Questions tagged [arithmetic]

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Problem adding two numbers in a quantum computer with Drapper's algorithm

I would like to add numbers. In this simple example a = 1 and b = 1. The circuit I created looks like this: We have two registers a and b. Both have a size of 3 qubits. I'm using Big Endian notation, ...
  • 37
0 votes
1 answer

Why a Fourier Adder Gives Multiple Faulty Results?

I followed this tutorial and wrote a code that implements the following circuit: By writing the following code: ...
1 vote
1 answer

Is it possible to implement an in-place multiplication quantum circuit?

How can a reversible multiplication quantum circuit be implemented? By "reversible" I mean one that performs a *= b on the inputs a and b of the ...
2 votes
1 answer

Oracle for amplitude addition

Assume one is given two oracle circuits providing access to matrices $A_{ij}$ and $B_{ij}$ as follows (see eq. (6.2) here): \begin{equation} O_A |0\rangle|i\rangle|j\rangle=\left(A_{ij}|0\rangle+\sqrt{...
  • 1,700
2 votes
1 answer

How can one sort two registers without leaving an entangled ancilla behind used for comparison?

If we have an state $\alpha|abc\rangle + \beta|bad\rangle$, and we know that $a<b$, how can we obtain state $\alpha|abc\rangle + \beta|abd\rangle$ without entangled ancillas, if we don't know $c$ ...
  • 421
3 votes
1 answer

How to verify a matrix-vector product with Grover search?

I am looking at the Ambainis et al. method of verifying whether $AB = C$ in $O(n^{7/4})$ queries, as described in Buhrman and Špalek. They have the following sentence: verify the matrix-vector ...
2 votes
1 answer

Formulate Controlled-Not as mapping (including modulo-2 addition)

We often see that the controlled-not gate is written as $CNOT |x y \rangle = |x\rangle |x \oplus y\rangle$. Now, would it be possible to further expand this to get a general equation? $$(\alpha_0 |0\...
  • 35
8 votes
4 answers

Computing $e^x$ on a quantum computer

Does anyone know how to make a quantum circuit to compute exponentials where the exponent can be a fraction? To be more precise, I'm looking for a fixed point quantum arithmetic circuit that does the ...