Abstract
Holonomic quantum computation (HQC) may not show its full potential in quantum speedup due to the prerequisite of a long coherent runtime imposed by the adiabatic condition. Here we show that the conventional HQC can be dramatically accelerated by using external control fields, of which the effectiveness is exclusively determined by the integral of the control fields in the time domain. This control scheme can be realized with net zero energy cost and it is fault-tolerant against fluctuation and noise, significantly relaxing the experimental constraints. We demonstrate how to realize the scheme via decoherence-free subspaces. In this way we unify quantum robustness merits of this fault-tolerant control scheme, the conventional HQC and decoherence-free subspace, and propose an expedited holonomic quantum computation protocol.
Highlights
The heart of Holonomic quantum computation (HQC) is the experimental implementation of the geometric phase acquired in a cyclic adiabatic passage
We propose a novel and composite strategy to tackle the long runtime issue in the HQC protocols via accelerating the adiabatic passage in decoherence-free subspace (DFS)
It is found that the particular design or shape of a control function, such as regular, random, chaotic and even noisy pulse sequences, is not as decisive as it seems to be, but only the integral of the control function in the time domain plays the crucial role in speeding up the adiabatic passage, which greatly relaxes constraints on experimental implementation of these control functions
Summary
The heart of HQC is the experimental implementation of the geometric phase acquired in a cyclic adiabatic passage. Wu, Zanardi and Lidar[17] initiated a scheme by embedding HQC into a decoherence-free subspace (DFS). We propose a novel and composite strategy to tackle the long runtime issue in the HQC protocols via accelerating the adiabatic passage in DFS. We further discover that our Hamiltonians in the adiabatic representation are periodical functionals of the integral of the control functions, resulting in a net zero-energy-cost control scheme – a new mechanism that accelerates adiabatic passages with the same effectiveness. These lead to a new type of fault-tolerance against control fluctuations
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