Q uantum C omputing

1. Quantum Computing By: Mike Neumiller & Brian Yarbrough

2. What is a quantum computer? A quantum computer is a computer that exploits the quantum mechanical properties of superposition in order to allow a single operation to act on a large number of pieces of data. In a quantum computer, the data to be manipulated, represented in quantum bits, exists in all possible states simultaneously, in superposition. This allows a single operation to operate over all of these states at once, in contrast with a classical computer, which must carry out an operation for each state separately. Definition from The American Heritage Science Dictionary

3. Why We need quantum computers • As the amount of processing power available increases, our demand for more increases. • Processing of data, AI, scientific and medical research, etc. all require more processing power than ever. Our ability to fit more computing power in the same space is becoming more and more difficult with traditional transistors. • It is estimated that if Moore’s Law had continued to be true, that we would hit the fundamental limit of transistor size sometime around the year 2020. • In February 2012, a research team at the University of New South Wales announced the development of the first working transistor consisting of a single atom placed precisely in a silicon crystal.

4. Why parallel computing isn’t enough • Parallel computing has limits that rely on available resources, power and transistor size. • Not all computations can easily be parallelized. • Parallelization of some algorithms can be extremely wasteful.

5. Quantum Parallelism Quantum parallelism is the method in which a quantum computer is able to perform two or more computations simultaneously. While classic parallel computing involves multiple processors working on the same computation, quantum parallelism has a single processor doing multiple computations at the same time.

6. Benefits of quantum computers • Large sets of data can be evaluated much quicker than with conventional computers / parallel computing. • Operations are reversible as long as the resulting state is still intact. • Quantum computers have the ability to be much smaller than a similarly powered Parallel computer.

7. Disadvantages of Quantum Computers • Measuring (reading / evaluating) the state of a qubit register destroys the original quantum state that was being measured. • Many algorithms only give the correct answer with a certain probability. • The probability can be increased by repeatedly reinitializing the computer, rerunning the algorithm and measuring the new results. • Quantum computers are still in their infancy and are extremely expensive.

8. The decoHerence Problem • One of the greatest challenges. • Outside influences affect the system like: • Vibration • Nuclear Radiation • Irreversibly changes the state of the quantum system. • Needs to be highly controlled or completely avoided.

9. The DECOHERENCE Problem • Error rate proportional to ratio of Operating time to Decoherencetime. • Make sure Operating time is much less than Decoherencetime. • In general, Operating time needs to be 1/10,000th of Decoherencetime. • This is somewhat reasonable, and can always be achieved by increasing the number of qubits in a system. • Still, more bits are expensive so it still needs to be minimized.

10. Uses of Quantum Computers • Integer factorization • Cryptography and code breaking • Simulations of quantum physical processes • Searching data using Grover’s algorithm

11. What is a Quantum Bit? A quantum bit, or qubit, is the quantum analogue of the classical bit. Qubits are a two-state quantum-mechanical system – that is, they have two distinguishable states, for example 0 and 1, but can also exist in a superposition of both states at the same time.

12. Qubits and superposition • Qubits are represented in Complex Coordinates. • Ex. 3-bit register in regular computer represents one 3-bit number. • In a quantum 3-Qubit register, any combination of the 8 possible 3-bit numbersin superposition can be represented.

13. Qubits and superposition • Represented as probabilities of state being in a given position. • In a normal computer the actual state has a probability of 1 while all others have a probability of 0. • Sum of probabilities is 1. • In a quantum computer each complex coordinate possesses an even distribution of probabilities among the valid states. • Square of the complex coordinates(probabilities) is equal to 1.

14. QUBITS AND SUPERPOSITION

15. Quantum gates and logic • Just like in a normal computer, logic gates take input and return output. • Quantum gates are required to be unary, but act on all superpositions in the qubitsystem. • Due to the nature of quantum mechanics, these gates are very complex compared to normal logic gates. • NOT and XOR gates along with special superposition creation gates have been made so that a normal computational system can be duplicated with quantum computing.

16. Quantum gates and logic • Hadamard Gate : → + maps to all superpositions • Phase Gate : → and → eiφ • These together can map any unary qubit operation on a single qubit.

17. What does this mean? • Quantum computers can do any parallelizable computations that normal computers can do. • Require specialized algorithms and techniques. • Difficult to make quantum programs. • Impossible to easily convert existing software for quantum computers. • Quantum physics is hard => Quantum programming is really hard. • Will likely require advanced programming languages to make the technology useable by the average programmer.

18. History of Quantum Computers • May 1, 1981 – Feynman suggests quantum computer model • March 4, 1985 – David Deutsch describes first quantum Turing machine • March 1, 1994 – Shor’s algorithm created • January 15, 1996 – Grover’s algorithm discovered • May 22, 1998 – First 3 qubit NMR computer built • August 15, 2000 – First 5 qubit NMR quantum computer built • November 7, 2000 – First 7 qubit NMR quantum computer built

19. History of Quantum Computers • December 19, 2001 – Shor’s algorithm executed on 7 qubit computer to find the factors of 15 (superseded by 21 & 143 in 2012) • December 1, 2005 – First qubyte quantum computer built • June 28, 2009 – Yale creates solid-state quantum processor • June 1, 2011 – D-Wave announces commercial quantum computer • November 14, 2013 – Coherent superposition of an ensemble of approximately 3 billion qubits for 39 minutes at room temperature. (Previous record was 2 seconds)

20. The Future of Quantum Computers • Improve suppression of quantum decoherence • Increase performance (currently not performing much better than classic optimized computers) • Reduce cost of manufacturing • Increase qubit capacity • Eventually replace digital computers 2014