Chapter 1
Quantum Neural Network
1.1 Introduction and Background
The eld of arti cial neural networks (ANNs) draws its inspiration from the
working of human brain and the way brain processes information. An ANN
is a directed graph with highly interconnected nodes called neurons.Each
edge of the graph has a weight associated with it to model the synaptic
eciency. The training process involves updating the weights of the network
in such a way that the network learns to solve the problem.
The neurons in the network work together to solve speci c problems.
The network can be trained to do various tasks like pattern recognition,
data classi cation,function approximation etc. ANNs are widely used in the
elds of computer vision and speech recognition.
1.1.1 Architecture of an Arti cial Neural Network
1.1.2 Backpropagation
Learning is the way we acquire knowledge about the world around us, and it
is through this process of knowledge acquisition, that the environment alters
our behavioural responses. Similarly, in arti cial neural networks, learning
rules are used, to modify the behaviour of the network in response to the
external stimuli (inputs).
For multilayered feedforward networks, a commonly used algorithm for
weight adjustment is the backpropagation algorithm. There is some math
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2 CHAPTER 1. QUANTUM NEURAL NETWORK
Figure 1.1: feedforward multilayer ANN
involved in the derivation of the formula which can be referred to from [4].
The nal form of the formula looks like:
wij = jyi
Where,
wij is the weight between the neurons i; j
j is the local gradient of the jth neuron
and, yi is the output of the ithneuron
1.2 Quantum Mechanics and ANN
There are problems that are computationally hard i.e. ...
... middle of paper ...
..., which are discussed in detail in [5].
1.3.3 Training and Performance
The training of the network can be carried out using the backpropagation
algorithm. Because of the unavailability of quantum hardware, the network
cannot be tested but we can simulate the network on a classical computer.
1.4 Summary and Discussion
Provide a summary and discuss what you have understood. summarize the
main points and also mention if have found some subtopics dicult.
Bibliography
[1] A. Narayanan, T. Menneer, Information Sciences 128 (2000) 231-255
[2]
[3] H. Everett, Relative state formulation of quantum mechanics, Reviews
of Modern Physics 29 (1957) 454-462.
[4] Satish Kumar, Neural Networks: A Classroom Approach
[5] T.S.I. Menneer, Quantum arti cial neural networks, Ph.D. Thesis, De-
partment of Computer Science, University of Exeter, Exeter, EX4 4PT,
UK, 1998
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In the novel Alice in Quantumland by Robert Gilmore, a young girl named Alice, bored with her family and friends away, wishes she could be more like the Alice in her book- “Alice in Wonderland”. Alice decides to watch T.V., but when she notices something strange happening around her she’s sucked into a world of wonder and science.
The novel, Alice and Quantum Land, by Robert Gilmore is an adventure in the Quantum universe. Alice, a normal teenage girl, goes through quantum land and understands what quantum is and how it works. The quantum world is a difficult one to understand, as its nature is one of complex states of being, natures, principles, notions, and the like. When these principles or concepts are compared with the macro world, one can find great similarities and even greater dissimilarities between the world wherein electrons rule, and the world wherein human beings live. In Alice in Quantumland, author Robert Gilmore converts the original tale of Alice in Wonderland from a world of anthropomorphic creatures into the minute world of quantum mechanics, and attempts to ease the reader into this confusing world through a series of analogies (which comprise an allegory) about the principles of quantum mechanics. Through Alice’s adventure she comes across some ideas or features that contradict real world ideas. These ideas are the following: Electrons have no distinguishing spin, the Pauli Exclusion Principle, Superposition, Heisenberg Uncertainty Principle, and Interference and Wave Particle Duality.
Kandel, E. R., J. H. Schwarz, and T. M. Jessel. Principles of Neural Science. 3rd ed. Elsevier. New York: 1991.
Quantum entanglement is when two or more particles interact with each other in such a way that you cannot describe one particle without mentioning the other particle or particles. When these particles become entangled, we are able to observe and measure certain traits of one, and know, with certainty, the traits of the others across negligible distances. However, there are drawbacks. For example, only one trait can be measured at a given time. If the velocity of a photon was measured, it is impossible to simultaneously measure the spin of the entangled photon.1,2 The theory of quantum entanglement has been prevalent since it was first discovered by Albert Einstein, published in a 1935 paper written with Boris Podolsky and Nathan Rosen titled “EPR Paradox”, and expanded upon soon after by Erwin Schrödinger in a paper titled “Entanglement”.3 Today, quantum entanglement, along with quantum theory, is one of the most researched topics in physics. There are currently applications in of quantum entanglement in quantum cryptography, quantum computing and superdense coding, as well as even teleportation.
The study of neurobiology has long involved the actions and interactions among neurons and their synapses. Changes in concentrations of various ions carry impulses to and from the central nervous system and are responsible for all the information processed by the nervous system as a whole. This has been the prominent theory for many years, but, now, there is a new one to be reckoned with; the Quantum Brain Theory (QBT). Like many new theories, the QBT has merits and flaws. Many people are wholeheartedly sold on it; however, this vigor might be uncalled for. Nevertheless, this could prove to be a valid and surprisingly accurate theory of brain function.
Stergiou, C., & Siganos, D. (2011, August 6). Neural Networks. Retrieved August 6, 2011, from
Quantum Mechanics developed over many decades beginning as a set of controversial mathematical explanations of experiments that the math of classical mechanics could not explain. It began in the turn of the 20th century, a separate mathematical revolution in physics that describes the motion of things at high speeds. The origins of Quantum Mechanics cannot be credited to any one scientists. Multiple scientists contributed to a foundation of three revolutionary principles that gradually gained acceptance and experiment verification from 1900-1930 (Coolman). Quantum Mechanics is
Quantum entanglement is a fascinating phenomenon that was discovered by Max Planck and has been researched up until now. Basically, entanglement, or “spooky action at a distance” as Albert Einstein called it, is the mysterious connection between two subatomic particles. They were entangled by natural occurrences, such as a particle collision, and can send each other info on what happens to them. If you think about it, this could be a huge step for mankind because we can theoretically use it for secret communication, high end internet, teleportation, and even communication with the future. So, what is quantum entanglement and how can it be manipulated to human’s advantage?
By the strange laws of quantum mechanics, Folger, a senior editor at Discover, notes, an electron, proton, or other subatomic particle is "in more than one place at a time," because individual particles behave like waves, these different places are different states that an atom can exist in simultaneously. Ten years ago, Folger writes, David Deutsch, a physicist at Oxford University, argued that it may be possible to build an extremely powerful computer based on this peculiar reality. In 1994, Peter Shor, a mathematician at AT&T Bell Laboratories in New Jersey, proved that, in theory at least, a full-blown quantum computer could factor even the largest numbers in seconds--an accomplishment impossible for even the fastest conventional computer.
"Artificial Intelligence and Consciousness." Encyclopedia of Consciousness. Oxford: Elsevier Science & Technology, 2009. Credo Reference. Web. 26 April 2011.
The most common refutation to the notion of mental states in digital computers is that there are inherent limits of computation and that there are inabilities that exist in any algorithm to...
So, using the above qubit representations, a BB84 transmission for the binary 11010011 could look like this:
Von Neumann architecture, or the Von Neumann model, stems from a 1945 computer architecture description by the physicist, mathematician, and polymath John von Neumann and others. This describes a design architecture for an electronic digital computer with a control unit containing an instruction register and program counter , external mass storage, subdivisions of a processing unit consisting of arithmetic logic unit and processor registers, a memory to store both data and commands, also an input and output mechanisms. The meaning of the term has grown to mean a stored-program computer in which a command fetch and a data operation cannot occur at the same time because they share a common bus. This is commonly referred to as the Von Neumann bottleneck and often limits the performance of a system.
The date is April 14, 2035 a young woman is woken up by the silent alarm in her head. She gets up and steps into her shower where the tiles sense her presence and calculate the water to the precise temperature that she likes. The news flashes in her eyes announcing that today is the tenth anniversary of the day quantum computing was invented. She gets dressed and puts on her favorite hat with a smartband embedded in the rim, allowing her access to anything she needs just by thinking it. Her car is waiting with her trip preprogrammed into it. She arrives at the automated airport to see her associate waiting for her. By the look in his eyes she can tell he is doing a quick online search in his mind. Technology is constantly growing and soon this future will be a reality.
Quantum mechanics is a form of physics that is used to study very tiny objects like atoms. Many people have heard of quantum mechanics before whether it was from a book or a television show. Automatically people think “nerd” or “geek” which is pretty much correct, but those people themselves have no idea how quantum mechanics improved their lives or even how it works. It may sound difficult, but it is really not that hard to understand.