Quantum computers

Quantum computers

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  Quantum Computers Abstract—This paperconsists of introduction to quantum computers, Theorems related to quantum computers like superposition and entanglement. Advances and advantages of quantum computers are also included in this paper. Later on description of the company named D-wave is also given who is the only one who makes Quantum processors and how that company evolved. Keywords—Quantum computers; Entanglement; Superposition; D-wave; INTRODUCTION Till now Computers on which we were working on were based on Principles of Digital electronics whereas Quantum Computers are based on principles of Quantum Theory. Quantum Theories like Entanglement, Superposition, etc. Quantum computers have been made to do complex calculations or processes which humans can’t do. Digital Computers encode data into binary bits whereas Quantum Computers encode data into Q-bits or Quantum Bits. A Quantum Turing machine is an example of theoretical model of Quantum Computers. To understand Quantum computers we first need to understand concept of Superposition and Entanglement [1]. ABBREVIATIONS AND ACRONYMS • Alanine: an amino acid used to analyze quantum state decay • Flops: Floating point operations per second • Josephson Junction: tunneling junctions with superconducting electrodes • NMR: Nuclear Magnetic Resonance • Q-bits: Q-bits or qubits are also known as Quantum bits which are used instead of binary bits in digital computers. • Trichloroethylene: a chlorinated hydrocarbon used for quantum error correction THEOREMS BASED ON QUANTUM MECHANICS A. Superposition Theorem In Digital electronics as mentioned above we use digital binary bits for communication which are either 1 or 0 at a time. But Q-bits or quantum bits has a property that it can show both 0 and 1 states at a time. They superposes each other while communicating [3]. B. Quantum Entanglement Quantum Entanglement is nothing but strong correlation between many pairs of particles. For example if there are two particles entangled together then they will complement each other’s spin, momentum, polarization, position, etc. And this correlation is so strong that, it will exist even if both of the particles are kept at either ends of the universe. Entanglement is a very important principle for building Quantum Computers. Because of this principle scientists and researchers are concerned only for 1 qubit out of two, if we are talking about 2-Qubit Quantum Computer [4]. TIMELINE OF QUANTUM COMPUTING In late 90s physicist came across some problems while doing complex calculation in Digital Computers. They were not able to do it quickly or sometimes can’t even solve the problem. From here the idea of quantum computers came. C. Timeline First successful effort was made in 1970 by Stephen Wiesner invented conjugate coding. Then in 1973 Alexander Holevo gave information about Q- bits. In 1975 R.P. Poplavskii gave the superposition Theory. In 1976 Polish mathematical physicist Roman Stainslaw Ingarden gave information on Quantum information theory on replacement of Shannon information theory as it was not directly applicable to Quantum Case. In 1980 Yuri gave an idea of Quantum computing. In 1981 Tommaso Toffoli introduced the reversible Toffoli GATE which together with the NOT and XOR gates provides a universal set of classical computation. In 1982 Paul Benioff proposed the first recognizable theoretical quantum computer. In 1984 Caharles Bennett and Gilles Brassard used Wieser’s conjugate coding for distribution of cryptographic keys. In1985 David Deutsch described the first theoretical universal quantum computer. In 1991 Artur Ekert invented entanglement based secure communication. In 1993 Dan Simon invented oracle problem of digital computer for which quantum computers are faster.
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  In 1994 PeterShor discovered an important algorithm called Shore’s Algorithm. Also Ignacio Cirac and Peter Zoller proposed an experimental realization of the controlled NOT GATE with trapped ions. In 1995 Peter shore and Andrew steane togather gave the first schemes for quantum error correction. Also Christopher Monroe and David Wineland experimentally realized first practical C-NOT GATE. In 1996 Lov Grover invented quantum database search algorithm. David P. DiVincenzo, from IBM, gave a list of minimum requirements for creating a quantum computer. • In 1997 Cory, Fahmy, Havel and Neil Gershenfeld and Chuang published the first papers realising gates for quantum computers based on bulk spin resonance, or thermal ensembles. This technology is based on a nuclear magnetic resonance (NMR) machine, which is similar to the medical magnetic resonance imaging machine. Kitaev described the laws of topological quantum computation as a method for combating decoherence. Loss and DiVincenzo gave the Loss- DiVincenzo quantum computer, using as qubits the intrinsic spin-1/2 degree of freedom of individual electrons sooner defined as quantum dots. In 1998, A 2-qubit NMR quantum computer used to solve Deutsch’s problem was shown by Johnathan and Mosca shortly after by Chuang. first execution of Grover’s algorithm on an NMR computer. Braunstein and others scientists told that there was no mixed state quantum entanglement in any bulk NMR experiment. In 2000,5 Qbit NMR computer showed at technical university of Munich. First 7-qubit NMR Computer was showed using Shore’s algorithem. In 2001, The number 15 was factored using 1018 identical molecules, each containing 7 active nuclear spins. In 2003, Pittman and his colleagues and simultaneously Jeremy O’ Brein and his colleagues at the University of Queensland, showed quantum controlled NOT gates using only linear optical elements. In 2004, pure state NMR Quantum computer showed at Oxford University and University of York. First five photon entanglement showed by Jian-Wei Pan’s team. Harvard and GIT scientists succeeded in transferring quantum information between “quantum memories” – from atoms to photons and back again. In 2006, 12 Qbit quantum computer was patented. Two dimensional ion trap made for quantum computing Boehme demonstrates the liability of reading spin data on a silicon phosphorous quantum computer. In 2007, best method of Q-bit coupling was made. Successful demonstration of controllably coupled Q- bits. Innovation in applying spin-based electronics to silicon. Diamond quantum register was made. Nitrogen in Buckminster fullerene used in quantum computing. Large number of electron quantum coupled. Single electron Q-bit memory. D-wave systems claims to have 28 Q-bit computer, through this claim has yet to be verified. Graphene quantum dot spin qubit was delivered. Latest research includes optically addressable nuclear spins in a solid with a six hour coherence time. Quantum information encoded by simple electrical pulses. Quantum error detection code using a square lattice of four superconducting Q-bits [2]. WHY QUANTUM COMPUTING? Since years Computer Scientists and researchers were trying to increase the speed of Digital Computers. And they were successful till now. Computers were very slow in earlier times and were also unable to do complex calculations. Alan Turing, a British mathematician built world’s first theoretical Computer in 1930s and he named it ‘Turing Machine’. Based on his principle we made computers that were able to do multiple tasks unlike Turing machine, which was able to do only one task at a time. As years passed according to Moore’s law we were able to maintain the increment of number of transistors which is double after every 18 months. And if we continue to do so we’ll be able to make processors measured on atomic scale which will tend to transform into Quantum computers. Such Quantum computers are also known as quantum Turing machines. Basically Quantum computers are made to do complex calculations faster which digital computers cannot do. Quantum computers works on the principle of superposition and entanglement as stated in topic 4 and 5, that is why they are better than Classical Computers. As the superposition theorem stated in topic 4, qubits can show both the polarities at the same time due to its ‘spin’. An electron spins so fast that before capturing or utilizing its first state, it changes to second state. That means within a particular time period the probability of the occurrence of 1 or 0 is approximately 50% for a single qubit. Controlling of qubits can be done in many ways like ion trap using optical or magnetic field, quantum dots, semiconducting impurities, semiconducting circuits, etc. The basic advantage of quantum computer is that it can do parallel tasks really fast. According to scientist Deutsch, parallelism allows a quantum computer to work on a million processes at the same time, while your desktop Computer works on one. A 30 Q-bit computer’s processing power is equal to conventional computer that could work at 10 Teraflops (trillions of floating-point operations per second). Today's typical desktop personal computers run at speed measured in Gigaflops (billions of floating-point operations per second) [5]. ADVANCES IN QUANTUM COMPUTING • In 1998, Los Alamos and MIT scientists were able to spread a single Q-bit across three nuclear spins in each molecule of a liquid solution of alanine or trichloroethylene molecules. Spreading out the Q-bit made it harder to change, allowing scientists to use entanglement to study correlation between states as an
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  indirect method foranalyzing the quantum information. • In 2000, Researchers introduced a 7 Q-bit Computer. It used NMR to manipulate particles in the atomic nuclei of molecules of trance – crotonic acid, a simple fluid consisting of molecules consists of 6 hydrogen and 4 carbon atoms. Nuclear Magnetic Resonance is used to apply electromagnetic pulses, which force the particle to line up. This action is done to do parallel processing. Scientists at IBM developed a 5 Q-bit Quantum Computer which allowed the nuclei of five fluorine atoms to react with each other as Q-bits, which can be programmed by radio frequency pulses and detected by NMR instruments. Dr. Chuang, and the IBM team was able to cater a problem called order finding problem which involves finding the period of the particular function. Which is a typical aspect of many mathematical problems present in cryptography. • In 2001, researchers from IBM and Stanford successfully showed shore’s algorithem on the Quantum Computer. Shor's Algorithem is basically a method for finding the prime factors of numbers (which plays a crucial role in cryptography). They used a 7 Q-bit Quantum computer to find the factors of 10. The computer correctly sorted out that the prime factors were 2 and 5. • In 2005, The Institute of Quantum Optics and Quantum Information declared that scientists had created the first Q-byte, or series of 8 Q-bits, using ion traps. Scientists in Waterloo and MIT revised methods for quantum control on a 12 Q-bit system. Quantum control becomes harder as systems employ more Q- bits. • In 2007, D-Wave a Canadian startup company showed a 16 Q-bit quantum computer. It has catered Sudoku problem and other pattern matching problems. Practical Quantum computers are still decades away. If practical quantum computers can be built, they will play an important role in factoring large numbers, and therefore to encode and decode secret information. Quantum computers must have at least several dozen Q-bits to be able to solve real time problems, and thus serve as a feasible computing method [6]. D-WAVE SYSTEMS D-Wave is a company that makes Quantum processors for making quantum computers. Quantum computers are very hard to maintain its states as we defined above. As trapped ions have a lot of energy therefore to cool them we need to operate the processor in really cool temperature near to 0 Kelvin. One of the processors of D-wave systems is ‘2X’. It is shielded to 50000 times less than earth’s magnetic field. In a vacuum pressure it turns out to be 10 billion times lower than atmospheric pressure. 192 input, output and control lines from room temperature to the chip. Power consumption of this system is very less i.e. 25kW and also it won’t rise as it scales to some thousands of Q-bits. A lattice of 1000 very small super conducting circuits, well known as Q-bits, is chilled near to absolute zero to get quantum effects. A user transforms a problem into a search for the “lowest point in a vast landscape”. The processor takes all possibilities at a time to determine the lowest energy needed to from those relationships. Multiple solutions are given back to the user, scaled to show best answers. Recently in June 22, 2015 D- wave breaks the 1000 Q-bit computer barrier. Being the only manufacturer of quantum processor in the world D-wave broke the record of making 1000 Q-bit quantum computer in collaboration with NASA and Google. It is double the size of the processor they have made so far. It runs on an annealing algorithm to find out the lowest points, referring to optimal or near optimal solutions, in a virtual “energy landscape”. As number of Q-bits increases the amount of parallel processing increases. Take a 1000 qubit computer, it can consider 21000 possibilities at a time, a search which dwarfs the 2512 possibilities available to the 512 Q-bit D-wave - 2 . D-wave breaks new record with every succeeding generation it develops. The processor comprising over 128,000 Josephson tunneling junctions, are believed to be the most complicated semiconductor integrated circuits ever successfully manufactured. Temperature Noise, and precision all play very important role in how quantum processors solve problem. Beyond scaling up the technology by doubling the number of Q-bits, it has also got key technology advances prioritize around their impact on performance. Apart from achievement of making more than 100 Q-bit processor other measurable innovation consists of following: D. Low Operating Temperature Previously they were able to achieve temperature that was near to absolute zero but now in order to enhance the quantum effect they have achieved the temperature even 40% colder than that. E. Reduced Noise With the help of a combination of improved design, architectural changes and material changes, noise levels have been decreased by 50%. Low noise increased performance. F. Increased control circuit Precision In the testing to date, the improved precision with the noise reduction has showed improved precision by up to 40%. G. Advanced fabrication Latest processor comprises over 128,000 Josephson junctions in a 6-metel layer planer process with 0.25µm features, believed to be the most complicated superconductor IC ever built. H. New models of use Latest technology extend the boundaries of ways to exploit quantum resources. In addition to performing discrete optimization like its predecessor, firmware and software updates will make it easier to use the system for sampling applications [7]. APPLICATION OF QUANTUM COMPUTER
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  Scientists at D-waveare using their 512-qubit computer to make artificial intelligence, to improve voice activation device technology, development of new drugs, climate change modeling, optimization of traffic control, development of Robotics and machine navigation and shape recognition. ACKNOWLEDGEMENT I would like to express my special thanks to Prof. Dhaval Shah as well as my director and HOD Dr. P.N. Tekwani and our section head Dr. D.K Kothari who gave me such a wonderful opportunity to do the research on the topic “Quantum Computers” which also helped me increase my knowledge and I came to know about so many new things that I am really thankful to them. Also I would like to thank my parents and friends who helped me a lot in finalizing this topic within the time period. CONCLUSION Quantum Computers have both advantages and disadvantages. Advantage is that it can parallelly process data faster than any other classical computer but if you want to play high definition games or want to access faster internet then at that time quantum computers shows slower result than classical computers. REFERENCES [1] https://en.wikipedia.org/wiki/Quantum_computing [2] https://en.wikipedia.org/wiki/Timeline_of_quantum_com puting [3] https://en.wikipedia.org/wiki/Quantum_superposition [4] https://en.wikipedia.org/wiki/Quantum_entanglement [5] http://computer.howstuffworks.com/quantum- computer1.htm [6] http://computer.howstuffworks.com/quantum-computer2.htm [7] http://www.dwavesys.com/press-releases/d-wave- systems-breaks-1000-qubit-quantum-computing-barrier