I must admit, I think this line of research is of dubious value. What they do is to encode the value of each pixel in a different branch of the wave function. Since they only need to store the colour value of a single pixel and it's index location, ultimately they only need a very small register, with a number of qubits that scales logarithmically in the number of pixels in the image.

A quantum state can be thought of a simply a vector of unit length in a complex vector space, and the state of a system of N qubits is described by a 2^N dimensional complex vector. The entries of this vector are simply the complex amplitudes associated with a particular classical string. In this case N is very small. For the numerics, it seems that they have a 64x64 pixel image, and so they require: 1 qubit for colour, 6 for x position and 6 for y position, for a total of 13 qubits. Thus they only need to store a vector of 8192 complex numbers in order to store the state of the corresponding quantum system. So they are basically classically simulating the quantum system.

You can always use this approach to simulate quantum computation. However, the reason that quantum algorithms cannot be implemented efficiently classically is due to the fact that the length of the vector grows very fast: in order to store a classical representation of the state of 40 qubits with reasonable accuracy you would need around 2 TB, and 100 qubits would require significantly more storage than exists anywhere.

The reason I say I regard this line of research as dubious is because you cannot recover the image from the quantum system. There is a bound on the amount of data that can be recovered from a quantum state (the Holevo bound) which says that you can at most extract 1 bit per qubit. Hence this "compression" is extremely lossy: You can never retrieve more than 13 bits of the original image. This makes the encoding of extremely limited value, but this issue gets glossed over in that paper, and indeed in other papers proposing similar techniques.

You can mail [email protected] for the codes.

I am not sure to what extent you are familiar with quantum computing, but from your post it sounds as if you understand it to be basically just a new approach to algorithms. This is not the case: quantum computing requires information to be stored and manipulated coherently as quantum states, and the current hardware we tend to use for conventional computing simply cannot support these operations. You need a device which can maintain and coherently manipulate quantum states in order to implement a quantum algorithm, and frankly these devices are extremely difficult to build and current attempts only support a handful of qubits (quantum bits). So, you cannot simply implement a quantum algorithm in matlab, you need new hardware, which to a large extent does not yet exist. You could in principle simulate quantum algorithms classically, but would then lose any performance advantage. It sounds like you are asking for something which does not (and cannot) exist.

Dear Joseph, 

Thanks for your reply. 

I am very new in this field. 

I have read a paper "A Flexible Representation and Invertible Transformations for Images on Quantum Computers" of Phuc Q. Le, Abdullahi M. Iliyasu, Fangyan Dong, Kaoru Hirota 

http://link.springer.com/chapter/10.1007%2F978-3-642-11739-8_9

They showed quantum image simulation by Matlab. How they did it ? I asked them  but they never reply me.

Another e is   "Optimal Estimation of States in Quantum Image Processing" , Mario Mastriani , email: [email protected]

I have also mail him & got no reply.

Question is that what are they actually doing ?

Have a nice day.

Kuldip

I must admit, I think this line of research is of dubious value. What they do is to encode the value of each pixel in a different branch of the wave function. Since they only need to store the colour value of a single pixel and it's index location, ultimately they only need a very small register, with a number of qubits that scales logarithmically in the number of pixels in the image.

A quantum state can be thought of a simply a vector of unit length in a complex vector space, and the state of a system of N qubits is described by a 2^N dimensional complex vector. The entries of this vector are simply the complex amplitudes associated with a particular classical string. In this case N is very small. For the numerics, it seems that they have a 64x64 pixel image, and so they require: 1 qubit for colour, 6 for x position and 6 for y position, for a total of 13 qubits. Thus they only need to store a vector of 8192 complex numbers in order to store the state of the corresponding quantum system. So they are basically classically simulating the quantum system.

You can always use this approach to simulate quantum computation. However, the reason that quantum algorithms cannot be implemented efficiently classically is due to the fact that the length of the vector grows very fast: in order to store a classical representation of the state of 40 qubits with reasonable accuracy you would need around 2 TB, and 100 qubits would require significantly more storage than exists anywhere.

The reason I say I regard this line of research as dubious is because you cannot recover the image from the quantum system. There is a bound on the amount of data that can be recovered from a quantum state (the Holevo bound) which says that you can at most extract 1 bit per qubit. Hence this "compression" is extremely lossy: You can never retrieve more than 13 bits of the original image. This makes the encoding of extremely limited value, but this issue gets glossed over in that paper, and indeed in other papers proposing similar techniques.

Dear Joseph,

Once again thanks for your kind information .

Have a nice time.

Bye

Kuldip

I am also wonder how could they implement it using MATLAB. It is very interesting to keep trying with MATLAB to reach that point 

We are working on what we call Quantum Inspired Algorithms, which are novel algorithms that are developed by applying concepts from quantum information to the representation and processing of classical information. That is, they are algorithms that can be implemented and run on conventional computers, whose design is inspired by concepts from quantum information processing, in the same way that evolutionary algorithms are inspired by natural evolution. We have applied this approach to a number of practical problems, and found that it can lead to novel solutions that outperform conventional ones. We use MATLAB to implement our algorithms. If you want to play around with quantum information operations in MATLAB, you might find Toby Cubitt's Quantum Information Package useful:

http://www.dr-qubit.org/matlab.php

If you are interested in what I and my colleagues have been doing, you can get a flavour of it from my two most recent publications on ResearchGate, which are posters, one of which is explained in more detail in:

http://arxiv.org/abs/1108.5720