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Quantum computation with coherent spin states and the close Hadamard problem

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Abstract

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.

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Notes

  1. See, e.g., paragraph 6.1 in [23] for an introduction to information theoretic lower bounds.

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Acknowledgments

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).

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Authors and Affiliations

  1. Institute for Quantum Science and Technology, University of Calgary, Calgary, AB, T2N 1N4, Canada

    Mark R. A. Adcock, Peter Høyer & Barry C. Sanders

  2. Department of Computer Science, University of Calgary, 2500 University Drive N.W, Calgary, AB, T2N 1N4, Canada

    Peter Høyer

  3. Program in Quantum Information Science, Canadian Institute for Advanced Research, Toronto, ON, M5G 1Z8, Canada

    Barry C. Sanders

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  1. Mark R. A. Adcock
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  2. Peter Høyer
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  3. Barry C. Sanders
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Correspondence to Mark R. A. Adcock.

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Adcock, M.R.A., Høyer, P. & Sanders, B.C. Quantum computation with coherent spin states and the close Hadamard problem. Quantum Inf Process 15, 1361–1386 (2016). https://doi.org/10.1007/s11128-015-1229-0

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