Nielsen explains how a search algorithm can access a classic database. I have a few questions. I hope you can help me a bit :) I work with a few quotes from the book.

The principle of operation is a means by which the binary encoded state of the quantum index (where $$0$$ to $$2^n − 1$$ is represented by n qubits) is translated into a unary encoding (where $$0$$ to $$2^n − 1$$ is represented by the position of a single probe within $$2^n$$ possible locations) which addresses the classical database.

Ok, if I understand that correctly, the quantum index register is translated into a unary system that specifies the position in the classic database. What I understand less is this statement: "represented by the position of a single probe within $$2^n$$ possible locations" what is being said with "a single probe within $$2^n$$ possible locations"?

The database effects a change on a degree of freedom within the probe which is unrelated to its position.

What is the "probe"? And what is behind "degree of freedom"? The sentence is not clear to me.

Each circle represents a switch, addressed by the qubit inscribed within.

OK, so the qubit controls the switch and thus the route.

The data register qubits enter at the top of the tree, and are routed down to the database

How does that work exactly? So where is the connection with the switches from earlier?

The binary to unary encoding is then reversed, leaving the data register with the desired contents.

That is, the entries in the database affect the qubits that penetrate the schema. So that the qubits can then accept their content?

The qubits are then routed back into a deﬁnite position

How does the way back work?

• Chapter number & page number? Commented Apr 4, 2019 at 17:09
• Chapter 6.5, pages 265-268, especially figure 6.9
– user4961
Commented Apr 4, 2019 at 18:53
• Can anybody help me further? If something is unclear, I like to improve the questions :)
– user4961
Commented Apr 7, 2019 at 20:01

what is being said with "a single probe within $$2^𝑛$$ possible locations"

It wants to say the process has translated the qubit (binary representation) into a single location in memory.

What is the "probe"? And what is behind "degree of freedom"?

A probe is an abstraction of a device that could visit a location (the degree of freedom related to location) in memory, and processes/stores the information (the so-called degree of freedom unrelated to location) retrieved from the location it's at.

The data register qubits enter at the top of the tree, and are routed down to the database - where is the connection with the switches from earlier?

The CPU has an index register $$|x\rangle$$ and a data register $$|d\rangle$$ (mentioned in text above your quote in the book), the CPU would like to add contents $$d_x$$ of the $$x^{th}$$ memory cell to the data register, i.e. $$|d\rangle \rightarrow |d\bigoplus d_x\rangle$$. The switches guide the data register qubit, based on index register $$|x\rangle$$, to one of the $$2^n$$ locations.

The binary to unary encoding is then reversed, leaving the data register with the desired contents.

Yes, it just says we have gone from qubit index to a location in memory, then applied the information retrieved from that location to the data register

The qubits are then routed back into a deﬁnite position - How does the way back work?

Swithces form a binary tree. We can go from leaf node (a location on memory) to the root node ("a definite position") by recursively visiting the parent node.