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1500 questions
6
votes
1 answer
Show that if the Lindblad satisfy $\sum_\mu L_\mu L_\mu^\dagger=\sum_\mu L_\mu^\dagger L_\mu$ then the von Neumann entropy increases monotonically
How can we show that when the Lindblad operators satisfy the condition:
$$\sum_{\mu}L_{\mu} L_{\mu}^{\dagger} = \sum_{\mu} L_{\mu}^{\dagger}L_{\mu},\tag{1}$$
the master equation evolution monotonically increases the von Neumann entropy. When…
Sudhir Kumar Sahoo
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Register size in factoring 15 using Shor's algorithm
In Nielsen and Chuang's book: Quantum computation and quantum information (2016), there is an example in Box 5.4 which shows how to factor $15$ using Shor's algorithm. I am confused about a particular point in this example. They start with the…
Anne
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6
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3 answers
Why can't we simulate a Qubit using classical computer?
I am completely a noob in terms of quantum computing, have watched several videos to understand what Quantum computers are trying to achieve.
I am a programmer of classical computers. We have a concept called Duck typing :
Duck typing in computer…
Anurag Vohra
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6
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1 answer
Can we use Hadamard test to estimate phases?
There have been some questions discussing the Hadamard test and quantum phase estimation (QPE), but I did not find the answer to the following question. Suppose we are given $|\psi\rangle$, which is an eigenstate of $U$ such that $U|\psi\rangle =…
fagd
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6
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1 answer
Complexity of a distribution of measurement of output of quantum circuit
The Kolmogorov complexity of a string refers to a deterministic object. Here, I refer to the analogous "complexity of a distribution", or better, to the complexity of sampling from a distribution, in the sense defined this paper: the complexity of…
Doriano Brogioli
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6
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1 answer
How is the number of measurement outcomes linked to the rank of the observable?
I am thinking about the following question:
Assuming that we have some given state $\rho$ and we perform a
measurement with $k$ outcomes on this state. Then we can describe the
measurement in outcomes as eigenvalues of the measurable, i.e.,…
LeoW.
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6
votes
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What do commuting quantum channels look like?
Consider two channels, $\Phi,\Psi\in\mathrm C(\mathcal X)$ acting on some space $\mathcal X$, and suppose they commute, that is,
$$\Phi(\Psi(\rho))=\Psi(\Phi(\rho))$$
for all states $\rho$. Can anything be said about the structure, e.g. in terms of…
glS
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6
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Solovay-Kitaev Balanced Group Commutators in SU(2) Implementation
I am currently looking into quantum compilation and came across Dawson and Nielsen's paper on the Solovay-Kitaev Algorithm, which seems like a good starting point as it is referenced in a many of the papers on the subject. I have a working (although…
Alan
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6
votes
3 answers
Is the SWAP gate a Clifford Gate? How would I express it using the Clifford Gate generators?
By my calculations, it looks like the SWAP gate is a Clifford Gate. See the following table:
I follow the same method as in this paper for showing a gate is a Clifford Gate. I got the above table by performing calculations in Qiskit. How would I…
Quantum Guy 123
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How to obtain arbitrary distribution in quantum database
I was working on the Grover's algorithm and the most common example is for a unitary distribution in a quantum database, for example:
$|\psi\rangle = \frac{1}{2}|00\rangle + \frac{1}{2}|01\rangle + \frac{1}{2}|10\rangle + \frac{1}{2}|11\rangle.$
Is…
brzepkowski
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2 answers
How is Quantum Phase Estimation useful for simulating dynamics of a many-body system?
I am quite aware of the Quantum Fourier Transform (QFT) as well as the very closely related topic of Quantum Phase Estimation (QPE). The latter is usually motivated as follows:
Given a unitary $U$ and a state $|\psi \rangle$ that is promised to be…
Marion
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Could the Hamiltonian of a 2x2 Rubik's Cube be simulated with a NISQ device?
Consider the four cells on each of the six faces of the 2x2x2 Rubik's cube (the pocket cube). We can construct and simulate a quarter-turn Hamiltonian as below. $^*$
Let $\langle F_1,U_1,R_1\rangle$ be the quarter-turn moves that rotate each of…
Mark Spinelli
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6
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2 answers
Are there ''interesting'' examples of circuits where gates can all commute each other?
Are there ''interesting'' examples of circuits where gates can all commute each other?
More formally, there may be some group of circuits where gates and, particularly, CNOTs (as the only two-qubit gate in common universal sets), can all commute…
Daniele Cuomo
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Tripartite quantum marginal problem
Consider a tripartite quantum system with the three subsystems labeled $A, B,$ and $C$. Now take two states $\rho_{AB}$ on the joint system $AB$ and $\rho_{BC}$ on the joint system $BC$. Under what conditions are these compatible with the same…
biryani
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What are some of the interesting problems whose solutions have been proposed using quantum neural networks?
I know there are some "quantum versions" of hand-writing recognition algorithms which have been proposed using quantum neural networks. Example: "Recognition of handwritten numerals by Quantum Neural Network with fuzzy features" (J Zhou, 1999).…
Sanchayan Dutta
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