Quantum error correction is required to compensate for the fragility of the state of a quantum computer. We report the first experimental implementations of quantum error correction and confirm the expected state stabilization. In NMR computing, however, a net improvement in the signal-to-noise would require very high polarization. The experiment implemented the 3-bit code for phase errors in liquid state state NMR.Comment: 5 pages, three figure

We present experimental results which demonstrate that nuclear magnetic resonance spectroscopy is capable of efficiently emulating many of the capabilities of quantum computers, including unitary evolution and coherent superpositions, but without attendant wave-function collapse. This emulation is made possible by two facts.The first is that the spin active nuclei in each molecule of a liquid sample are largely isolated from the spins in all other molecules, so that each molecule is effectively an independent quantum computer. The second is the existence of a manifold of statistical spin states, called pseudo-pure states, whose transformation properties are identical to those of true pure states. These facts enable us to operate on coherent superpositions over the spins in each molecule using full quantum parallelism, and to combine the results into deterministic macroscopic observables via thermodynamic averaging. We call a device based on these principles an ensemble quantum computer.Our results show that it is indeed possible to prepare a pseudo-pure state in a macroscopic liquid sample under ambient conditions, to transform it into a coherent superposition, to apply elementary quantum logic gates to this superposition, and to convert it into the equivalent of an entangled state. Specifically, we have:• Implemented the quantum XOR gate in two different ways, one using Pound-Overhauser double resonance, and the other using a spin-coherence double resonance pulse sequence.• Demonstrated that the square root of the Pound-Overhauser XOR corresponds to a conditional rotation, thus obtaining a universal set of gates.• Devised a spin-coherence implementation of the Toffoli gate, and confirmed that it transforms the equilibrium state of a four-spin system as expected.• Used standard gradient-pulse techniques in NMR to equalize all but one of the populations in a two-spin system, so obtaining the pseudo-pure state that corresponds to |00 .• Validated that one can identify which basic pseudo-pure state is present by transforming it into one-spin superpositions, whose associated spectra jointly characterize the state.• Applied the spin-coherence XOR gate to a one-spin superposition to create an entangled state, and confirmed its existence by detecting the associated double-quantum coherence via gradient-echo methods.2

Calibration of the spatial sensitivity functions of coil arrays is a crucial element in parallel magnetic resonance imaging (PMRI). The most common approach has been to measure coil sensitivities directly using one or more low-resolution images acquired before or after accelerated data acquisition. However, since it is difficult to ensure that the patient and coil array will be in exactly the same positions during both calibration scans and accelerated imaging, this approach can introduce sensitivity miscalibration errors into PMRI reconstructions. This work shows that it is possible to extract sensitivity calibration images directly from a fully sampled central region of a variable-density k-space acquisition. These images have all the features of traditional PMRI sensitivity calibrations and therefore may be used for any PMRI reconstruction technique without modification. Because these calibration data are acquired simultaneously with the data to be reconstructed, errors due to sensitivity miscalibration are eliminated. In vivo implementations of self-calibrating parallel imaging using a flexible coil array are demonstrated in abdominal imaging and in real-time cardiac imaging studies. Magn Reson Med 47:529 -538, 2002.

A delay in the timing of ACL reconstruction from ≤ 6 months to > 6 months following injury is associated with a significant increase in the prevalence of medial meniscal tears (P = 0.012), with a relative risk of 4.07 (CI, 1.29-12.88).

Logic gates such as the controlled-NOT ͑c-NOT͒ and Toffoli gates play a key role in quantum information processing ͑QIP͒ and quantum computing. A natural extension of such gates would necessarily operate on one quantum bit ͑qubit͒ conditional on the state of the remaining qubits in the system. We show that such selective gates, termed (controlled) n -NOT gates, or c n -NOT gates, are convenient in nuclear magnetic resonance ͑NMR͒ implementations of QIP and are straightforward to implement. NMR pulse sequences for these gates can be built using classical methods as well as insights from geometric algebra. These methods yield equivalent NMR pulse sequences for the generation of c n -NOT gates for any number of control spins. In this work, a catalog of c n -NOT gates for systems of as many as 16 spins is provided along with an experimental implementation of a c 3 -NOT gate on a four spin system, 13 C alanine.