High-fidelity quantum gates are essential for large scale quantum computation, which can naturally be realized in a noise resilient way. It is well-known that geometric manipulation and decoherence-free subspace encoding are promising ways towards robust quantum computation. Here, by combining the advantages of both strategies, we propose and experimentally realize universal holonomic quantum gates in both a single-loop and composite scheme, based on nonadiabatic and non-Abelian geometric phases, in a decoherence-free subspace with nuclear magnetic resonance. Our experiment only employs two-body resonant spin-spin interactions and thus is experimental friendly. In particularly, we also experimentally verify that the composite scheme is more robust against the pulse errors over the single-loop scheme. Therefore, our experiment provides a promising way towards faithful and robust geometric quantum manipulation.
This paper describes a general method for manipulation of nuclear spins in zero magnetic field. In the absence of magnetic fields, the spins lose the individual information on chemical shifts and inequivalent spins can only be distinguished by nuclear gyromagnetic ratios and spin-spin couplings. For spin-1/2 nuclei with different gyromagnetic ratios (i.e., different species) in zero magnetic field, we describe the scheme to realize a set of universal quantum logic gates, e.g., arbitrary singlequbit gates and two-qubit controlled-NOT gate. This method allows for universal quantum control in systems which might provide promising applications in materials science, chemistry, biology, quantum information processing and fundamental physics.
We derive the explicit solution of the problem of time-optimal control by a common magnetic fields for two independent spin-1 2 particles. Our approach is based on the Pontryagin Maximum Principle and a novel symmetry reduction technique. We experimentally implement the optimal control using zero-field nuclear magnetic resonance. This reveals an average gate error of 1% and a 70% to 80 % decrease in the experiment duration as compared to existing methods. This is the first analytical solution and experimental demonstration of time-optimal control in such a system and it provides a route to achieve time optimal control in more general quantum systems. arXiv:1810.07905v1 [quant-ph]
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