I am unclear on how to input data into a quantum algorithm using the quantum gate model. I understand that if we need to process 2^n states, then we need n-Qubit. For example, the following 4 states (00, 01, 10, 11) require 2 Qubits, and the following 8 states of (000, 001, ..., 111) require 3 Qubits. Now, if we have a fairly large list with millions of of item, ( e.g., a network of people), using the quantum gate model, how to input these item to the algorithm for processing? Please feel free to discuss in detail. Thanks!
There are different ways to access classical data with a quantum computer. The most naive one would be to create a quantum state of the style
|psi> = \sum_{x=1}^{2^n} c_x |x>
with n the number of qubits, |x> a state in the computational basis (i.e. |x> = |0101110101...>), and c_x some amplitude. You could codify your data in the coefficients c_x. That should be possible if the data is classical and is stored in some classical memory. Another option is that |x> is just a pointer to the position in your classical list, and then you can manipulate the c_x to e.g. detect an element in the list (as in Grover's quantum search algorithm).
I guess there are more ways. But the above procedures have some nice features, since the states are usually (multipartite) entangled and are also a massive superposition of computational states.
To be able to answer this question, allow me first to simplify the problem:
1- Let's assume that the data can be stored in a form of binary vectors, each of equal size 2^m.
2- Let’s assume as well that all those binary vectors representing the various data are 2^n binary vectors.
Using a classical computer (i.e. electronic computer) to process such data, it will require 2^n steps only to read it (i.e. O(2^n)), assuming that this computer can read a single vector of size 2^m at a time.
Now on the “quantum” side, we have a quantum CPU that can do computations faster than classical CPU and a quantum memory. In order for the quantum CPU to process this huge amount of data, this data needs to be loaded into quantum memory; we need to have a quantum loading scheme (QLS).
In 2012, Pang proposed a QLS [1] to Loading N-dimensional vector into quantum memory from classical memory with O(log N) steps, which was later utilized in [2] for creating a quantum search algorithm for set operations on classical data.
In 2013, BenQiong et al. proposed quantum loading scheme [3] based on entangled states, capable of loading gray scale images of dimensions 2^p×2^p in quantum memory of size 2p+8 qubits in just O(p) steps. Their proposed QLS would enable quantum CPUs to be compatible with electronic memory and electronic data, and make possible quantum image compression and quantum signal processing that has classical input and output.
We could use QLS to load our classical data into quantum memory of size O(n+m) qubits, with only On steps,
Ref:
[1]https://arxiv.org/abs/quant-ph/0612061v3
[2]https://link.springer.com/article/10.1007%2Fs11128-012-0385-8
[3]https://link.springer.com/article/10.1007/s11432-013-4866-x
P.S.
Is there any way to write latex code in research gate?
@Igael Azoulay I was referring to the IBM-Q. Can that be done? --Ahmed
Thanks for all responses. IBM-Q is an actual quantum computer with real hardware capacities that are based on quantum mechanics. You can indeed represent data using the quantum gates model. I know how to represent small data items. Now I have the issue with the scale. This is what I need help with. Thanks!
Quantum circuits. It seems that you are mot familiar with that model. But that's ok, thanks for your effort!
In quantum algorithms, we often assume that the data points are stored in a stuitable structure (memory), so that we can have efficient access to them. All the data can be accessed in quantum parallel. Given n data vectors v1,v2,...vn stored in a quantum random access memory, we access them in quantum parallel as shown below.
\sum_i |i>|0>---->\sum_i |i>|v_i>.
I recommend the following reference:
Vittorio Giovannetti, Seth Lloyd, and Lorenzo Maccone, Quantum Random Access Memory, Phys. Rev. Lett. 100, 160501 (2008).
It is worthwhile noting that, if v_i can be efficient computed given i, the above access procedure can also be achieved without any quantum memory.
You may go through this paper for your initial help,
https://arxiv.org/pdf/1803.01958.pdf
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