# Questions tagged [quantum-computation]

Quantum Computation deals with considering computation as fundamentally physical, as well as replacing the classical binary digit (bit) with the quantum binary digit (qubit). While the classical bit is either 0 or 1, the qubit can be in a superposition of these states. Computation systems that use quantum phenomena, such as superposition and entanglement, can solve certain complex problems very quickly.

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### Can someone explain period finding in either the Discrete or Quantum Fourier Transform (Shor's algorithm)

I am learning about Shor's algorithm, a way to find factors of large numbers using a quantum computer. One of the main steps of this algorithm relies of the Quantum Fourier Transform (QFT) - a quantum ...
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### How to multiply the data distribution by the dirac delta function to get the original function?

Given data set $\{x_i, f(x_i)\}$, and $i\in[1, n]$, I try to get the original function for the $f(x)$. However, I can only access the $f(x_i)$ by using the $f(x_i)$ to multipy with dirac delta ...
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### Is {Z, CZ} an universal quantum gate set for diagonal gates with eigenvalues +1 and -1?

Consider diagonal quantum gates with eigenvalues $\pm 1$, i.e. all diagonal elements are either $+1$ or $-1$. Can these gates always be decomposed into a finite number of Z and controlled-Z gates? My ...
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### Help in understanding the symmetrical quantum system.

Help in understanding symmetrical quantum system. In some articles I read this sentence: When the tripartite quantum system is symmetrical, i. e., the state of the whole system is invariant under the ...
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### What's connection between eigenvalue/eigenvectors and outer products?

What's the connection between eigenvalues and vectors and outer products? For example, if an operator A has eigenvalues $\lambda_1$ and $\lambda_2$ corresponding to eigenvectors $|{\psi}_1\rangle$ and ...
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### Approximate matrix inverse by Fourier approach

Given a hermititan matrix $A$ with the possibility to generate $e^{-iAt}$ for $t\geq 0$ how would I proceed to approxiamte: $A^{-1}\approx\sum_j\alpha_je^{-iAt_j}$ $\quad$ with $\alpha_j\in\mathbb{C}$...
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### How much classical algorithmics and probability theory is necessary for quantum algorithmics?

I would like to learn more about quantum algorithmics in next months/years. I wonder - do I need to be very very good in "classical" algorithmics to be good in quantum algorithmics, or are ...
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### Prove that the tensor product of unitary matrices is also unitary

Show that if $A$ and $B$ are unitary matrices, then $C = A \otimes B$ is unitary.
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### Understanding the probability of measure in the Deutsch-Jozsa quantum algorithm

I am trying to understand my teacher's mathematical development. Just to give you some context, $\vec{c}$ is a boolean vector and this is the probability of measuring $\vec{c} = (c_1,...c_n)$. When ...
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### quantum tensor equation simplification

I've started learning quantum computing of late and got interested in some secret sharing. In a recent post on the site https://quantumcomputing.stackexchange.com/questions/13195/grover-search-with-...
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### How many unique values of $\cos(\frac{a\pi}{N})\cos(\frac{b\pi}{N})$ are there for the positive integers $a,b < N$

The Question How many unique values of $\cos(\frac{a\pi}{N})\cos(\frac{b\pi}{N})$ are there for the positive integers $a,b < N$ for a given $N$? I would like a function $f(N)$ which gives that ...
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### Group generated by quantum H-gate and T-gate

What is the group generated by Hadamard gate and T-gate? Or, in terms of Algebra: Let $U$ be the multiplicative group of 2-by-2 unitary matrices, and let $P$ be $\{e^{i\phi}I : \phi \in [0,2\pi)\}$. ...
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### Spotting the matrix representation of the quantum AND operation

https://people.maths.bris.ac.uk/~csxam/teaching/qc2020/lecturenotes.pdf Applying the above construction to AND we get the map $(x1,x2,y) \rightarrow (x1,x2,y⊕(x1∧x2))$ for $x1,x2,y \in \{0,1\}$. The ...
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### Unclear theorem about unitary transformations

I am currently working on quantum finite automata, when I came across a paper by Ambainis and Nahimovs. I am having some struggle with the "theorem from linear algebra" stated by them in ...
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### Probability of error for randomized algorithm solution to the Deutsch-Jozsa problem

The Deutsch-Jozsa problem asks to determine whether a function $f: \{0, \ldots, 2^n - 1 \} \to \{ 0, 1\}$ is constant or balanced (half of the inputs yield 1, the other half yield 0). Suppose we ...
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### Can I find the exponent of a matrix given only a vector and its image?

here is my problem : Given a $GL(m,2)$ matrix $A$, and $x,y$ two non-zero $F_2$ vectors of length $m$ with the premise that $y = x(A^n)$ for some positive integer $n$. The goal is to find n. Is it ...
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### If $m > n$ are coprime, then there (often) exists $p$, $q$ where $mq+1=n^p$. why?

One of the key reductions in Shor's algorithm in quantum computing for finding prime factors of $m$ is that if $n < m$ is coprime with $m$, then there likely exists integers $p$ and $q$ where \$mq+...