# Questions tagged [arithmetic]

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### On unitary matrix form suggested in the Elementary gates paper

In the Elementary gates for quantum computation paper by Barenco et al authors start their proofs by defining a generic form of 2x2 unitary matrix of $\mathbb{C}$ as follows: Can you help me with the ...
31 views

### Qiskit: RGQFTMultiplier is giving wrong answers for 28 bits number multiplication with MPS simulator

I am using RGQFTMultiplier for multiplying two unsigned integers. Starting from simpler example of 2 qbits input, I reached 24 and all worked fine. I am using MPS as backend and my RAM is 32. However ...
43 views

### Comparing qubit values in pairs of qubits

For $2N$ qubits $\{i_1,j_1\ldots i_N,j_N\}$ I would like to have a circuit changing the value of an ancillary register from $0$ to $1$ if $i_1=j_1$ AND $i_2=j_2$ AND ... AND $i_N=j_N$. One way to ...
1 vote
87 views

### 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, ...
192 views

### 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
180 views

### 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 ...
118 views

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{...
60 views

### 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 $c$ ...
79 views

### 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 ...
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\...