Quantum Information Processing

, Volume 15, Issue 4, pp 1361–1386 | Cite as

Quantum computation with coherent spin states and the close Hadamard problem

  • Mark R. A. Adcock
  • Peter Høyer
  • Barry C. Sanders


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.


Quantum 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).


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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • Mark R. A. Adcock
    • 1
  • Peter Høyer
    • 1
    • 2
  • Barry C. Sanders
    • 1
    • 3
  1. 1.Institute for Quantum Science and TechnologyUniversity of CalgaryCalgaryCanada
  2. 2.Department of Computer ScienceUniversity of CalgaryCalgaryCanada
  3. 3.Program in Quantum Information ScienceCanadian Institute for Advanced ResearchTorontoCanada

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