Living in a world where computers have solved some of the world’s biggest problems and revolutionised the way science and technology function in our day to day lives there still exists a number of problems that even classical computers cannot solve or take an incredibly large amount to do so. For example RSA encryption works on the basis that factoring large numbers takes incredible amounts of time even the most sophisticated classical factoring algorithms take unrealistic amounts to factor large numbers such as the ones used in RSA cryptography. The theory of the quantum computation model takes advantage of quantum mechanics to solve problems that normal computers cannot solve and solve problems much faster in reasonable amounts of time. …show more content…
However if we were to multiply the vector |ψ> by e^iϕ, puts the vector psi in a state that we cannot define. A system with an “N” number of qubits is described by a unit vector C^2⊗C^2⊗…⊗C^2 repeated “N” number of times each C^2 is the space of one single qubit with the basis |0> and |1> the space is denoted by B^(⊗n) the basis state for the space are all products of the form |X_1>⊗|X_2>⊗…⊗|X_n> while X is an element of a real number of zero or one. Having these basis states the N-qubit system can be represented in the form ∑_(〖xϵ{0,1}〗^n)▒〖a_x |x>.〗
Example 1: We have a quantum system composed of 2 qubits we can then write the vector including all the possible states like this |ψ> = α_00 |00> + a_01 |01> + α_10 |10> +α_11 |11>.
H|x> = ∑_(zϵ{0,1})▒〖(-1)〗^xz/√2
W|x,y> =|x,y⊕f(x)> ⊕means addition modulo 2. Let’s do a simple quantum algorithm say we have a function f: (0,1) is f one-one meaning the does the function return the same value when two different inputs are given, generally we would solve this by inputting 0 and then inputting 1 if both outputs are the same then f is one-one. However, we could also solve this problem with only one input. We do this by creating a
Alan Mathison Turing was born in Paddington, London on June 23, 1912. At a young age he displayed many signs of high intelligence. When his parents and teachers saw this, they sent him to the very prestigious Sherborne School at only thirteen years old. There, he studied math and science which sparked his interest for computers and coding. After finishing his studies at Sherborne, he enrolled at King’s College, or what is now known as the University of Cambridge. As he attended school there from 1931 to 1934, he developed a certain respect for physics and, more specifically, quantum-mechanics in which he proved the central limit theorem. His accomplishment was so massive that he graduated as a fellow at the school. Alan Turing, using his extensive
In this case, the Alain Aspect experiment was testing entanglement between co-generated and entangled particles. Their behavior was compared to results predicted by Quantum Mechanics and results predicted by Bell’s Inequality. The experiment
* 2D boolean array used to keep track of which coordinates are currently occupied by blocks
movement registers. The essential thought of the TMTO is to pre-process a huge set of states A,
This is the study focused on developing technology based on the principles of quantum theory (“Quantum Computing”, 2010). According to the creator Geordie Rose, “The computer is able to enter other dimensions to bring back the answers to questions that we haven’t even thought of yet! Not only that, but they are taking resources back into our dimension from wherever the other one lies” (“Forget Mandela Effects, Think Quantum Pollution”, 2016). Parallel universes overlap with ours which makes it easy for the computer to tap into them. It is claimed that testing of these computers causes some of the other universes to slip into ours. Another theory within quantum computing is quantum tunneling. “This is a two-way communication pathway where Qbits enter other dimensions and burrow into a parallel world. Upon receipt of a solution from another dimension it must be translated back to a form humans can use” (“Forget Mandela Effects, Think Quantum Pollution”, 2016). This causes some people to remember things one way and other people to remember things the other way. They are getting memories from two different
According to Everett's theory, in this timeline, the object is a particle, but there's another timeline where it's a wave. Even more baffling, this implies that quantum phenomena aren't the only things that split the universe into separate timelines. For everything that happens, every action you take or decide not to take, there are infinite other timelines—worlds, if we may—where something else took place. That's the many-worlds interpretation of quantum physics. It may not seem like it, but it's actually simpler than the Copenhagen interpretation—it doesn't strike an arbitrary line between the quantum world and everything else, because everything behaves in the same way. It also removes randomness from the picture, which helps the math work out nicely.
Von Neumann architecture is a type of computer architecture model that acts as a store-program digital computer which uses a processing unit and a separate storage system that holds instruction and data. The processing unit is a combination of the control unit which has program counter and an instruction register and processor registers with an Arithmetic logic Unit (ALU). The memory unit is a block of shared storage registers that stores both data and instructions (Petterson & Lennessy, 2014). The memory block has a data bus and an address bus for communication with the processor. A Von Neumann system is characterized by a common bus that does both instruction fetching and operations of data. This means handling of data and instructions has to be done in sequential order which is known as Von Neumann Bottleneck, since the bus cannot operate in a full duplex manner.
Mathematical operators such as products, sum, logical operations such as and, or, etc. .can be programmed along with the signal flow. Matrix multiplication becomes easy with the matrix gain block. Trigonometric functions such as sin or tan inverse (at an) are also available. Relational operators such as ‘equal to’, ‘greater than’ etc. can also be used in logic
The third step operates on each column separately. Each byte of a column is mapped into a new value which is a function of all the four bytes in that column. It is designed as a matrix multiplication in which each byte is treated as a polynomial in
The extremal case in this sense arises when we are given a system of K2 normalized vectors {|ψi:i=1,…,K2} in CK for which|ψi|ψj|2=1K+1,1≤i≠j≤K2.(2)Such POVMs are called symmetric informationally complete POVMs, or simply, SIC-POVMs.SIC-POVMs constitute a basic ingredient in many applications of quantum information processing; see, for example, Refs. 6–13, etc., and references therein).For the existence of SIC-POVMs, we have the following facts: (I)Explicit analytical constructions of SIC-POVMs satisfying (2) have been given for small dimension K, •K = 2, 3, 4, 5, see Refs. 6 and 7;•K = 6, see Ref. 8;•K = 7, 19, see Ref. 9;•K = 8, 12, 28, see Refs. 10–12;•K = 9, 11, 13–15, 35, 48, see Ref. 12;•K = 16, see Ref. 13. (II)It has been conjectured that SIC-POVMs exist in all dimensions [see Ref. 6 (Sec. 3.4) or Ref. 7] and numerical evidence exists for dimensions up to 67 (see Ref. 12). The most recent development in this area can be found in Ref. 14.Note also that Appleby15 studied SIC-POVMs for operators with arbitrary rank.C.Our resultsGenerally speaking, it is hard to explicitly construct SIC-POVMs. In fact, there are no known infinite families of SIC-POVMs and it is not even clear whether there exist SIC-POVMs for infinitely many K. Based on this observation, Klappenecker et al.1 proposed to construct approximately symmetric informationally complete positive operator-valued measures (ASIC-POVM) for possible applications in
During the late 1970s, Hall produced at least two papers on the COMS paradigm he called "encoding/decoding," in which he builds on the work of Roland Barthes. What follows is a synthesis of two of these papers, offered in the interest of capturing the nuances he gave his presentations. The numbers in brackets identify the two papers (the bibliographic details are provided at the end).
In the paper titled “The dynamical behaviors of complementary correlations under decoherence channels”, Du et.al have investigated the relationship between complementary correlations (CC) and the entanglement over noisy channels. In particular, for bipartite qubit systems, it has been shown that there exists an optimal threshold to which CC has to be compared in order to determine the dynamical behavior of entanglement. Furthermore, authors claim to derive a novel threshold on environment parameter as well which is based on the Pearson correlation between measured outcomes of complementary observables. This topic has already been investigated to some extent in Ref. [1], the main novelty of this work is the inclusion of the decoherence.
The advent of modern physics, however, suggests that although such model explains everyday observations, it fails to account for the behaviors of particles in a subatomic level. One of the most famous is the Observer’s Effect, according to which one can never determine a photon’s path and detect its existence at the same time, because while detecting its existence one has to collide it with another particle and thus making it go to a certain direction. Therefore, when not detected, a light beam behaves like a wave that goes to numerous possible paths simultaneously – the light is at the same time going through path A and non-path A.
XNOR, where NAND and NOR are universal gates since they can be combined to form any
One of the basic postulates of quantum mechanics is the Born’s rule of probabilities. It states that probability of a particle to lie within a certain volume element, at a particular time and position, is equal to the square of the wavefunction representing the quantum mechanical state multiplied by the volume element. This rule is foundational to the theory of quantum mechanics. However, it hasn 't yet been tested experimentally to appropriate precision although bounds for its validity have been suggested for triple slit interference experiment. One reason for limiting the accuracy of these tests can be systematic errors. Another possible source of error can be the wrong application of superposition principle. In the present work we are