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arXiv:quant-ph/0308067 · Physical Review A

Geometric phase gate without dynamical phases

Razmik G. Unanyan, Michael Fleischhauer

Published May 11, 2004• 45 citations
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Abstract

A general scheme for an adiabatic geometric phase gate is proposed which is maximally robust against parameter fluctuations. While in systems with SU(2) symmetry geometric phases are accompanied by dynamical phases and are thus not robust, we show that in the more general case of an $\text{SU}(2)\ensuremath{\bigotimes}\text{SU}(2)$ symmetry it is possible to obtain a nonvanishing geometric phase without dynamical contributions. The scheme is illustrated for a phase gate using two systems with dipole-dipole interactions in external laser fields which form an effective four-level system.

DOI
10.1103/physreva.69.050302

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A general scheme for an adiabatic geometric phase gate is proposed which is maximally robust against parameter fluctuations. While in systems with SU(2) symmetry geometric phases are accompanied by dynamical phases and are thus not robust, we show that in the more general case of an SU(2)\ensuremath⨂SU(2)\text{SU}(2)\ensuremath{\bigotimes}\text{SU}(2)SU(2)\ensuremath⨂SU(2) symmetry it is possible to obtain a nonvanishing geometric phase without dynamical contributions. The scheme is illustrated for a phase gate using two systems with dipole-dipole interactions in external laser fields which form an effective four-level system.
In this paper, we present a scheme for implementing the unconventional geometric two-qubit phase gate with nonzero dynamical phase based on two-channel Raman interaction of two atoms in a cavity. We show that the dynamical phase and the total phase for a cyclic evolution are proportional to the geometric phase in the same cyclic evolution; hence they possess the same geometric features as does the geometric phase. In our scheme, the atomic excited state is adiabatically eliminated, and the operation of the proposed logic gate involves only the metastable states of the atoms; thus the effect of the atomic spontaneous emission can be neglected. The influence of the cavity decay on our scheme is examined. It is found that the relations regarding the dynamical phase, the total phase, and the geometric phase in the ideal situation are still valid in the case of weak cavity decay. Feasibility and the effect of the phase fluctuations of the driving laser fields are also discussed.
We propose a controlled-PHASE gate for neutral atoms in which one of the qubit state components adiabatically evolves along the multiple-atom eigenstate formed by the chirped laser pulse coupling to Rydberg states and intrinsic dipole-dipole exchange interactions and, consequently, accumulates an interaction-induced geometric phase. The geometric Rydberg gate is not limited by an adiabatic condition, which is sped up by shortcuts to adiabaticity (STA). Analyses show that an STA scheme is more robust than a non-adiabatic case against the variations of control parameters and faster than an adiabatic case, which protects from the decay of Rydberg states. Furthermore, an intermediate value of dipole-dipole interaction strength is enough for our scheme.
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A nonadiabatic geometric quantum gate is realized by integrating nonadiabatic geometric phases with global geometric features into the unitary quantum control, thereby removing the limitation of a long evolution time in the adiabatic case. However, systematic errors are inevitable in practical quantum control; these lead to the deviation of the evolution from target conditions to inducing geometric phases, smearing the robustness of the induced geometric quantum gates. Here, we present a general theoretical framework with enhanced robustness for geometric quantum gates by preserving fundamental geometric conditions. We first analytically evaluate the influence of systematic errors on geometric gates and then propose an optimized approach to mitigate this influence. Numerical simulations indicate that, as the geometric conditions are still maintained in the presence of systematic errors in our scheme, the constructed geometric quantum gates exhibit strong robustness, far superior to that of conventional schemes. Furthermore, we propose implementing the scheme in superconducting quantum circuits, where geometric quantum gates can achieve high fidelity with current experimental parameters. Therefore, the enhanced gate performance highlights the promise of our scheme for large-scale quantum computations.