# For Grover's search: How can a quantum computer store the data, and how can it overall be faster than a classical computer

I think Grover's algorithm can be used to find which entry in a list of names contains a given name, say "Fred" in entry number 12345.

Each name can be seen as a binary number, so we might expect to load these numbers into the quantum computer, either retaining the list-sequence, or appending the entry number to the name-text.

Firstly, just loading this into the quantum computer requires the same classical processing as finding the name "Fred". So how can the total process be any faster than the classical. Could we use one loading to do many searches?

Secondly, where can we store this data.

(a) A qubit could store any amount of data in an amplitude, but I don't think there is any way to load data into amplitudes, or for quantum operators to see these amplitudes, or even to find an amplitude equal to a given value. And needing N qubits for a list of N entries is not helpful. So discount this solution.

(b) Entanglement base states can be seen as binary numbers/patterns that could represent data. For the entanglement of a set of n qubits, the list of qubit base states defining each entanglement base state could be seen as an n-digit binary pattern, which could be seen as stored data. But the set of all the entanglement base states and their n-digit binary patterns will always be equivalent exactly to the binary numbers from 0 to 2^n, not values specific to our problem-list.

If 'n' were large enough, some entanglement base states would be equivalent to the encoding of 'Fred/1", 'Fred/2' etc. But the only entry valid to our problem is 'Fred/12345'. And there is no way to distinguish base states that correspond to our data from those that don't, or to sequence them to correspond to our list.

I understand that Grover's algorithm incrementally modifies the entanglement superposition state until the 'solution base state' has amplitude near 1. This seems to be based on this option (b). But how does option (b) store data?

I seem to have some major misunderstandings. Please can you help. Please can I have an answer in plain English (and that distinguishes between qubit states, entanglement states, base states and superposition states), and not using mathematical notation.

• I would focus the question to ask about a single, more specific aspect (you can ask multiple questions if needed). The time required to load the data into the quantum computer is surely to be taken into account, but you can imagine a situation in which the data has been preloaded into a quantum computer, and the search is only performed when the information is needed, in which case only the time required by the algorithm has to be taken into account. You might also have a look at the questions about Grover's algorithm on quantumcomputing.stackexchange.com – glS Jul 3 at 13:22