Tracking Quantum Error Correction

To implement fault-tolerant quantum computation with continuous variables, the Gottesman--Kitaev--Preskill (GKP) qubit has been recognized as an important technological element. We have proposed a method to reduce the required squeezing level to realize large scale quantum computation with the GKP qubit [Phys. Rev. X. {\bf 8}, 021054 (2018)], harnessing the virtue of analog information in the GKP qubits. In the present work, to reduce the number of qubits required for large scale quantum computation, we propose the tracking quantum error correction, where the logical-qubit level quantum error correction is partially substituted by the single-qubit level quantum error correction. In the proposed method, the analog quantum error correction is utilized to make the performances of the single-qubit level quantum error correction almost identical to those of the logical-qubit level quantum error correction in a practical noise level. The numerical results show that the proposed tracking quantum error correction reduces the number of qubits during a quantum error correction process by the reduction rate $\left\{{2(n-1)\times4^{l-1}-n+1}\right\}/({2n \times 4^{l-1}})$ for $n$-cycles of the quantum error correction process using the Knill's $C_{4}/C_{6}$ code with the concatenation level $l$. Hence, the proposed tracking quantum error correction has great advantage in reducing the required number of physical qubits, and will open a new way to bring up advantage of the GKP qubits in practical quantum computation

Analog quantum error correction with encoding a qubit into an oscillator

To implement fault-tolerant quantum computation with continuous variables, Gottesman-Kitaev-Preskill (GKP) qubits have been recognized as an important technological element. However, the analog outcome of GKP qubits, which includes beneficial information to improve the error tolerance, has been wasted, because the GKP qubits have been treated as only discrete variables. In this paper, we propose a hybrid quantum error correction approach that combines digital information with the analog information of the GKP qubits using the maximum-likelihood method. As an example, we demonstrate that the three-qubit bit-flip code can correct double errors, whereas the conventional method based on majority voting on the binary measurement outcome can correct only a single error. As another example, a concatenated code known as Knill's C4/C6 code can achieve the hashing bound for the quantum capacity of the Gaussian quantum channel. To the best of our knowledge, this approach is the first attempt to draw both digital and analog information from a single quantum state to improve quantum error correction performance

BIOMECHANICAL ANALYSIS OF THE MOMENT ABOUT THE CENTER OF MASS DURING THE DOWNSWING PHASE IN WOMEN’S DRIVER SHOT

The purpose of this study was to investigate the moment about the center of mass (CM) acting on the golfer-club system during the downswing phase in women’s driver shots. Fourteen female golfers volunteered as subjects. The maximum clubhead speed, angular momentum ot the thorax and moment about the CM were calculated. There was a strong significant correlation between the frontal-plane moment about the CM and the maximum clubhead speed (

Theoretical Aspects of the Orientation Problem for Stereo MSS Data Coverage

The orientation problem of MSS data is generally much more complicated than that of an optical photograph. The main reason is that MSS imagery produced from MSS data is not a central perspective representation of the ground surface, because the recording of MSS data is not instantaneous. Many studies about the geometry and the orientation problem for single MSS data coverage from aircraft have been made. Also, some effective orientation and restitution methods have already been developed by G. Konecny, et al.. Little, however, has been done in the way of investigating the orientation problem for stereo MSS data coverage from aircraft. Therefore, the author proposes in this paper an orientation technique of stereo MSS imageries based on the simultaneous determination of the exterior orientation parameters for stereo photographs. This method will soon be tested with some experimental models so as to investigate the accuracies attainable, and to clarify the difficulties in the practical analysis of stereo MSS data

THE RELATIONSHIP BETWEEN THE INWARD PULL MOTION AND BODY MOVEMENT DURING THE DOWNSWING PHASE IN GOLF SWING

The purpose of this study was to investigate the relationship between the inward pull motion and body movement to increase the maximum velocity of the clubhead during the downswing phase in men’s driver shot. Four male professional and five male amateur golfers were volunteered as subjects (age = 37.2 ± 14.8 yrs, 1.73 ± 0.05 m, 67.5 ± 7.1 kg). A 10-camera (250 Hz) VICON system was used in an indoor motion analysis facility to capture 3D trajectories of 57 reflective markers attached to each golfer’s body and the driver. The joint force about the grip, the left hand’s radius of curvature, and the Cardan angles of the pelvis and the thorax were calculated during the downswing phase in men’s driver shot. The results revealed that the pelvis and the thorax were bending toward the right side (Y-axis) just before impact. These movements lead to elevation in the left shoulder and consequently the left hand moves inward from the orbit of the hub path just before impact. On that occasion, it is important the thorax is facing the front (Z-axis) to elevate the left shoulder along the swing plane

Orientation Problem of SLAR Imagery

This report treats the orientation and restitution problem of SLAR imagery theoretically. The orientation problem is discussed for single SLAR configuration and also for stereo SLAR configuration. For the former, this paper proposed an analytical orientation method constructed on the geometrical basis of SLAR imagery already studied. For the latter, the author developed an orientation technique to calculate the exterior orientation parameters of the antenna for stereo SLAR imageries simultaneously. With this method the analysis of SLAR imagery may be performed three-dimensionally and more accurately than before. In both cases, some functional form, such as polynomials and Fourier's series, is used to model the behaviors of the exterior orientation elements of the antenna along the flight path, as in the analysis of MSS imagery. Linearizing the determination equations for the orientation problem of single SLAR imagery, one obtains error equations for the restitution problem of SLAR imagery. This report introduced simple restitution methods of SLAR imagery for a flat terrain and also for a hilly ground surface, and further, clarified some characteristics

THE CONTRIBUTION OF JOINT TORQUE TO THE ACCELERATION OF THE CLUBHEAD DURING THE DOWNSWING PHASE IN GOLF: A CASE STUDY

The purpose of this study was to investigate the contribution of joint torque to the acceleration of the club during the downswing phase in golf. Three professional golfers volunteered as participants (age: 37.7 ± 4.5 years, height: 1.70 ± 0.03 m, weight: 63.3 ± 4.3 kg). Their driver shots were recorded using a 10-camera (250 Hz) VICON system. The forces and torques applied to their drivers during the downswing phase were calculated based on Newton-Euler equations. Joint force power and joint torque power were also calculated. The mechanical work was obtained as an integral value of the power during the downswing phase. The mechanical work done by the joint torque accounted for about 15% of the total mechanical work in the downswing phase. Therefore, these results suggest that the grip torque applied to the club plays an important role in power generation in a golf swing

THE RELATIONSHIP BETWEEN ANGULAR MOMENTUM OF BODY SEGMENT AND VELOCITY OF THE CLUBHEAD IN WOMEN’S DRIVER SHOT

The purpose of this study was to investigate the relationship between angular momentum of body segments and maximum velocity of the clubhead during the downswing phase in women’s driver shot. Six female professional and eight female amateur golfers were volunteered as subjects(age = 27.8 ± 15.1 yrs, height = 1.62 ± 0.05 m, mass = 59.6 ± 7.6 kg). Motion was captured by using a VICON motion capture system. Maximum clubhead velocity was calculated. Then angular velocity and angular momentum of pelvis and thorax were calculated. The maximum velocity of clubhead was 38.4 ± 1.9 m/s. The maximum angular momentum of pelvis and thorax about the Z-axis were 0.91 ± 0.16 kgm2/s and 1.48 ± 0.25 kgm2/s, respectively. There was a significant correlation between the angular momentum of thorax about the Z-axis and the maximum velocity of clubhead. In conclusion, inorder to get higher clubhead velocity it is important to generate the larger angular momentum of thorax about the Z-axis and transfer to the clubhead

High-threshold fault-tolerant quantum computation with analog quantum error correction

To implement fault-tolerant quantum computation with continuous variables, the Gottesman-Kitaev-Preskill (GKP) qubit has been recognized as an important technological element. However,it is still challenging to experimentally generate the GKP qubit with the required squeezing level, 14.8 dB, of the existing fault-tolerant quantum computation. To reduce this requirement, we propose a high-threshold fault-tolerant quantum computation with GKP qubits using topologically protected measurement-based quantum computation with the surface code. By harnessing analog information contained in the GKP qubits, we apply analog quantum error correction to the surface code.Furthermore, we develop a method to prevent the squeezing level from decreasing during the construction of the large scale cluster states for the topologically protected measurement based quantum computation. We numerically show that the required squeezing level can be relaxed to less than 10 dB, which is within the reach of the current experimental technology. Hence, this work can considerably alleviate this experimental requirement and take a step closer to the realization of large scale quantum computation.Comment: 14 pages, 7 figure