QUANTUM COMPUTERS/QUANTUM PROCESSING

Quantum Computers/Quantum Processing

A quantum computer is a device for computation that makes direct use of quantum mechanical phenomena, such as superposition and entanglement. Quantum computers are different based on transistors. The basic principle behind quantum computation is that quantum properties can be used to represent data and perform operations on these data.¹  A theoretical model is the quantum Turing machine, also known as the universal quantum computer. Quantum computers share theoretical similarities with non-deterministic and probabilistic computers (e.g., the ability to be in more than one state simultaneously). The field of quantum computing began with Richard Feynman in 1982.²

Quantum computing is still new and experiments have been carried out in which quantum computational operations were executed on a very small number of qubits (quantum bits) and quantum computers are being developed for cryptanalysis.³

Large-scale quantum computers solve certain problems much faster than any classical computer by using the best currently known algorithms, like integer factorization using Shor's algorithm or the simulation of quantum many-body systems. There exist quantum algorithms, such as Simon's algorithm, which run faster than any possible probabilistic classical algorithm.⁴   However, in practice infinite resources are never available and the computational basis of 500 qubits, for example, would already be too large to be represented on a classical computer because it would require 2⁵⁰⁰ complex values to be stored.⁵

A classical computer has a memory made up of bits, where a quantum computer maintains a sequence of qubits. A single qubit can represent a one, a zero, or, crucially, any quantum superposition  with a pair of qubits in any quantum superposition of 4 states, and three qubits in any superposition of 8.  In general a quantum computer with n qubits can be in an arbitrary superposition of up to 2ⁿ different states simultaneously while a normal computer is only in one of these 2ⁿ states at any one time. A quantum computer operates a fixed sequence of quantum logic gates with quantum algorithm sequence of gates.

Integer factorization is unfeasible with an ordinary computer for large integers if they are the product of few prime numbers (e.g., products of two 300-digit primes).⁶   By comparison, a quantum computer could efficiently solve this problem using Shor's algorithm to find its factors. This ability would allow a quantum computer to decrypt many of the cryptographic systems in use today, in the sense that there would be a polynomial time (in the number of digits of the integer) algorithm for solving the problem.  The popular public key ciphers are based on the difficulty of factoring integers (or discrete logarithm problem which can also be solved by Shor's algorithm), including forms of RSA. These are used to protect secure Web pages, encrypted email, and many other types of data and breaking these codes would have significant ramifications for electronic privacy and security.  However, other existing cryptographic algorithms do not appear to be broken by these algorithms.⁷

Works Cited

¹ "Quantum Computing with Molecules" article in Scientific American by Neil Gershenfeld and Isaac L. Chuang

² Quantum computation. David Deutsch, Physics World, 1/6/92

³Quantum Information Science and Technology Roadmap for a sense of where the research is heading.

⁴Simon, D.R. (1994). "On the power of quantum computation". Foundations of Computer Science, 1994 Proceedings., 35th Annual Symposium on: 116–123.

⁵Nielsen, Michael A.; Chuang, Isaac L.. Quantum Computation and Quantum Information. p. 17.

⁶Arjen K. Lenstra (2000). "Integer Factoring". Designs, Codes and Cryptography 19: 101–128.

^{7 a b} Daniel J. Bernstein, Introduction to Post-Quantum Cryptography. Introduction to Daniel J. Bernstein, Johannes Buchmann, Erik Dahmen (editors). Post-quantum cryptography. Springer, Berlin, 2009. ISBN 978-3-540-88701-0

MRAM

Magnetoresistive Random Access Memory (MRAM)

Magnetoresistive  Random Access Memory is a non-volatile computer memory (NVRAM) technology under development since the 1990s and the advantages over SRAM, DRAM, EEPROM, and flash are so overwhelming that magnetoresistive RAM will eventually dominate all types of memory, becoming a true universal memory.^[

MRAM (magnetoresistive random access memory) uses magnetic charges instead of the electrical charges used by DRAM (dynamic random access memory) to store data.  By combining the high speed of static RAM and the high density of DRAM, MRAM significantly improves electronic products by storing greater amounts of data, accessed faster while consuming less battery power than existing electronic memory. 

·                     Storage Resources

Computer chips store information as long as electricity flows through them. Once power is turned off, the information is lost unless transferred to hard drive of disk storage.   MRAM, however, retains data after a power supply is cut off. Replacing DRAM with MRAM could prevent data loss and enable computers that start instantly without boot up.

The U.S. Defense Advanced Research Projects Agency (DARPA) funds private industry research into the potential of MRAM. IBM, Motorola, and Honeywell. Hewlett-Packard, Matsushita, NEC, Fujitsu, Toshiba, Hitachi, and Siemens also have invested in MRAM research.

Motorola Labs development allows the integration of several memory options within a single chip, resulting in a chip that uses less power. The chip is a three-volt MRAM with an address access time of about 15 nanoseconds. IBM and Infineon Technologies AG are worked on a proposed 256-megabit chip.

Development of MRAM basically followed two scientific schools: 1) spin electronics, the science behind giant magnetoresistive heads used in disk drives and 2) tunneling magnetic resistance, or TMR, which is expected to be the basis of future MRAM.²

In June of 2010 Hitachi and Tohoku University announced Multi-level SPRAM.³   SPRAM, the next-generation MRAM or memory that uses the magnetism of electron spin to provide non-volatility, with unlimited fortitude but difficult to manufacture in mass. Spin-transfer torque random access memory (STT-RAM) technology is a second-generation magnetic-RAM technology . It can solve some of the problems posed by conventional MRAM structures. STT-RAM technology can eventually replace DRAM, NAND and MRAM, said Grandis Inc, a developer of STT-RAM technology.⁴

^{Works Cited}

¹ Johan Åkerman, “Toward a Universal Memory”, Science, Vol. 308. no. 5721 (22 April 2005), pp. 508 - 510, DOI: 10.1126/science.1110549

²http://searchstorage.techtarget.com/definition/MRAM

³ Y. Huai, AAPPS Bulletin, December 2008, vol. 18, no. 6, p.33, "Spin-Transfer Torque MRAM (STT-MRAM): Challenges and Prospects."

⁴http://www.ciol.com/Semicon/SemiPipes/News-Reports/Hitachi-plans-SPRAM-RD-spin-off/137594/0/

Data Representation/Boolean Logic

DATA REPRESENTATION/BOOLEAN LOGIC

How amazing is it that computers can play chess or balance a check book?  The answer to this is the very basis of something called Boolean logic.  It was used first by George Boole, the British born Irish mathematician, in the mid 1800’s and enables many things to be mapped into bits and bytes.  It really comes down to the very basis of computers when you want to explain how Boolean logic works and it is so simple.  It starts with logic “gates” and relays and becomes something useful.

A Primer in Boolean Logic can be explained in an Internet search of this vast computer database based on the principles of Boolean logic.  Boolean logic is the logical relationship of search terms.

Boolean logic consists of three logical operators:

• OR
• AND
• NOT

Each operator can be visually described by using Venn diagrams, as shown below.

OR logic

college OR university

• the shaded circle with the word college representing all the records that contain the word "college"
• the shaded circle with the word university representing all the records that contain the word "university"
• the shaded overlap area representing all the records that contain both "college" and "university"

OR logic is most commonly used to search for synonymous terms or concepts.   The more terms or concepts we combine in a search with or logic, the more results.
OR logic collates the results to retrieve all the unique records containing one term, the other term, or both of them.

AND logic

poverty AND crime

• In this search, we retrieve records in which BOTH of the search terms are present
• This is illustrated by the shaded area overlapping the two circles representing all the records that contain both the word "poverty" and the word "crime"
• We do not retrieve any records with only "poverty" or only "crime"

The more terms or concepts we combine in a search with AND logic, the fewer results retrieved.
poverty AND crime AND gender
Some search engines use the proximity operator NEAR to determine the closeness of terms of a source document. NEAR is a restrictive AND.  Most search engines default to proximity.

NOT logic

cats NOT dogs

• This search, we retrieve records in which ONLY ONE of the terms is present.
• This is illustrated by the shaded area with the word cats - all the records containing the word "cats"
• No records are retrieved in the area overlapping the two circles where the word "dogs" appears, even if the word "cats" appears there too

Here is an example of how NOT logic works:
NOT logic excludes from your search results. When you use NOT: the term you do want may be present in an important way in documents that will be excluded because you wish to avoid that word. For example, consider a Web page that includes the statement that " cats are smarter than dogs." The search NOT would exclude this document from your results.

Combined AND and OR logic

Question: I want information about the behavior of cats.
Search: behavior AND (cats OR felines)
You can combine both AND and OR logic in a single search, as shown above.
The use of parentheses in this search is known as forcing the order of processing. In this case, we surround the OR words with parentheses so that the search engine will process the two related terms as a unit. The search engine will use AND logic to combine this result with the second concept. Using this method, we are assured that the semantically-related OR terms are kept together as a logical unit.

Quick Comparison Chart:
Full Boolean vs. Implied Boolean vs. Search Form

	Full Boolean	Implied Boolean	Search Form Terminology
OR	college or university	[rarely available]	any of the words at least one of the words should contain the words
AND	poverty and crime	poverty   crime	all of these words must contain the words
NOT	cats not dogs	cats   -dogs	must not contain the words should not contain the words
NEAR, etc.	cats NEAR dogs	N/A

http://www.internettutorials.net/boolean.asp