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Abdullah Hakmi ID: 20122 Prof: AC Quantum computing MIS 201 Project 3 Sunday, July 19, 2009 Executive Summary: A quantum computer is a device for computation that makes direct use of quantum mechanical phenomena, such as superposition and entanglement, to perform operations on data. The basic principle behind quantum computation is that quantum properties can be used to represent data and perform operations on these data. Introduction: The massive amount of processing power generated by computer manufacturers has not yet been able to quench our thirst for speed and computing capacity. In 1947, American computer engineer Howard Aiken said that just six electronic digital computers would satisfy the computing needs of the United States. Others have made similar errant predictions about the amount of computing power that would support our growing technological needs1. Of course, Aiken didn't count on the large amounts of data generated by scientific research, the proliferation of personal computers or the emergence of the Internet, which have only fueled our need for more, more and more computing power. Will we ever have the amount of computing power we need or want? If, as Moore's Law states, the number of transistors on a microprocessor continues to double every 18 months, the year 2020 or 2030 will find the circuits on a 1 University of Illinois at Urbana-Champaign microprocessor measured on an atomic scale. And the logical next step will be to create quantum computers, which will harness the power of atoms and molecules to perform memory and processing tasks. Quantum computers have the potential to perform certain calculations significantly faster than any silicon-based computer. Although quantum computing is still in its immaturity, experiments have been carried out in which quantum computational operations were executed on a very small number of qubits (quantum binary digits). Both practical and theoretical research continues with interest, and many national government and military funding agencies support quantum computing research to develop quantum computers for both civilian and national security purposes, such as cryptanalysis. If large-scale quantum computers can be built, they will be able to solve certain problems much faster than any of our current classical computers (for example Shor's algorithm). Quantum computers are different from other computers such as DNA computers and traditional computers based on transistors. Some computing architectures such as optical computers may use classical superposition of electromagnetic waves. Without some specifically quantum mechanical resources such as entanglement, it is conjectured that an exponential advantage over classical computers is not possible. Methodology: While a classical three-bit state and a quantum three-qubit state are both eight-dimensional vectors, they are manipulated quite differently for classical or quantum computation, respectively. For computing in either case, the system must be initialized, “for example into the all-zeros string, corresponding to the vector (1,0,0,0,0,0,0,0). In classical randomized computation, the system evolves according to the application of stochastic matrices, which preserve that the probabilities add up to one (i.e., preserve the L1 norm). In quantum computation, on the other hand, allowed operations are unitary matrices, which are effectively rotations (they preserve that the sum of the squares add up to one, the Euclidean or L2 norm). (Exactly what unitaries can be applied depend on the physics of the quantum device.) “2Consequently, since rotations can be undone by rotating backward, quantum computations are reversible. Technically, quantum operations can be probabilistic combinations of unitaries, so quantum computation really does generalize classical computation. Finally, upon termination of the algorithm, the result needs to be read off. In the case of a classical computer, it is sampled from the probability distribution on the three-bit register to get one distinct three-bit string, say 000. Quantum mechanically measures the three-qubit state, which is equivalent to collapsing the quantum state down to a classical distribution (with the coefficients in the classical state being the squared magnitudes of the Quantum Computing with Molecules" article in Scientific American by Neil Gershenfeld and Isaac L. Chuang - a generally accessible overview of quantum computing and so on. 2 coefficients for the quantum state, as described above) 3followed by sampling from that distribution. Many algorithms will only give the correct answer with a certain probability, however by repeatedly initializing, running and measuring the quantum computer, the probability of getting the correct answer can be increased. Limitations of the technology: Scientists have already built basic quantum computers that can perform certain calculations; but a practical quantum computer is still years away. Quantum computing is still in theory and this is the main limitation that it has so far. There are future problems and challenges that are expected to happen if scientists have reached this technology and wanted to implement it into use. One of the greatest challenges is controlling or removing decoherence. This usually means isolating the system from its environment as the slightest interaction with the external world would cause the system to decohere. This effect is irreversible, as it is non-unitary, and is usually something that should be avoided, if not highly controlled. Decoherence times for candidate systems, in particular the transverse relaxation time T2, typically range between nanoseconds and seconds at low temperature. 3 M. I. Dyakonov, Université Montpellier (2006-10-14). "Is Fault-Tolerant Quantum Computation Really Possible?". Retrieved on 2007-02-16. These issues are more difficult for optical approaches as the timescales are orders of magnitude lower and an often cited approach to overcoming them is optical pulse shaping. Error rates are typically proportional to the ratio of operating time to decoherence time, hence any operation must be completed much more quickly than the decoherence time. If the error rate is small enough, it is thought to be possible to use quantum error correction, which corrects errors due to decoherence, thereby allowing the total calculation time to be longer than the decoherence time. An often-cited figure for required error rate in each gate is 10−4. This implies that each gate must be able to perform its task 10,000 times faster than the decoherence time of the system. Meeting this scalability condition is possible for a wide range of systems. However, the use of error correction brings with it the cost of a greatly increased number of required qubits. The number required to factor integers using Shor's algorithm is still polynomial, and thought to be between L and L2, where L is the number of bits in the number to be factored; error correction algorithms would inflate this figure by an additional factor of L. For a 1000-bit number, this implies a need for about 104 qubits without error correction. A very different approach to the stability-decoherence problem is to create a topological quantum computer with anyons, quasi-particles used as threads and relying on braid theory to form stable logic gates. Benefits of the technology to the business: This technology will not only affect business, it will cause to solve so many of the world’s technical problems, it may even cause new discoveries for scientists. With this new invention, computers will help businesses to work more efficiently by speeding up the process of analyzing and transforming data. It would also open new doors for E-businesses by making it more secure and efficient. Conclusion: In conclusion, quantum computing is just a theory and a concept for the future of the computer world and technology. Quantum computer could be a replacement to the technology we now use which is silicon ships. This invention with its ability to solve complicated algorithm real fast and the ability to store information and exchange it widely will help scientists to discover new things. References 1. Quantum Computing with Molecules" article in Scientific American by Neil Gershenfeld and Isaac L. Chuang - a generally accessible overview of quantum computing and so on. 2. Neumann, P.; Mizuochi, N.; Rempp, F.; Hemmer, P.; Watanabe, H.; Yamasaki, S.; Jacques, V.; Gaebel, T.; et al. (June 6, 2008), "Multipartite Entanglement Among Single Spins in Diamond", Science 320 (5881): 1326–1329, doi:10.1126/science.1157233, PMID 18535240, http://www.sciencemag.org/cgi/content/abstract/320/5881/1326 3. http://news.cnet.com/Start-up-demos-quantum-computer/2100-1008_36159152.html 4. University of Illinois at Urbana-Champaign. Quantum computer solves problem, without running, www.physorg.com/news11087.html 5. M. I. Dyakonov, Université Montpellier (2006-10-14). "Is Fault-Tolerant Quantum Computation Really Possible?". Retrieved on 2007-02-16.