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Results tagged with mathematics
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user 119
DO NOT use this tag. Use more specific tags such as [linear-algebra] instead.
3
votes
Can I find the states of individual qubits in a quantum register using only linear algebra?
Here's a simple method that will work on any state that is not entangled with other qubits. It's also pretty efficient; it's the method used by the amplitude displays in Quirk.
Find the index $k$ of …
- 42k
1
vote
Accepted
Why do we search for square roots of 1 in Shor's algorithm unlike the quadratic sieve?
The two problems are equivalent.
If you give me a pair $a, b$ such that $a^2 = b^2$ with $a \neq \pm b$ then $c = a b^{-1}$ satisfies $c \neq \pm 1$ and $c^2 = 1$.
If you give me a $c$ such that $c^ …
- 42k
3
votes
In Shor's factorization algorithm for $N$, why can we always find $n$ such that $N^2\le 2^n\...
If $2^k$ is less than $x$, you can increase $k$ by 1 without exceeding $2x$. Because if $2^k < x$ then $2 \cdot 2^k < 2 \cdot x$ and so $2^{k+1} < 2x$. If you start at $k=0$ and keep incrementing, $2^ …
- 42k
6
votes
Accepted
What is the HOG test and how would it help proving quantum supremacy?
There are a couple variants of the HOG test.
"Old HOG" computed the proportion of unique samples whose probability is larger than the median probability of the distribution. It then compares that pro …
- 42k