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Expected repetitions of the quantum part of Shor's algorithm

Shor's algorithm to factor a number $N$ goes as follows: Pick a random value $b \in (0, N)$. Use a specific quantum computation to a sample a value $v$ that should be close to $2^{m} k/p$ where $m$ is a precision parameter of the quantum…
Craig Gidney
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How much faster is “D-Wave Two” compared to its predecessor?

I don't have any specific task or algorithm in mind, so depending on how they were tested – Is there any research which shows just how the D-Wave Two computer was faster (in terms of computation performance) than its predecessor (D-Wave One)?
kenorb
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Quantum algorithms for problems outside NP

What is known about quatum algorithms for problems outside NP (eg NEXP-complete problems), both theoretically like upper & lower speedup bounds and various (im)possibility results, as well as concrete algorithms fro specific problems? The reason I…
Daniel Mahler
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How can we be sure that for every $A$, $A^\dagger A$ has a positive square root?

In the Polar Decomposition section in Nielsen and Chuang (page 78 in the 2002 edition), there is a claim that any matrix $A$ will have a decomposition $UJ$ where $J$ is positive and is equal to $\sqrt{A^\dagger A}$. Firstly, how can we be sure that…
Mahathi Vempati
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Shor's algorithm weaknesses & uniqueness of close rational

I'm working through a problem set, and am stuck on the following problem: a) What can go wrong in Shor’s algorithm if Q (the dimension of the Quantum Fourier Transform) is not taken to be sufficiently large? Illustrate with an example. b) What can…
Commutator
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What limits scaling down the size of superconducting qubits?

There are multiple ways of building a qubit: Superconducting (transmons), NV-centers/spin-qubits, topological qubits, etc. The superconducting qubits are the most well-known qubits and are also the easiest to build. The machines by IBM and Google,…
nippon
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Qubits specification on IBMQ devices

As it is shown here, CNOT gates between different qubits have different error rates. I have the following questions: 1) While defining a circuit on QISkit, does q[0] always correspond to the same qubit on a device (e.g. the qubit labeled q0 on the…
Mathist
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Is there a general method to implement a 'greater than' quantum circuit?

I am interesting in finding a circuit to implement the operation $f(x) > y$ for an arbitrary value of $y$. Below is the circuit I would like to build: I use the first three qubits to encode $|x⟩$, use the other three qubits to encode $|f(x) = x⟩$,…
Max
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Decomposition of arbitrary 2 qubit operator

As you know, universal quantum computing is the ability to construct a circuit from a finite set of operations that can approximate to arbitrary accuracy any unitary operation. There also exist some results proving that exact decompositions of…
PDRX
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Can a stored programming model be applied to a Quantum Computer?

A stored programming computer model is that where a central memory is used to store both instructions and data that they operate on. Basically all the classical computers of today that follow the von Neumann architecture use the stored programming…
K Sarkar
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Generalization for $n$ quantum teleportations

In Breaking Down the Quantum Swap, it is stated: Thanks to the CNOT, we can implement a xor-swap on a quantum computer. All we need to do is chain three CNOTs back and forth. In a comment to a previous question, the author of the aforementioned…
user820789
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What good references would you recommend to understand the (continuous-variable) CV model of computation?

If you have good references about the CV model that are understandable from a computer science background, that would be great. If they include numerical examples, that would even be better.
cnada
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What is quantum computing vs. what is not quantum computing

That is to say, what are some common or popular misconceptions about what constitutes quantum computing? and how are those things misconceptions? It could help in explaining to frame this while imagining as if you were explaining for a…
PowerLuser
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What does it mean for a quantum computer to have $X$ qubits?

I want to preface with a disclaimer that I am a physicist with minimal knowledge of computer hardware. I have a solid understanding of quantum information from a theoretical standpoint but zero knowledge of how it is implemented. Here goes... When a…
Jackson
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Does conditional gate collapse controller's superposition?

I've created a simple circuit in Q-Kit to understand conditional gates and outputted states on each step: In the beginning there is clear 00 state, which is the input The first qubit is passed through the Hadamard gate, it gets into superposition,…
CodeSandwich
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