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arXiv:quant-ph/0204030 · Physical Review A

Holonomic quantum computation with neutral atoms

Alessio Recati, Tommaso Calarco, Paolo Zanardi A, J. I. Cirac, P. Zoller

Published Sep 17, 2002• 125 citations
arXivHTMLPDF

Abstract

We propose an all-geometric implementation of quantum computation using neutral atoms in cavity QED. We show how to perform generic single- and two-qubit gates, the latter by encoding a two-atom state onto a single, many-level atom. We compare different strategies to overcome limitations due to cavity imperfections.
DOI
10.1103/physreva.66.032309

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To implement a set of universal quantum logic gates based on non-Abelian geometric phases, it is conventional wisdom that quantum systems beyond two levels are required, which is extremely difficult to fulfill for superconducting qubits and appears to be a main reason why only single-qubit gates were implemented in a recent experiment [A. A. Abdumalikov, Jr. et al., Nature (London) 496, 482 (2013)]. Here we propose to realize nonadiabatic holonomic quantum computation in decoherence-free subspace on circuit QED, where one can use only the two levels in transmon qubits, a usual interaction, and a minimal resource for the decoherence-free subspace encoding. In particular, our scheme not only overcomes the difficulties encountered in previous studies but also can still achieve considerably large effective coupling strength, such that high-fidelity quantum gates can be achieved. Therefore, the present scheme makes realizing robust holonomic quantum computation with superconducting circuits very promising.
Holonomic quantum computation exploits the geometric evolution of eigenspaces of a degenerate Hamiltonian to implement unitary evolution of computational states. In this work we introduce a framework for performing scalable quantum computation in atom experiments through a universal set of fully holonomic adiabatic gates. Through a detailed differential geometric analysis, we elucidate the geometric nature of these gates and their inherent robustness against classical control errors and other noise sources. The concepts that we introduce here are expected to be widely applicable to the understanding and design of error robustness in generic holonomic protocols. To underscore the practical feasibility of our approach, we contextualize our gate design within recent advancements in Rydberg-based quantum computing and simulation.
Holonomic quantum computation exploits the geometric evolution of eigenspaces of a degenerate Hamiltonian to implement unitary evolution of computational states. In this work we introduce a framework for performing scalable quantum computation in atom experiments through a universal set of fully holonomic adiabatic gates. Through a detailed differential geometric analysis, we elucidate the geometric nature of these gates and their inherent robustness against classical control errors and other noise sources. The concepts that we introduce here are expected to be widely applicable to the understanding and design of error robustness in generic holonomic protocols. To underscore the practical feasibility of our approach, we contextualize our gate design within recent advancements in Rydberg-based quantum computing and simulation.
Nonadiabatic holonomic quantum computation provides the means to perform fast and robust quantum gates by utilizing the resilience of non-Abelian geometric phases to fluctuations of the path in state space. While the original scheme [E. Sj\"oqvist et al., New J. Phys. 14, 103035 (2012)] needs two loops in the Grassmann manifold (i.e., the space of computational subspaces of the full state space) to generate an arbitrary holonomic one-qubit gate, we propose single-loop one-qubit gates that constitute an efficient universal set of holonomic gates when combined with an entangling holonomic two-qubit gate. Our one-qubit gate is realized by dividing the loop into path segments, each of which is generated by a $\mathrm{\ensuremath{\Lambda}}$-type Hamiltonian. We demonstrate that two path segments are sufficient to realize arbitrary single-loop holonomic one-qubit gates. We describe how our scheme can be implemented experimentally in a generic atomic system exhibiting a three-level $\mathrm{\ensuremath{\Lambda}}$-coupling structure by utilizing carefully chosen laser pulses.