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Is the trace of a positive map always positive?
Obviously, positive semi-definite operators always admit a positive trace as ${\rm tr}(A)=\|A\|_1\geq 0$ whenever $A\geq 0$. This motivates the following "lifted" question:
Given any positive, linear map $\Phi:\mathbb C^{n\times n}\to\mathbb…
Frederik vom Ende
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6
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If Alice measures a qubit and doesn't tell Bob the result, what's Alice's state from Bob's perspective?
Suppose Alice has a qubit $|\phi\rangle=\alpha|0\rangle+\beta|1\rangle$ and measures it. Bob knows the initial state but not the result of her measurement.
So after the measurement, Alice knows what state her qubit is…
mp12853
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Where does the "error propagation formula" $(\Delta \theta)^2=(\Delta M)^2/|\partial_\theta\langle M\rangle|^2$ come from, in estimation theory?
Consider the single parameter estimation setting, where we have a distribution depending on $\theta$ and we're looking for a "good" estimator for $\theta$.
A commonly mentioned strategy, found e.g. in Eq. (7) of [TA2014], is to measure some…
glS
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6
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Anyon alternatives in topological quantum computing
A topological quantum computer is a theoretical quantum computer that employs two-dimensional quasiparticles called anyons. -Wikipedia
Are there other instances of topological quantum computing models that do not use anyons?
Are there alternative…
user820789
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1 answer
Clifford group without the phase gate
The Clifford group is generated by the Hadamard gate $H$, the phase gate $S=\sqrt{Z}$, and the $\text{CNOT}$ gate. I was wondering what happens if we dropped $S$, so that all matrices are real.
I found Does the real Clifford group contain all real…
Jun_Gitef17
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6
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Quantum error correction: necessary and sufficient condition
For quantum error correction, the necessary and sufficient condition is given in standard texts as:
$\langle \phi| E^{\dagger}_{a} E_{b} |\psi \rangle = C_{ab} \langle \phi|\psi \rangle $
$|\psi\rangle$ and $|\phi\rangle$ are codewords. $E_{a}$ and…
BlackHat18
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What kind of mathematics is common in quantum computing?
From what I have seen so far, there is a lot of linear algebra. Curious what other kinds of maths are used in QC & the specific fields in which they are most predominately invoked.
user820789
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Can a CPTP map increase the purity of a state?
I am wondering if there exist CPTP maps $T$ such that the purity of a quantum state $\rho$ can increase, i.e.
$$ \text{tr} ( T ( \rho )^2 ) \geq \text{tr} ( \rho ^2). $$
If so, what are the conditions on $T$ and/or $\rho$ for this to be possible?
Rell
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Resources on the energy consumption of IBM quantum computers?
I am seeking information regarding the energy consumption of IBM Quantum Computers, specifically inquiring about the energy requirements associated with individual gate operations.
Could you also provide any available resources or documentation…
goga suknidze
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Finding all small stabilizer codes
Given some choice of parameters $ [[n,k,d]] $ with $ n $ small, is there any computationally easy way to find all of (or at least many of) the stabilizer codes with those parameters?
For certain parameters this is easy, for example it is known that…
Ian Gershon Teixeira
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Is the Steane code the only $ [\![7,1,3]\!] $ CSS code?
Is the Steane code the only $ [\![7,1,3]\!] $ CSS code?
This paper claims there are 10 non-equivalent $ [\![7,1,3]\!] $ stabilizer codes. How many of these are CSS codes? Is it just the Steane code?
Ian Gershon Teixeira
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6
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Is QFT qubit recycling compatible with Zeckendorf's Fibonacci representation of integers?
Background
Phase estimation circuits prepare $n$ qubits $Q_0, \dots, Q_{n-1}$ in the $|+\rangle$ state, then apply $U^{2^q}$ controlled by $Q_q$ for each $q$, then apply a quantum Fourier transform, then measure $Q_0, \dots, Q_{n-1}$.
"Qubit…
Craig Gidney
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Codes saturating the bound d=(n+1)/2
An $ n $ qudit code always has distance bounded above by $ d \leq \frac{n+1}{2} $ (Edit: the correct bound appears to be $ d \leq \frac{n}{2}+1 $ but the $ [[6,0,4]] $ hexacode and the $ [[2,0,2]] $ Bell state are the only qubit codes that violates…
Ian Gershon Teixeira
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5 answers
Evolution of a state vector: Why is the action of $N$ equivalent to the action of $UNU^{†}$?
There is another question asked on this on stack exchange but I did not find any answers there that fully answered the question. In Gottesman's paper "The Heisenberg Representation of Quantum Computers", he says:
Suppose we have a quantum computer…
am567
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Is the "unitary twirling operation" physically realizable?
In this neat answer by Markus Heinrich, it is shown that twirling an arbitrary quantum channel $\Lambda$ over the unitary group $U(d)$ yields a depolarizing channel $\tilde{\Lambda}$ given by
$$
\tilde{\Lambda}(M) = \Pi_{U(d)}(\Lambda)(M) =…
Eric Kubischta
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