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Physical Review A

Nonadiabatic holonomic quantum computation in decoherence-free subspaces with trapped ions

Zhen-Tao Liang, Yan-Xiong Du, Wei Huang, Zheng‐Yuan Xue, Hui Yan

Published Jun 10, 2014• 98 citations
Publisher

Abstract

Implementing nonadiabatic holonomic quantum computation in decoherence-free subspaces may consolidate the advantages of both strategies and thus leads to suppression of both local and collective noises. In a recent paper, Xu et al. [Phys. Rev. Lett. 109, 170501 (2012)] proposed an interesting implementation of such a scheme; however, four-body interaction, which is hard to achieve in a realistic system, is required there. In this paper we propose a simplified scheme to implement such single-qubit and two-qubit logical operations by utilizing only two-body interactions, which is much easier to realize in a trapped ion system.

DOI
10.1103/physreva.89.062312

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Implementing nonadiabatic holonomic quantum computation in decoherence-free subspaces may consolidate the advantages of both strategies and thus leads to suppression of both local and collective noises. In a recent paper, Xu et al. [Phys. Rev. Lett. 109, 170501 (2012)] proposed an interesting implementation of such a scheme; however, four-body interaction, which is hard to achieve in a realistic system, is required there. In this paper we propose a simplified scheme to implement such single-qubit and two-qubit logical operations by utilizing only two-body interactions, which is much easier to realize in a trapped ion system.
Nonadiabatic holonomic quantum computation in decoherence-free subspaces has attracted increasing attention recently, as it allows for high-speed implementation and combines both the robustness of holonomic gates and the coherence stabilization of decoherence-free subspaces. Since the first protocol of nonadiabatic holonomic quantum computation in decoherence-free subspaces, a number of schemes for its physical implementation have been put forward. However, all previous schemes require two noncommuting gates to realize an arbitrary one-qubit gate, which doubles the exposure time of gates to error sources as well as the resource expenditure. In this paper, we propose an alternative protocol for nonadiabatic holonomic quantum computation in decoherence-free subspaces, in which an arbitrary one-qubit gate in decoherence-free subspaces is realized by a single-shot implementation. The present protocol not only maintains the merits of the original protocol but also avoids the extra work of combining two gates to implement an arbitrary one-qubit gate and thereby reduces the exposure time to various error sources.
Quantum computation that combines the coherence stabilization virtues of decoherence-free subspaces and the fault tolerance of geometric holonomic control is of great practical importance. Some schemes of adiabatic holonomic quantum computation in decoherence-free subspaces have been proposed in the past few years. However, nonadiabatic holonomic quantum computation in decoherence-free subspaces, which avoids a long run-time requirement but with all the robust advantages, remains an open problem. Here, we demonstrate how to realize nonadiabatic holonomic quantum computation in decoherence-free subspaces. By using only three neighboring physical qubits undergoing collective dephasing to encode one logical qubit, we realize a universal set of quantum gates.
The implementation of holonomic quantum computation is meaningful. We can effectively resist local and collective noise in the process of physical implementation by using the advantage of non-Abelian geometric phase. In this paper, we set out from the simplest and most fundamental Jaynes-Cummings model of ion trap system to implement single-qubit logical operations, and taking advantage of the interaction of two ions with a pair of laser pulses to implement two-qubit logical operations, respectively. Compared with the previous proposal, the whole process of our proposal are in tunable way and the universal holonomic quantum qubit gates can be made robust to systematic error and decay which pushes the gate fidelities in the presence of decoherence and systematic error to well high level. Thus our scheme affords an experimentally feasible and simple way to make realizing the robust nonadiabatic holonomic quantum computation.
Abstract Adiabatic holonomic gates possess the geometric robustness of adiabatic geometric phases, i.e., dependence only on the evolution path of the parameter space but not on the evolution details of the quantum system, which, when coordinated with decoherence-free subspaces, permits additional resilience to the collective dephasing environment. However, the previous scheme [Phys. Rev. Lett. 95 130501 (2005)] of adiabatic holonomic quantum computation in decoherence-free subspaces requires four-body interaction that is challenging in practical implementation. In this work, we put forward a scheme to realize universal adiabatic holonomic quantum computation in decoherence-free subspaces using only realistically available two-body interaction, thereby avoiding the difficulty of implementing four-body interaction. Furthermore, an arbitrary one-qubit gate in our scheme can be realized by a single-shot implementation, which eliminates the need to combine multiple gates for realizing such a gate.
Non-adiabatic holonomic quantum computation in decoherence-free subspaces protects quantum information from control imprecisions and decoherence. For the non-collective decoherence that each qubit has its own bath, we show the implementations of two non-commutable holonomic single-qubit gates and one holonomic nontrivial two-qubit gate that compose a universal set of non-adiabatic holonomic quantum gates in decoherence-free-subspaces of the decoupling group, with an encoding rate of (N - 2)/N. The proposed scheme is robust against control imprecisions and the non-collective decoherence, and its non-adiabatic property ensures less operation time. We demonstrate that our proposed scheme can be realized by utilizing only two-qubit interactions rather than many-qubit interactions. Our results reduce the complexity of practical implementation of holonomic quantum computation in experiments. We also discuss the physical implementation of our scheme in coupled microcavities.