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Non-Adiabatic Holonomic Quantum Computation in Noiseless Subsystems

Zhang Jian, L. C. Kwek, Erik Sjöqvist, D. M. Tong, Paolo Zanardi A

Published Aug 8, 2013• 0 citations
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Abstract

Quantum information processing requires a high degree of isolation from the detrimental effects of the environment as well as an extremely precise level of control on the way quantum dynamics unfolds in the information-processing system. In this paper, we show how these two goals can be ideally achieved by hybridizing the concepts of noiseless subsystems and of holonomic quantum computation. An all-geometric universal computation scheme based on non-adiabatic and non-Abelian quantum holonomies embedded in a four-qubit noiseless subsystem for general collective decoherence is proposed. The implementation details of this synergistic scheme along with the analysis of its stability against symmetry-breaking imperfections are presented.

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Quantum information processing requires a high degree of isolation from the detrimental effects of the environment as well as an extremely precise level of control on the way quantum dynamics unfolds in the information-processing system. In this paper, we show how these two goals can be ideally achieved by hybridizing the concepts of noiseless subsystems and of holonomic quantum computation. An all-geometric universal computation scheme based on non-adiabatic and non-Abelian quantum holonomies embedded in a four-qubit noiseless subsystem for general collective decoherence is proposed. The implementation details of this synergistic scheme along with the analysis of its stability against symmetry-breaking imperfections are presented.
Quantum-information processing requires a high degree of isolation from the detrimental effects of the environment as well as an extremely precise level of control of the way quantum dynamics unfolds in the information-processing system. In this paper we show how these two goals can be ideally achieved by hybridizing the concepts of noiseless subsystems and of holonomic quantum computation. An all-geometric universal computation scheme based on nonadiabatic and non-Abelian quantum holonomies embedded in a four-qubit noiseless subsystem for general collective decoherence is proposed. The implementation details of this synergistic scheme along with the analysis of its stability against symmetry-breaking imperfections are presented.
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.
Quantum information and quantum computation is an area of quantum mechanics which utilizes quantum properties of particles in schemes for computation. These quantum schemes have been shown to improve computational capabilities for some systems. In quantum computation, the decoherence problem is a limiting factor. Decoherence is the process of loss of quantum information due to interaction from the environment, which puts a limit to how long a quantum computation is valid. There are ways to limit the effect of decoherence. The idea of a noiseless subsystem is to encode the quantum information in a smaller subsystem of the physical system that is not affected by decoherence. Holonomic quantum computation encodes quantum information in holonomies, making it more robust and less affected by decoherence. In this report, these two concepts are combined by encoding one logical qubit in three physical spin-1 particles. The approach to combine these concepts is entirely analytical. A Hamiltonian acting on the physical system is derived. To achieve a result which is possible to implement experimentally, the analytical derivation utilizes permutation operators to derive the Hamiltonian, which is known to be implementable experimentally. A resulting Hamiltonian to implement the scheme is derived, using only permutaion operators. Both a one-qubit gate and a two-qubit gate is derived, which forms a universal set allowing all possible quantum computation. The resulting scheme seems to only use two-body interactions. The project has shown that holonomic quantum computation in a noiseless subsystem using threephysical spin-1 particles is possible. The resulting scheme only using two-body interactions is of a large interest since this simplifies the experimental implementation.
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.