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Is there a closure property for the entire Clifford hierarchy?
TL;DR
Is the entire Clifford hierarchy (as opposed to any one level), a group?
Background.
The Clifford hierarchy (on $n$ qubits), is a collection of nested subsets $\mathcal C^{(1)} \subset \mathcal C^{(2)} \subset \mathcal C^{(3)} \subset \cdots…
Niel de Beaudrap
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19
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1 answer
Quantum phase estimation and HHL algorithm - knowledge of eigenvalues required?
The quantum phase estimation algorithm (QPE) computes an approximation of the eigenvalue associated to a given eigenvector of a quantum gate $U$.
Formally, let $\left|\psi\right>$ be an eigenvector of $U$, QPE allows us to find…
Adrien Suau
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19
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No-cloning theorem and distinguishing between two non-orthogonal quantum states
I'm currently reading Nielsen and Chuang's Quantum Computation and Quantum Information and I'm not sure if I correctly understand this exercise (on page 57) :
Exercise 1.2: Explain how a device which, upon input of one of two non-orthogonal quantum…
TheAmazingKitchen
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19
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2 answers
Quantum simulation of environment-assisted quantum walks in photosynthetic energy transfer
This question is related to Can the theory of quantum computation assist in the miniaturization of transistors? and Is Quantum Biocomputing ahead of us?
About 10 years ago, several papers discussed the environment-assisted quantum walks in…
agaitaarino
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19
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3 answers
What does it mean for two qubits to be entangled?
I have done some sort of online research on qubits and the factors making them infamous i.e allowing qubits to hold 1 and 0 at the same time and another is that qubits can be entangled somehow so that they can have related data in them no matter how…
Arshdeep Singh
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19
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4 answers
Alternative to Bloch sphere to represent a single qubit
In order to represent the single qubit $|\psi\rangle$ we use an unitary vector in a $\mathbb{C}^2$ Hilbert space whose (one of the) orthonormal base is $(|0\rangle, |1\rangle)$.
We can draw $|\psi\rangle$ using a Bloch ball. However, I found this…
incud
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19
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What's meant by the depth of a quantum circuit?
I'm using Qiskit to create quantum circuits wherein I've this attribute called depth. The documentation states it is the length of the critical path here. What does it represent and how to find it out manually?
Van Peer
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How does topological quantum computing differ from other models of quantum computing?
I've heard the term Topological Quantum Computer a few times now and know that it is equivalent to quantum computers using circuits with respect to some polynomial-time reduction.
However, it is totally unclear to me how such a quantum computer…
dtell
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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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19
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3 answers
What is the current state of the art in quantum sorting algorithms?
As a result of an excellent answer to my question on quantum bogosort, I was wondering what is the current state of the art in quantum algorithms for sorting.
To be precise, sorting is here defined as the following problem:
Given an array $A$ of…
Discrete lizard
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18
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3 answers
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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18
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4 answers
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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3 answers
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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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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Can a quantum computer easily determine the mixing time of the Rubik's cube group?
Officials in Rubik's cube tournaments have used two different ways of scrambling a cube. Presently, they break a cube apart and reassemble the cubies in a random order $\pi\in G$ of the Rubik's cube group $G$. Previously, they would apply a random…
Mark Spinelli
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