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1

Given an arbitrary classical algorithm, you can trivially convert it into a "quantum algorithm" by simply making it into a reversible circuit. There are standard ways to do this. Of course, this doesn't really give you any "quantum advantage". Any quantum algorithm obtained this way will have the same efficiency as the same algorithm run ...


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Following Dehaene and de Moor (Theorem 6 in particular), every Clifford unitary can be represented (up to a global scalar factor) by an expression of the form $$ U = 2^{-k/2} \!\!\!\!\!\!\sum_{\substack{x_r,x_c \in \{0,1\}^k \\ x_b \in \{0,1\}^{n-k}}}\!\!\!\!\! i^{p(x_b,x_c,x_r)} (-1)^{q(x_b,x_c,x_r)} \bigl\lvert T_1[x_r;x_b] \bigr\rangle\!\bigl\langle T_2[...


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Here's a simple strategy based on the idea that Clifford operations conjugate Pauli products into other Pauli products. If $U$ is a Clifford operation, then $U P U^\dagger$ (where $P$ is a Pauli operation on one of the qubits) will be a matrix equivalent to a product of Pauli operations. If you check this for each $X_q$ and $Z_q$ for each qubit $q$, the ...


0

what is being said with "a single probe within $2^𝑛$ possible locations" It wants to say the process has translated the qubit (binary representation) into a single location in memory. What is the "probe"? And what is behind "degree of freedom"? A probe is an abstraction of a device that could visit a location (the degree of ...


0

For quantum communication to be practical, transmission has to occur over large distances. The effects of noise accumulate over distance, leading to a possibly crippling loss of entanglement. Therefore, it is of great importance to increase the entanglement. Protocols exist to increase entanglement in weakly entangled systems. One way of doing this is by ...


1

It depends on what you mean by converting classical algorithm to quantum one. One angle of view can be: Is it possible to run any classical algorithm on quantum computer? If this is a case then answer is yes. Since so-called Toffoli gate is effectivelly NAND gate (in case the controlled qubit is set to state $|1\rangle$ before) and such gate enables to ...


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$\newcommand{\calU}{\mathcal{U}}\newcommand{\ket}[1]{\lvert#1\rangle}$Suppose such a circuit existed, and denote with $\calU$ the unitary describing its overall action. For this to be a "circuit detecting entanglement", there should be two types of output states, one corresponding to the answer "yes, the input was entangled" and the other ...


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Apply a CNOT gate with one of the qubits as control and the other as target. You'll get $$\frac{1}{\sqrt{2}}(|0\rangle+e^{i\theta}|1\rangle) \otimes |0\rangle$$ Use the methodology from How to get the relative phase of a qubit? for the first qubit :-)


2

No. For instance, if I either give you $|00\rangle$ or $|11\rangle$ with 50% probability each, or $|00\rangle\pm|11\rangle$ with 50% probability each, there is no way to distinguish these two cases - not even with any whatsoever small probability. The mathematical reason is that those are described by the same density matrix - but you always get some pure ...


3

In general, you want to understand the process by which you compute the matrix elements if you were doing it by hand. In the example you give, for instance, you're effectively computing $|i-j|==1$. This has a classical algorithm which you can figure out, and there's your oracle. In this specific instance there are probably some smarter things you can do. For ...


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It is referring the the "function variable" register of figure 1. It consists of $\log_2N$ qubits, all prepared in the $|0\rangle$ state.


3

To be more specific and as an addendum to Drito's answer which provides a good starting point for your search, I would like to narrow it down for you, by recommending Quantum Information Processing. Since this journal is good, and moreover it has papers regarding Image Processing related topics like its Representation, security.


2

This is a good list made by Prof. Rod Van Meter. Maybe you could look at the papers you based your work off of and see where they were published? That should give you a sense of which journals are interested in the sort of work you've done.


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No, quantum computers can't run for-loops faster in general. There are certain specific tasks that can be done using a for-loop that can instead be done in a different way on a quantum computer, with fewer total operations. For example, Grover search can replace the loop for x in range(N): if predicate(x): y = x with something that uses $O(\sqrt{N})$ calls ...


0

On paper I think this a cool idea. Though the terms you are using like cost threshold, cost function, and weights will all have to be transformed. Classically this a well thought out idea and then to ask "If done on classical can I just tweak a few things and make them quantum?" is an awesome idea. The terms you used must be extended to the quantum ...


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