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1500 questions
7
votes
1 answer
Status of software packages for quantum compiling
By "quantum compiling", what I mean is classical algorithms to solve the following problem: given a $SU(D)$ matrix $U$ (the goal) and a set of $SU(D)$ unitary matrices $V_1 \cdots V_N$ (the gates), find a string $i_1\cdots i_K$ such that
$$
U…
Scott Lawrence
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7
votes
3 answers
Partial trace over a product of matrices - prove that ${\rm Tr}(\rho^{AB}(\sigma^A\otimes I))={\rm Tr}(\rho^A\sigma^A)$
$$Tr(\rho^{AB} (\sigma^A \otimes I/d)) = Tr(\rho^A \sigma^A)$$
I came across the above, but I'm not sure how it's true. I figured they first partial traced out the B subsystem, and then trace A, but I don't see how you are allowed to partial trace…
Mahathi Vempati
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7
votes
2 answers
Is the set of all states with negative conditional Von Neumann entropy convex?
I have read somewhere / heard that the set of all states that have non-negative conditional Von Neumann entropy forms a convex set. Is this true? Is there a proof for it?
Can anything be said about the reverse - set of all states that have negative…
Mahathi Vempati
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7
votes
2 answers
How to find the operator sum representation of the depolarizing channel?
In Nielsen and Chuang (page:379), it is shown that the operator sum representation of a depolarizing channel $\mathcal{E}(\rho) = \frac{pI}{2} + (1-p)\rho$ is easily seen by substituting the identity matrix with
$$\frac{\mathbb{I}}{2} = \frac{\rho +…
user1936752
- 2,859
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7
votes
1 answer
How does the CNOT gate operate when the control qubit is a superposition?
If a control qubit is in superposition, how it will affect target qubit if it is collapsed or in superposition? Is it true that CNOT works only if the control bit collapsed to 1? Also, is it possible to collapse or Hadamard control qubit “on the…
Olexander Korenyuk
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7
votes
1 answer
Magic State Distillation Understanding Check
I'm currently trying to understand the T magic state distillation algorithm described in "Universal Quantum Computation with Ideal Clifford Gates and Noisy Ancillas" [1] (Section V starting on Page 6). I need to understand the basics of magic state…
Malcolm Regan
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7
votes
2 answers
Deduce the Kraus operators of the dephasing channel using the Choi
I'm trying to deduce the Kraus representation of the dephasing channel using the Choi operator (I know the Kraus operators can be guessed in this case, I want to understand the general case).
The dephasing channel maps a density operator $\rho$…
user2723984
- 1,066
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7
votes
3 answers
Can one ever find the elements of a superposition state?
Given some set of basis states $\{\vert 0\rangle, \vert 1\rangle, \vert 2\rangle...\vert N\rangle\}$ and an unknown superposition of the form $\frac{1}{\sqrt{2}}(\vert i \rangle + \vert j \rangle)$, what exactly forbids us from computing $i$ and…
Al Jones
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7
votes
0 answers
Is it better to use fewer gates or fewer working qubits?
I have a script that takes a while to simulate. I can modify it in such a way where I can use fewer qubits at a time, but it will require more iterations of manipulation. I believe this will cut down on simulation time, but does is it worse when…
nikojpapa
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7
votes
1 answer
How are Rigetti and IBM QX device parameters related to Kraus operators?
Rigetti reports the following parameters: (https://www.rigetti.com/qpu)
T1, T2* times
1-qubit gate fidelity (F1q)
2-qubit gate fidelity (F2q) and,
read-out fidelity (Fro)
IBM QX reports the following:…
Edifice
- 429
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7
votes
2 answers
How is the Deutsch-Jozsa algorithm faster than classical for practical implementation?
There is something I really misunderstand about the Deutsch-Jozsa algorithm.
To check if $f$ is balanced or constant, we use the following algorithm:
where $U_f$ gives $(x,y) \rightarrow (x, y \oplus f(x))$.
Let's take $n=1$ for simplicity (thus…
Marco Fellous-Asiani
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7
votes
2 answers
Clarification needed: "Simulation" of $e^{-iHt}$ and its time complexity
On page 3 here it is mentioned that:
However, building on prior works [32, 36, 38] recently it has been
shown in [39] that to simulate $e^{−iHt}$ for an $s$-sparse Hamiltonian
requires only $\mathcal{O}(s^2||Ht||\text{poly}(\log N,
…
Sanchayan Dutta
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7
votes
4 answers
Maximally mixed states for more than 1 qubit
For 1 qubit, the maximally mixed state is $\frac{\mathrm{I}}{2}$.
So, for two qubits, I assume the maximally mixed state is the maximally mixed state is $\frac{\mathrm{I}}{4}$?
Which is:
$\frac{1}{4} (|00\rangle \langle 00| + |01\rangle \langle…
Mahathi Vempati
- 1,621
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7
votes
0 answers
How can blackholes be fast information scramblers?
I noticed that there was already a post discussing the fast scrambling property of black holes. But it seems no satisfactory answer was given.
As mentioned by L. Susskind et. al, the fast scrambling property of BHs seems to say BHs are infinite…
XXDD
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7
votes
1 answer
In which paper was the CHSH game first presented?
The CHSH inequality was presented in the paper Proposed Experiment to Test Local Hidden-Variable Theories published in 1969 by J.F. Clauser, M.A. Horne, A. Shimony, and R.A. Holt. I'm interested in which paper first presented their proposed…
ahelwer
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