Realizing repeated quantum error correction in a distance-three surface code.

Quantum computers hold the promise of solving computational problems that are intractable using conventional methods1. For fault-tolerant operation, quantum computers must correct errors occurring owing to unavoidable decoherence and limited control accuracy2. Here we demonstrate quantum error correction using the surface code, which is known for its exceptionally high tolerance to errors3-6. Using 17 physical qubits in a superconducting circuit, we encode quantum information in a distance-three logical qubit, building on recent distance-two error-detection experiments7-9. In an error-correction cycle taking only 1.1 µs, we demonstrate the preservation of four cardinal states of the logical qubit. Repeatedly executing the cycle, we measure and decode both bit-flip and phase-flip error syndromes using a minimum-weight perfect-matching algorithm in an error-model-free approach and apply corrections in post-processing. We find a low logical error probability of 3% per cycle when rejecting experimental runs in which leakage is detected. The measured characteristics of our device agree well with a numerical model. Our demonstration of repeated, fast and high-performance quantum error-correction cycles, together with recent advances in ion traps10, support our understanding that fault-tolerant quantum computation will be practically realizable.

Comparison of compartmental analytical Blood-Oxygen-Level-Dependent functional Magnetic Resonance Imaging models against Monte Carlo simulations performed over cortical micro-angiograms.

Blood oxygen level-dependent functional magnetic resonance imaging (BOLD fMRI) arises from a physiological and physical cascade of events taking place at the level of the cortical microvasculature which constitutes a medium with complex geometry. Several analytical models of the BOLD contrast have been developed, but these have not been compared directly against detailed bottom-up modeling methods. Using a 3D modeling method based on experimentally measured images of mice microvasculature and Monte Carlo simulations, we quantified the accuracy of two analytical models to predict the amplitude of the BOLD response from 1.5 to 7 T, for different echo time (TE) and for both gradient echo and spin echo acquisition protocols. We also showed that accounting for the tridimensional structure of the microvasculature results in more accurate prediction of the BOLD amplitude, even if the values for SO2 were averaged across individual vascular compartments. A secondary finding is that modeling the venous compartment as two individual compartments results in more accurate prediction of the BOLD amplitude compared with standard homogenous venous modeling, arising from the bimodal distribution of venous SO2 across the microvasculature in our data.

Modeling of vascular space occupancy and BOLD functional MRI from first principles using real microvascular angiograms.

PURPOSE: The vascular space occupancy (VASO) is a functional MRI technique for probing cerebral blood volume changes noninvasively, including during neuronal activation in humans. An important consideration when implementing VASO is the BOLD effect in the signal. Assessing the physical origin of this BOLD contamination and the capabilities of correction methods could improve the quantification of cerebral blood volume changes with VASO. METHODS: Given the heterogeneity of cerebral microvascular architecture, the vascular geometry within an MRI voxel can influence both BOLD and VASO signals. To investigate this effect, 3D high-resolution images of mouse cerebral vasculature measured with two-photon microscopy were used to model BOLD and VASO signals from first principles using Monte Carlo diffusion of water protons. Quantitative plots of VASO together with intravascular and extravascular BOLD signals as a function of TE at B0 fields 1.5 T to 14 T were obtained. RESULTS: The BOLD contamination of the VASO response was on the order of 50% for gradient echo and 5% for spin echo at 7 T and TE = 6 ms and significantly increased with TE and B0 . Two currently used correction schemes were shown to account for most of this contamination and recover accurate relative signal changes, with optimal correction obtained using TEs as short as possible. CONCLUSION: These results may provide useful information for optimizing sequence parameters in VASO and BOLD functional MRI, leading the way to a wider application of these techniques in healthy and diseased brain.