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Resonant transition-based quantum computation

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Abstract

In this article we assess a novel quantum computation paradigm based on the resonant transition (RT) phenomenon commonly associated with atomic and molecular systems. We thoroughly analyze the intimate connections between the RT-based quantum computation and the well-established adiabatic quantum computation (AQC). Both quantum computing frameworks encode solutions to computational problems in the spectral properties of a Hamiltonian and rely on the quantum dynamics to obtain the desired output state. We discuss how one can adapt any adiabatic quantum algorithm to a corresponding RT version and the two approaches are limited by different aspects of Hamiltonians’ spectra. The RT approach provides a compelling alternative to the AQC under various circumstances. To better illustrate the usefulness of the novel framework, we analyze the time complexity of an algorithm for 3-SAT problems and discuss straightforward methods to fine tune its efficiency.

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Notes

  1. In this case, the initial state \(\left| \Psi _s \right\rangle \) is also the eigenstate of \(H_s\) with eigenvalue \(-1\) such that \(\left| \Psi _s \right\rangle \) that will be excited to other eigenstates with higher eigenvalues.

  2. On Mathematica, harmonicnumber(M,2), is bounded from above by \(\frac{\pi ^2}{6} - \frac{2M-1}{2M^2}\) by use of Laurent series.

  3. On Mathematica, harmonicnumber(M,1/2)/M, is approximately \(2\sqrt{\frac{1}{M}}\) by Puiseux series.

  4. On Mathematica, (harmonicnumber \(((M*(M+1)/2),1/2))/M\) converges around 1.5. Since \(K=\frac{M(M+1)}{2}\), then \( O\left( \frac{2 \times 1.5\sqrt{N}}{\gamma (M+1)}\right) \simeq O\left( \sqrt{N}/(n\gamma )\right) \).

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Acknowledgements

C. C. gratefully acknowledges the support from the State University of New York Polytechnic Institute.

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Authors and Affiliations

  1. Department of Computer Science, State University of New York Polytechnic Institute, Utica, NY, 13502, USA

    Chen-Fu Chiang

  2. Department of Chemistry, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA

    Chang-Yu Hsieh

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  1. Chen-Fu Chiang
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Correspondence to Chang-Yu Hsieh.

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Chiang, CF., Hsieh, CY. Resonant transition-based quantum computation. Quantum Inf Process 16, 120 (2017). https://doi.org/10.1007/s11128-017-1552-8

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