Experimental Realization of Nonunitary Multiqubit Operations

We demonstrate a novel experimental tool set that enables irreversible multiqubit operations on a quantum platform. To exemplify our approach, we realize two elementary nonunitary operations: the or and nor gates. The electronic states of two trapped ^{40}Ca^{+} ions encode the logical information, and a cotrapped ^{88}Sr^{+} ion provides the irreversibility of the gate by a dissipation channel through sideband cooling. We measure 87% and 81% success rates for the or and nor gates, respectively. The presented methods are a stepping stone toward other nonunitary operations such as in quantum error correction and quantum machine learning.

Experimental quantum compressed sensing for a seven-qubit system

Well-controlled quantum devices with their increasing system size face a new roadblock hindering further development of quantum technologies. The effort of quantum tomography—the reconstruction of states and processes of a quantum device—scales unfavourably: state-of-the-art systems can no longer be characterized. Quantum compressed sensing mitigates this problem by reconstructing states from incomplete data. Here we present an experimental implementation of compressed tomography of a seven-qubit system—a topological colour code prepared in a trapped ion architecture. We are in the highly incomplete—127 Pauli basis measurement settings—and highly noisy—100 repetitions each—regime. Originally, compressed sensing was advocated for states with few non-zero eigenvalues. We argue that low-rank estimates are appropriate in general since statistical noise enables reliable reconstruction of only the leading eigenvectors. The remaining eigenvectors behave consistently with a random-matrix model that carries no information about the true state.

Quantum compressed sensing can provide a scalable way to characterize quantum states and devices, but has been so far limited to states with quickly decaying eigenvalues. Here the authors show that it can be appropriate even in the general case, demonstrating reconstruction the state of a seven-qubit system.

Cryogenic setup for trapped ion quantum computing

We report on the design of a cryogenic setup for trapped ion quantum computing containing a segmented surface electrode trap. The heat shield of our cryostat is designed to attenuate alternating magnetic field noise, resulting in 120 dB reduction of 50 Hz noise along the magnetic field axis. We combine this efficient magnetic shielding with high optical access required for single ion addressing as well as for efficient state detection by placing two lenses each with numerical aperture 0.23 inside the inner heat shield. The cryostat design incorporates vibration isolation to avoid decoherence of optical qubits due to the motion of the cryostat. We measure vibrations of the cryostat of less than ±20 nm over 2 s. In addition to the cryogenic apparatus, we describe the setup required for an operation with ⁴⁰Ca⁺ and ⁸⁸Sr⁺ ions. The instability of the laser manipulating the optical qubits in ⁴⁰Ca⁺ is characterized by yielding a minimum of its Allan deviation of 2.4 ⋅ 10^-15 at 0.33 s. To evaluate the performance of the apparatus, we trapped ⁴⁰Ca⁺ ions, obtaining a heating rate of 2.14(16) phonons/s and a Gaussian decay of the Ramsey contrast with a 1/e-time of 18.2(8) ms.

Realization of universal ion-trap quantum computation with decoherence-free qubits

Any residual coupling of a quantum computer to the environment results in computational errors. Encoding quantum information in a so-called decoherence-free subspace provides means to avoid these errors. Despite tremendous progress in employing this technique to extend memory storage times by orders of magnitude, computation within such subspaces has been scarce. Here, we demonstrate the realization of a universal set of quantum gates acting on decoherence-free ion qubits. We combine these gates to realize the first controlled-NOT gate towards a decoherence-free, scalable quantum computer.

Realization of the quantum Toffoli gate with trapped ions

Gates acting on more than two qubits are appealing as they can substitute complex sequences of two-qubit gates, thus promising faster execution and higher fidelity. One important multiqubit operation is the quantum Toffoli gate that performs a controlled NOT operation on a target qubit depending on the state of two control qubits. Here we present the first experimental realization of the quantum Toffoli gate in an ion trap quantum computer, achieving a mean gate fidelity of 71(3)%. Our implementation is particularly efficient as the relevant logic information is directly encoded in the motion of the ion string.

Absolute frequency measurement of the 40Ca+ 4s(2)S_(1/2)-3d(2)D_(5/2) clock transition

We report on the first absolute transition frequency measurement at the 10;{-15} level with a single, laser-cooled 40Ca+ ion in a linear Paul trap. For this measurement, a frequency comb is referenced to the transportable Cs atomic fountain clock of LNE-SYRTE and is used to measure the 40Ca+ 4s ;{2}S_{1/2}-3d ;{2}D_{5/2} electric-quadrupole transition frequency. After the correction of systematic shifts, the clock transition frequency nu_{Ca;{+}}=411 042 129 776 393.2(1.0) Hz is obtained, which corresponds to a fractional uncertainty within a factor of 3 of the Cs standard. In addition, we determine the Landé g factor of the 3d;{2}D_{5/2} level to be g_{5/2}=1.200 334 0(3).

Process tomography of ion trap quantum gates

A crucial building block for quantum information processing with trapped ions is a controlled-NOT quantum gate. In this Letter, two different sequences of laser pulses implementing such a gate operation are analyzed using quantum process tomography. Fidelities of up to 92.6(6)% are achieved for single-gate operations and up to 83.4(8)% for two concatenated gate operations. By process tomography we assess the performance of the gates for different experimental realizations and demonstrate the advantage of amplitude-shaped laser pulses over simple square pulses. We also investigate whether the performance of concatenated gates can be inferred from the analysis of the single gates.

Echocardiographic criteria of physiological left ventricular hypertrophy in combined strength- and endurance-trained athletes

In combined strength- and endurance-trained athletes who are showing both unusual large body dimensions as well as a high physical fitness, the dimensions of the 'athlete's heart' are expected to reach physiological limits. Therefore we investigated 75 male and 77 female competitive rowers by means of doppler-echocardiography. The absolute "critical" heart weight of 500 g was exceeded by 61% of the male and 10% of the female rowers. Maximal values of the left ventricular (LV) muscle mass were measured at 170 (men) and 133 (women) g.m-2 body surface area, respectively. The LV end-diastolic internal diameter was measured to be above the upper clinical limit of 55 mm in 55% of the male and 17% of the female rowers. A LV wall thickness of 13 and 12 mm was only exceeded by 3 male and 1 female athlete, respectively (maximal values: 14 and 12.5 mm). The LV wall/internal diameter ratio did not exceed 48-50%. The systolic LV function as well as ECG and blood pressure did not reveal any pathological finding, the diastolic LV function was always measured within the normal range. The LV wall thicknesses, internal diameter and hypertrophic index (relation between wall thickness and internal diameter) of the rowers were significantly higher than those of 62 non-endurance trained athletes (pairwise matched according to the body dimensions) and similar to 28 male 'pure' endurance athletes (pairwise matched according to the absolute heart volume). In conclusion, upper limits of echocardiographic volume measurements that are considered critical may be clearly exceeded by healthy strength-endurance trained athletes with simultaneously high body dimensions. The clinical limits, however, are still valid in subjects with a body mass up to approximately 70 kg. The LV wall thickness only exceptionally exceed the clinical limits. A specific influence of the strength elements in training on the LV hypertrophy had not be found.

Sports-specific adaptation of left ventricular muscle mass in athlete's heart. II: An echocardiographic study with 400-m runners and soccer players

Regarding the influence of the left ventricular (LV) adaptation by sports-specific factors the supposed endurance training have so far been compared mainly to strength conditioning. In the present study we investigated the echocardiographic LV measurements of endurance-trained athletes in different kinds of endurance sports (running and ball games) by using matched-pair procedures. We examined 22 male soccer players (S) and 22 male 400-m runners (R) on a regional up to a national level with--each similar in pairs--the following body mass (S: 75.7 +/-5.0 kg; R: 75.2 +/- 5.6), body surface area (S: 1.97 +/- 0.09 m2; R: 1.98 +/- 0.09), fat-free body mass (S: 68.4 +/- 4.6 kg; R: 68.3 +/- 5.3) and individual anaerobic threshold as a criterion to determine the running endurance (S: 14.23 +/- 0.79 km.h-1; R: 14.25 +/- 0.80). The body dimensions-related heart volume (HV/lean body mass: S: 14.2 +/- 1.5 ml.kg-1; R: 13.4 +/- 1.0) as well as the absolute and body surface-related LV internal diameter (EDD: S: 55.0 +/- 3.8 mm; R: 52.7 +/- 3.3; EDD/body-surface area: S: 27.8 +/- 1.9 mm.m-2; R: 26.6 +/- 1.3) were measured significantly higher in S as compared to R (p < 0.05 and p < 0.01, respectively). In both groups, free LV wall thickness, enddiastolic diameter and LV muscle mass correlated significantly with the body dimensions (fat-free body mass: r = 0.42 - 0.48 - 0.56; p < 0.004, respectively). In conclusion, specific sport-related strain like frequent exercises in interval form (typical for ball games) and a different volume/intensity ratio could significantly influence the LV adaptation beside the endurance performance as well as constitutional and genetic factors.

Sports-specific adaptation of left ventricular muscle mass in athlete's heart. I. An echocardiographic study with combined isometric and dynamic exercise trained athletes (male and female rowers)

The differentiation of the physiological left ventricular (LV) hypertrophy of the athlete's heart in opposition to a pathological finding may be problematic especially in both strength and endurance trained athletes with simultaneously large body dimensions: 64 male and 71 female rowers of regional up to national level were examined by (Doppler) echocardiography. In addition, the rowers were compared by matched-pair procedures both with 32 male and 30 female non-endurance trained (pairwise similar body surface area) and with 28 male endurance athletes (pairwise similar absolute heart volume). The so-called critical heart weight of 500 g was exceeded by 63% of the male and 11% of the female rowers. 9% of the male rowers showed even an LV muscle mass above the limit of 3.5 g.kg-1 body mass. The individual maximal body surface area-related values were 170 g.m-2 (men) and 133 g.m-2 (women). The LV enddiastolic internal diameter was measured to be above the upper clinical limit of 55 mm in 69% or 23% of the male and female rowers, although a maximal LV wall thickness of 14 or 13 mm, respectively, was never exceeded. The systolic LV function as well as ECG and blood pressure did not reveal any pathological findings, the diastolic LV function was measured within the (supra) normal range. The LV wall thicknesses, internal diameter and hypertrophic index (relation between wall thickness and internal diameter) were significantly higher in rowers than in non-endurance trained subjects, but similar if compared to the endurance athletes. The clinical limits, however, keep their validity until a body mass of about 70 kg. In conclusion, some upper absolute clinical limits, especially those referring to volume measurements, so far considered critical (LV internal diameter, heart weight and LV mass), may be clearly exceeded by healthy strength endurance trained athletes presenting high body dimensions. The LV wall thickness, however, rather exceptionally exceeded the clinical limits. If referring to body dimensions, the cardiac dimensions in rowers are still lower in comparison to highly-trained "pure" endurance athletes. A specific influence of the isometric exercise component on the LV hypertrophy cannot be observed.