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arXiv:quant-ph/0209049 · Physical Review A

Robust Ising gates for practical quantum computation

Jonathan A. Jones

Published Jan 28, 2003• 87 citations
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Abstract

I describe the use of techniques based on composite rotations to combat systematic errors in controlled phase gates, which form the basis of two-qubit quantum logic gates. Although developed and described within the context of nuclear magnetic resonanace quantum computing these sequences should be applicable to any implementation of quantum computation based on Ising couplings. In combination with existing single-qubit gates this provides a universal set of robust quantum logic gates.

DOI
10.1103/physreva.67.012317

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I describe the use of techniques based on composite rotations to combat systematic errors in controlled phase gates, which form the basis of two-qubit quantum logic gates. Although developed and described within the context of nuclear magnetic resonanace quantum computing these sequences should be applicable to any implementation of quantum computation based on Ising couplings. In combination with existing single-qubit gates this provides a universal set of robust quantum logic gates.
The composite rotation approach has been used to develop a range of robust quantum logic gates, including single qubit gates and two qubit gates, which are resistant to systematic errors in their implementation. Single qubit gates based on the BB1 family of composite rotations have been experimentally demonstrated in a variety of systems, but little study has been made of their application in extended computations, and there has been no experimental study of the corresponding robust two qubit gates to date. Here we describe an application of robust gates to nuclear magnetic resonance studies of approximate quantum counting. We find that the BB1 family of robust gates is indeed useful, but that the related NB1, PB1, B4, and P4 families of tailored logic gates are less useful than initially expected.
We propose a universal gate set for quantum computing with all-to-all connectivity and intrinsic robustness to bit-flip errors based on parity encoding. We show that logical controlled phase gate and R_{z} rotations can be implemented in parity encoding with single-qubit operations. Together with logical R_{x} rotations, implemented via nearest-neighbor controlled-NOT gates and an R_{x} rotation, these form a universal gate set. As the controlled phase gate requires only single-qubit rotations, the proposed scheme has advantages for several cornerstone quantum algorithms, e.g., the quantum Fourier transform. We present a method to switch between different encoding variants via partial on-the-fly encoding and decoding.