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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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Why are non-Clifford gates more complex than Clifford gates?
There are two groups of quantum gates - Clifford gates and non-Clifford gates.
Representatives of Clifford gates are Pauli matrices $I$, $X$, $Y$ and $Z$, Hadamard gate $H$, $S$ gate and $CNOT$ gate. Non-Clifford gate is for example $T$ gate and…
Martin Vesely
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Reference that explains how to read 3d topological diagrams for surface code computations
I like making diagrams to describe computations. For the surface code, an excellent tool is 3d topological diagrams. Here is an example diagram (made by me in SketchUp):
The basic idea is that white boundaries are places where Z observable chains…
Craig Gidney
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Is quantum computing mature enough for a computer scientist with no physics background?
Sligthly related to this question, but not the same.
Traditional computer science requires no physics knowledge for a computer scientist to be able to research and make progress in the field. Of course, you do need to know about the underlying…
denidare
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Are all quantum algorithms hidden subgroup algorithms?
I am reading the paper "Quantum Hidden Subgroup Algorithms: An Algorithmic Toolkit" by Samuel Lomonaco and Louis Kauffman from the book, "Mathematics of Quantum Computation and Quantum Technology." See also, this arxiv link.
The authors suggest…
user2521987
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What's the Difference between T2 and T2*?
$T_2$ generally refers to the measurement of the coherence of the qubit with respect to its dephasing (that's a rotation through the $|0\rangle$ - $|1\rangle$ axis of the Bloch sphere for those of us visualizing). But sometime in the literature,…
psitae
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Purpose of using Fidelity in Randomised Benchmarking
Often, when comparing two density matrices, $\rho$ and $\sigma$ (such as when $\rho$ is an experimental implementation of an ideal $\sigma$), the closeness of these two states is given by the quantum state fidelity $$F =…
Mithrandir24601
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Quantum circuits explain algorithms, why didn't classical circuits?
When explaining a quantum algorithm, many revert to 'circuit-speak' by drawing a diagram of how qubits split off into transformations and measurements, however, rarely if not never would someone explaining a classical math algorithm revert to its…
develarist
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Can arbitrary matrices be decomposed using the Pauli basis?
Is it possible to decompose a Hermitian and unitrary matrix $A$ into the sum of the Pauli matrix Kronecker products?
For example, I have a matrix 16x16 and want it to be decomposed into something like $$A…
C-Roux
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Is VQE a class of algorithms or a specific algorithm?
Is VQE a class of algorithms or a specific algorithm? For example, is QAOA a VQE or is VQE an algorithm distinct from QAOA that solves the same class of problems?
If VQE is a specific algorithm, what are its defining features that distinguish it…
Malcolm Regan
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What exactly is meant by "noise" in the following context?
The strengthened version of the Church-Turing thesis states that:
Any algorithmic process can be simulated efficiently using a Turing machine.
Now, on page 5 (chapter 1), the book Quantum Computation and Quantum Information: 10th Anniversary Edition…
Sanchayan Dutta
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Implementing "Classical AND Gate" and "Classical OR Gate" with a quantum circuit
Quantum cNOT Gate (Classical XOR Gate)
A "Controlled NOT (cNOT) Gate" flips the 2nd qubit if the 1st qubit is $\left|1\right>$, and returns the 2nd qubit as-is if the 1st qubit is $\left|0\right>$. The 1st qubit is simply not changed.
The net effect…
Siu Ching Pong -Asuka Kenji-
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Blind quantum computing — generic structure variable selection
Background
Recently I came upon a research article entitled Experimental Demonstration of Blind Quantum Computing. Within this research article, the scientists claimed that - through the proper choice of a generic structure - a data engineer can…
Daniel Burkhart
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Connection between stabilizer generators and parity check matrices in the Steane code
I'm working through Mike and Ike (Nielsen and Chuang) for self-study, and I'm reading about stabilizer codes in Chapter 10. I'm an electrical engineer with somewhat of a background in classical information theory, but I'm by no means an expert in…
Travis C Cuvelier
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What is the Helstrom measurement?
I have been reading the paper Belief propagation decoding of quantum
channels by passing quantum messages by Joseph Renes for decoding Classical-Quantum channels and I have crossed with the concept of Helstrom Measurements.
I have some knowledge…
Josu Etxezarreta Martinez
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