1 / 10

The Limits of Adiabatic Quantum Algorithms

The Limits of Adiabatic Quantum Algorithms. Alper Sarikaya Advised by Prof. Dave Bacon Computer Science & Engineering Chemistry University of Washington Undergraduate Research Symposium May 15, 2009. Quantum Computing Theory Group: http://cs.washington.edu/homes/dabacon/qw/. Motivation.

ivana-avila
Download Presentation

The Limits of Adiabatic Quantum Algorithms

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. The Limits of Adiabatic Quantum Algorithms Alper Sarikaya Advised by Prof. Dave Bacon Computer Science & Engineering Chemistry University of Washington Undergraduate Research Symposium May 15, 2009 Quantum Computing Theory Group: http://cs.washington.edu/homes/dabacon/qw/

  2. Motivation • Transistors aregetting smaller • In 1994, Paul Shorshowed that quantum algorithms have an exponential speed-up over their classical counterpartsin factoring large prime numbers cm µm nm pm bits noisy bits quantum bit

  3. Quantum Computation • Qubit versus a classical bit .. where‘s the information stored? • Adiabatically: take an incoming vector (input data), evolve the vector with an operator (a Hamiltonian); the answer is the smallest eigenvalue • Think linear algebra (Math 308)! Deterministic Probabilistic “Quantum” 1 1 1 0.6 0.5 0.4 0.3 -1 0.7 0.5 -1

  4. Simulating an Adiabatic Algorithm • Benefit of Quantum Algorithms: • Infinite precision analog computation can efficiently solve NP-complete problems • Adiabatic theorem - A physical system remains in its instantaneous eigenstate if a given perturbation is acting on it slowly enough and if there is a gap between the eigenvalue and the rest of the Hamiltonian's spectrum. - Max Born, Vladimir Fock (1928) • What is the benefit of building anadiabatic quantum computer? • Let’s compare the algorithm to a classical computer

  5. Testing efficiency hypothesis numerically:If the relationship between the eigenvalue gap and the number of qubits is negatively proportional, then an adiabatic quantum computer only offers a polynomial speedup over a classically-based counterpart. • To emulate a quantum computer classically, use the Markovian matrix as the operator in this study: where n is the number of qubits, β is varied between 0 and n, and the following two Hamiltonians are defined:

  6. Data from a sample run:

  7. Data from sample results:

  8. Conclusions • There is indeed an inverse exponential relationship between the number of qubits and the smallest eigenvalue gap • Adiabatic quantum computers only offer a polynomial speedup! • This is only a numerical simulation of the hypothesis, not a proof

  9. Future Directions • Move from numerical evidence in support of the hypothesis to a formal proof to conclusively uphold the efficiency concerns • Remember D-Wave? • Currently building an adiabatic quantum computer and gaining lots of capital from its promise – butit probably only offers a polynomial increase in efficiency!

  10. Acknowledgments • Advisor: Professor Dave BaconUW Computer Science & Engineering • Gregory CrosswhiteUW Physics, Graduate Student • Quantum Computing Theory Grouphttp://cs.washington.edu/homes/dabacon/qw/ • This work supported in part by the National Science Foundation

More Related