Accelerated Randomized Benchmarking

Quantum information processing offers promising advances for a wide range of fields and applications, provided that we can efficiently assess the performance of the control applied in candidate systems. That is, we must be able to determine whether we have implemented a desired gate, and refine accordingly. Randomized benchmarking reduces the difficulty of this task by exploiting symmetries in quantum operations. Here, we bound the resources required for benchmarking and show that, with prior information, we can achieve several orders of magnitude better accuracy than in traditional approaches to benchmarking. Moreover, by building on state-of-the-art classical algorithms, we reach these accuracies with near-optimal resources. Our approach requires an order of magnitude less data to achieve the same accuracies and to provide online estimates of the errors in the reported fidelities. We also show that our approach is useful for physical devices by comparing to simulations. Our results thus enable the application of randomized benchmarking in new regimes, and dramatically reduce the experimental effort required to assess control fidelities in quantum systems. Finally, our work is based on open-source scientific libraries, and can readily be applied in systems of interest.Comment: 10 pages, full source code at https://github.com/cgranade/accelerated-randomized-benchmarking #quantuminfo #benchmarkin

Spin diffusion of correlated two-spin states in a dielectric crystal

Reciprocal space measurements of spin diffusion in a single crystal of calcium fluoride (CaF$_2$) have been extended to dipolar ordered states. The experimental results for the component of the spin diffusion parallel with the external field are $D_{D}^{||}=29 \pm 3 \times 10^{-12}$ cm$^{2}$/s for the [001] direction and $D_{D}^{||}=33 \pm 4 \times 10^{-12}$ cm$^{2}$/s for the [111] direction. The diffusion rates for dipolar order are significantly faster than those for Zeeman order and are considerably faster than predicted by simple theoretical models. It is suggested that constructive interference in the transport of the two spin state is responsible for this enhancement. As expected the anisotropy in the diffusion rates is observed to be significantly less for dipolar order compared to the Zeeman case.Comment: 4 pages, 2 figures. Resubmitted to PRL - new figure added / discussion expande

Simulations of Information Transport in Spin Chains

Transport of quantum information in linear spin chains has been the subject of much theoretical work. Experimental studies by nuclear spin systems in solid-state by NMR (a natural implementation of such models) is complicated since the dipolar Hamiltonian is not solely comprised of nearest-neighbor XY-Heisenberg couplings. We present here a similarity transformation between the XY-Heisenberg Hamiltonian and the grade raising Hamiltonian, an interaction which is achievable with the collective control provided by radio-frequency pulses in NMR. Not only does this second Hamiltonian allows us to simulate the information transport in a spin chain, but it also provides a means to observe its signature experimentally

Extending Quantum Coherence in Diamond

We experimentally demonstrate over two orders of magnitude increase in the coherence time of nitrogen vacancy centres in diamond by implementing decoupling techniques. We show that equal pulse spacing decoupling performs just as well as non-periodic Uhrig decoupling and has the additional benefit that it allows us to take advantage of "revivals" in the echo (due to the coherent nature of the bath) to explore the longest coherence times. At short times, we can extend the coherence of particular quantum states out from T_2*=2.7 us out to an effective T_2 > 340 us. For preserving arbitrary states we show the experimental importance of using pulse sequences, that through judicious choice of the phase of the pulses, compensate the imperfections of individual pulses for all input states. At longer times we use these compensated sequences to enhance the echo revivals and show a coherence time of over 1.6 ms in ultra-pure natural abundance 13C diamond.Comment: 7 pages, 7 figures; minor syntax/typo. changes and updated reference