal set, e.g. Clifford+T gates or $\{T,H\}$ gates.
A well known approach to solve the problem is to use…
Yaroslav Kharkov
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Shortest sequence of universal quantum gates that correspond to a given unitary
Question: Given a unitary matrix acting on $n$ qubits, can we find the shortest sequence of Clifford + T gates that correspond to that unitary?
For background on the question, two important references:
Fast and efficient exact synthesis of single…
user120404
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How efficient is Qiskit's unitary decomposition?
In Qiskit's extension package we have the UnitaryGate module that you can initialize using a unitary matrix and then add it to your circuit. How efficiently is this decomposition done under the hood?
Also, if I wanted to do the decomposition myself,…
Dani007
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What would be the simplest addition that would make the D-Wave architecture universal?
The D-Wave system, as I understand it, allows us to program Ising models and to find their ground states. In this form, it is not universal for quantum computation: it can not simulate a circuit model quantum computer.
What would be the simplest…
James Wootton
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