Quantum

1. Quantum Computing Corby Ziesman

2. Future of Computing? • Transistor-based Computing • Move towards parallel architectures • Biological Computing • DNA computing / Peptide computing • Optical Computing • Quantum Computing

3. Quantum Mechanics is Weird • Prism will reflect laser at internal angles of 45° • Light travels freely through prism material • We see no dot on the vertical paper, only the bottom • We conclude that no light passes that angled prism edge

4. Quantum Mechanics is Weird • Place a 2nd prism close, but not touching • The gap is a wall in the probability of where that laser will travel • There is a small probability that the laser can tunnel through that wall • So we now see a dot on the vertical paper, even though we just concluded that no light passes the angled prism edge • Quantum mechanics is all about probabilities, and quantum computing takes this into account

5. What’s a Quantum Computer? • A quantum computer uses quantum mechanics in some way to perform calculations • There are a number of quantum computing candidates, among those: • "Superconductor-based quantum computers (including SQUID-based quantum computers) • "Trapped ion quantum computer • "Electrons on helium quantum computers • "Nuclear magnetic resonance on molecules in solution"-based • "Quantum dot on surface"-based (e.g. the Loss-DiVincenzo quantum computer) • "Cavity quantum electrodynamics" (CQED)-based • "Molecular magnet"-based • Fullerene-based ESR quantum computer • Solid state NMR Kane quantum computers • Optic-based quantum computers (Quantum optics) • Topological quantum computer • Spin-based quantum computer • Adiabatic Quantum Computing • So what quantum properties could be used?

6. Probability • Probability governs quantum mechanics and the world around us • Classical models suggest that it may be possible to completely know the state of a system, and that – the state being known – it should be possible to predict with 100% accuracy the behavior of the system.

7. Probability • We know that it is impossible to completely know all aspects of a system • e.g. Heisenberg’s uncertainty principle, states that as we know the position of a particle with higher accuracy, we know the momentum with less accuracy, and vice-versa • We can only say what the probability is (e.g. we now view electron orbits as “fuzzy clouds” of where the electron is likely to be

8. Wavefunctions • Wavefunctions describe probabilities • There are areas with very low or zero probability • When an electron changes energy states, it does not physically move from one orbit to another, it instantaneously jumps to the other orbit

9. Superposition and Wavefunction Collapse • Wavefunctions can be combined in superposition • Each wavefunction corresponds to a state, with a complex number coefficient describing its probability among other states • Coefficient is complex because each element can interact with or destroy other states • When observed, the wavefunction collapses randomly into an observable state with probability based on the square of the amplitude of that wavefunction in the combination

10. Qubits • A quantum bit is a two-state unit of quantum information • Can have superposition however (both states at once) • The information in a qubit is equal to one bit, but may be handled more efficiently when processing information • This efficiency may make many previously difficult computing tasks easy • Shor’s algorithm is a quantum algorithm to factor a number in polynomial time (major consequences for cryptography). • Factoring is reduced to the problem of order-finding, which can be done on a normal computer. • Order-finding problem is done on a quantum computer. • Quantum algorithms tend to only probably give the right answer, but confidence can be increased by repeating the computation

11. Complexity • As mentioned, Shor’s quantum algorithm can factor numbers in polynomial time • Normally we are familiar with NP, NP-Complete, P, etc. which deal with deterministic and non-deterministic Turing machines • There is also BPP (Bounded-error, Probabilistic, Polynomial-time) which relates to probabilistic Turing machines • BPP defines algorithms that can flip coins and make random decisions, as long as the algorithm has at least a 50% chance of getting it right • The algorithm can be repeated, and then the probability of having a wrong answer drops off exponentially • Since quantum computing (and quantum mechanics) is all about probabilities, the analog to BPP is BQP (Bounded-error, Quantum, Polynomial-time) • Suspected relationship to BQP:

12. Quantum Algorithms • A normal 3-bit register can store up to 8 possible sequences of number, such as 000, 001, 010, etc. • A quantum computer can keep all possible states at once, as described by a wavefunction: • The data can then by transformed by multiplying it by a unitary matrix described by the physics of the computer • May mean the computer is specifically designed for solving only one problem, not a general quantum computer • Quantum computing is reversible • When measured, the result is one of the states, according to the probability coefficients • By measuring, the stored data has been altered and becomes useless • However, by repeating the algorithm, the correct result will occur most often, and so the most frequent result among runs of the algorithm can be selected as the correct answer • It’s also possible (as in factoring) to simply verify the result using a classical computer, and then no more trials need to be done once the correct result is found

13. How to Encode Data • Atomic Spin (“Spintronics”) • Up, Down, or Up/Down in superposition • Quantum Entanglement Properties • Two particles are in a quantum state and are described in relation to each other • Can prepare particles so that when one is observed to be spin-up, the other will always be spin-down and vice-versa • This is despite the fact the particles may be spatially separated by incredible distances • Does not violate causality, which states – in the most general sense – that information can not travel faster than the speed of light, because these observations are a result of wavefunction collapse • Particles’ behavior is related and intertwined, but do not influence each other

14. Quantum Gates • Quantum gates derive from reversible computing • They are described by unitary matrices such as the Hadamard gate or Controlled NOT gate: • From these, reversible quantum circuits may be created • Physically connecting the gates may lead to problems relating to quantum decoherence

15. Challenges • Decoherence • As mentioned, the states in a system can interfere with each other • If the external environment interacts with the system, the quantum superpositions in the new wavefunction (that includes external influences) may not be able to interfere with each other • Need to isolate the system from the environment and remove all noise

16. Challenges • As mentioned, the physics of the device may be specific to solving one problem • May be some time before a general quantum computer comes along with the flexibility of modern computers

17. Recent News • D-Wave Systems demoed last week a quantum computer, which it plans to make into a commercial product • There are questions of whether or not the computer actually makes use of quantum phenomena or if it is merely an analog computer • D-Wave states that progress is continuing, and that isolating the system from the external environment is a major concern in the design

18. Timeline Wikipedia Article as on Feb 19, 2007 on the history of Quantum Computing

19. The End Questions

20. References • PHY360 (Modern Physics) at ASU • Wikipedia articles: • Quantum computer, Quantum superposition, Quantum entanglement, Quantum information, Quantum state, Quantum gate, Quantum circuit, Uncertainty principle, Quantum leap, Wavefunction, Shor’s algorithm, Quantum mechanics, Qubit, BQP • Google news search results for “dwave quantum” • Slashdot and Scientific American articles I’ve read over the years