1. Quantum Corby Ziesman Computing

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 2 nd 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