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Implementing gate operations between uncoupled qubits in linear nearest neighbor arrays using a learning algorithm

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Abstract

We propose a new scheme to implement gate operations in a one dimensional linear nearest neighbor array, by using dynamic learning algorithm. This is accomplished by training quantum system using a back propagation technique, to find the system parameters that implement gate operations directly. The key feature of our scheme is that, we can reduce the computational overhead of a quantum circuit by finding the parameters to implement the desired gate operation directly, without decomposing them into a sequence of elementary gate operations. We show how the training algorithm can be used as a tool for finding the parameters for implementing controlled-NOT (CNOT) and Toffoli gates between next-to-nearest neighbor qubits in an Ising-coupled linear nearest neighbor system. We then show how the scheme can be used to find parameters for realizing swap gates first, between two adjacent qubits and then, between two next-to-nearest-neighbor qubits, in each case without decomposing it into 3 CNOT gates. Finally, we show how the scheme can be extended to systems with non-diagonal interactions. To demonstrate, we train a quantum system with Heisenberg interactions to find the parameters to realize a swap operation.

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Abbreviations

LNN:

Linear nearest neighbor

CNOT:

Controlled-NOT

RMS:

Root mean square

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Acknowledgments

This material is based upon work supported, in part, by the National Science Foundation under Award No. EPS-0903806 and matching support from the State of Kansas through Kansas Technology Enterprise Corporation. We would like to thank Dr. James Steck and Dr. Elizabeth Behrman for providing some of the source code to run simulations.

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Authors and Affiliations

  1. Department of Electrical Engineering and Computer Science, Wichita State University, Wichita, KS, 67260, USA

    Rudrayya Chowdary Garigipati & Preethika Kumar

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  1. Rudrayya Chowdary Garigipati
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  2. Preethika Kumar
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Correspondence to Preethika Kumar.

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Garigipati, R.C., Kumar, P. Implementing gate operations between uncoupled qubits in linear nearest neighbor arrays using a learning algorithm. Quantum Inf Process 12, 2291–2308 (2013). https://doi.org/10.1007/s11128-013-0526-8

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  • DOI: https://doi.org/10.1007/s11128-013-0526-8

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