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Given an entangled state on two systems, when can a subsystem of one decouple from the other?
Suppose you have the following quantum state:
$$\frac{1}{\sqrt{2^n}}\sum_{i}|\bar{i}\rangle_A|i\rangle_S$$
where $\{|i\rangle_A\}$ and $\{|i\rangle_S\}$ are orthonormal bases for an $n$-qubit ancilla and $n$-qubit quantum system respectively. The…
ssd42
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Why aren’t electrons in our atoms suffering from decoherence?
I know about how the current era of quantum computing is trying to find ways in order to improve the coherence times of the quantum states and so on and that decoherence and noise are the greatest obstacles, some needing extremely isolated…
yousef elbrolosy
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How do we derive the density operator of a subsystem?
The density operator can be used to represent uncertainty of quantum state from some perspective, aka a subsystem of the full quantum system. For example, given a Bell state:
$|\psi\rangle = \frac{|00\rangle + |11\rangle}{\sqrt{2}}$
where Alice has…
ahelwer
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Can a half-classical, half-quantum rat settle on finding the cheese faster than a fully classical or fully quantum one?
TL/DR: With $t$ being the classical mixing time of an connected, non-bipartite, unweighted, undirected graph on $n$ vertices, and $\pi_n=\frac{1}{n}$ being the stationary probability at vertex $v_n$, what strategy, if any, is there to interpolating…
Mark Spinelli
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6
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Inclusion of the normalizer in the centralizer
From wiki, a centralizer $C(S)$ and a normalizer $N(S)$ of stabilizer group $S$ are defined as (1), (2):
$$C(S) = \{g \in G \,|\, gs = sg \, \text{for all}\, s \in S\} \tag{1}$$
$$N(S) = \{g \in G \,|\, gSg^{\dagger} = S\} \tag{2}$$
where G is Pauli…
taketoshi kinoshita
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6
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How is measurement modelled when using the density operator?
I've just learned about the density operator, and it seems like a fantastic way to represent the branching nature of measurement as simple algebraic manipulation. Unfortunately, I can't quite figure out how to do that.
Consider a simple example: the…
ahelwer
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6
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1 answer
Preserving distance during stabilizer measurements by alternating interaction order from round to round?
On the rotated surface code, it is known that choosing a "bad" interaction order when measuring stabilizers leads to a halving of the effective code distance. This is because of hook errors: a single error on the measurement qubit can propagate to…
Exorus Koh
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To what degree could additional ancilla qubits affect the complexity of a quantum algorithm?
It is a known trick in quantum computing to use additional ancilla qubits and uncomputation to construct efficient quantum circuits.
I wonder, are there some rigorous results that estimate how big this effect could be?
For example, is it possible to…
Danylo Y
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Transmons and cooper pair box qubits: two islands or a single island and a reservoir
In scientific literature, one typically describes Cooper pair boxes as a small superconducting island coupled to a superconducting reservoir (say, a large ground plane of superconducting metal, or a large piece in any case) via a Josephson junction.…
user129412
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What happens when we permute the vertices of a (small) graph by unitarily walking along a (larger) graph of the symmetric group?
Let $G$ be an unweighted, undirected graph on $n$ vertices with vertex labels $\{1,2,\cdots,n\}$; let $A$ be its $n\times n$ adjacency matrix. We can prepare a state $|\psi\rangle$ representing $A$ with $n^2$ qubits; for example, with $n=10$ we…
Mark Spinelli
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6
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Are the coefficients of Clifford gates in the Pauli basis always of equal magnitude?
I'm currently interested in writing Clifford gates in the Pauli basis i.e. $C = \sum_{P}\alpha_P P$, where we are summing over all pauli strings of fixed length. For example:
$H =\frac{1}{\sqrt{2}}(X+Z)$
$CX = \frac{1}{2}(II+XI+IZ-XZ)$
$HS =…
Ethan Davies
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Does the matrix representation of quantum gates depend on the basis?
I have read that I can chose any orthonormal basis $\{|0⟩, |1⟩\}$ of $\mathbb{C}^2$ as my basis states for a single qubit. Usually $|0⟩ = \begin{pmatrix}1\\0\end{pmatrix}$ and $|1⟩ = \begin{pmatrix}0\\1\end{pmatrix}$ is chosen, but say I chose…
Hebol
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Can we learn anything interesting about a claw by taking the square-root-of-NOT of each qubit?
Consider being given a circuit for a two-to-one Boolean function $f$ from $n$ (qu)bits to $m\ge n-1$ (qu)bits, and prepare the following state:
$$\frac{1}{\sqrt {2^n}}\sum_0^{2^n-1}|x\rangle|f(x)\rangle.$$
Upon measuring the second register in the…
Mark Spinelli
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6
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3 answers
Are Quantum Algorithms better than classical algorithms for all problems?
My question basically boils down whether Quantum Computers are better computers or are they only different computers?
Is there a quantum algorithm for every problem which is at least as fast as the classical algorithm? If yes, then the fact that it…
user93353
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Total number of (unique) moments of the Haar distribution
This is probably a standard fact but I cannot find it in my usual references. Let $G$ be one of the classic matrix Lie groups $\mathrm{U}(N), \mathrm{SU}(N), \mathrm{O}(N), \mathrm{SO}(N)$, equipped with the Haar measure $\mu$. One way to study the…
Banach space fan
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