Quantum computation with coherent spin states and the close Hadamard problem
- 215 Downloads
We study a model of quantum computation based on the continuously parameterized yet finite-dimensional Hilbert space of a spin system. We explore the computational powers of this model by analyzing a pilot problem we refer to as the close Hadamard problem. We prove that the close Hadamard problem can be solved in the spin system model with arbitrarily small error probability in a constant number of oracle queries. We conclude that this model of quantum computation is suitable for solving certain types of problems. The model is effective for problems where symmetries between the structure of the information associated with the problem and the structure of the unitary operators employed in the quantum algorithm can be exploited.
KeywordsQuantum algorithms Continuous variable quantum computation Simple harmonic oscillator quantum computer Oracle decision problems
We appreciate financial support from the Alberta Ingenuity Fund (AIF), Alberta Innovates Technology Futures (AITF), Canada’s Natural Sciences and Engineering Research Council (NSERC), the Canadian Network Centres of Excellence for Mathematics of Information Technology and Complex Systems (MITACS), and the Canadian Institute for Advanced Research (CIFAR).
- 4.Adcock, M.R.A.: Continuous-Variable Quantum Computation of Oracle Decision Problems. Ph.D. thesis, University of Calgary, (2012). http://theses.ucalgary.ca/bitstream/11023/387/2/ucalgary_2012_adcock_mark
- 16.Bernstein, E., Vazirani, U.: Quantum Complexity Theory. In: Proceedings of the Twenty-fifth Annual Association for Computing Machinery Symposium on Theory of Computing, pp. 11–20. (1993). doi: 10.1145/167088.167097
- 17.Mosca, M.: Quantum Computer Algorithms, Ph.D. thesis, University of Oxford, (1999). http://www.iqc.ca/~mmosca/web/papers/moscathesis
- 21.Michelson, A.M., Levesque, A.H.: Error Control Techniques for Digital Communication. Wiley, New York (1985)Google Scholar
- 24.Jin, W. L.: Dynamical Analysis of Grover’s Search Algorithm in Arbitrarily High-Dimensional Search Spaces, (2015). http://vixra.org/abs/1506.0069