scholarly journals Logical-qubit operations in an error-detecting surface code

2021 ◽  
Author(s):  
Jorge Marques ◽  
Boris Varbanov ◽  
Miguel Moreira ◽  
Hany Ali ◽  
Nandini Muthusubramanian ◽  
...  
Keyword(s):  
Error Detection ◽  
Fault Tolerant ◽  
The Road ◽  
Logical Operations ◽  
The Difference ◽  
Surface Code ◽  
On The Road ◽  
Qubit Operations ◽  
Quantum Error ◽  
Logical Qubit

Abstract Future fault-tolerant quantum computers will require storing and processing quantum data in logical qubits. We realize a suite of logical operations on a distance-two logical qubit stabilized using repeated error detection cycles. Logical operations include initialization into arbitrary states, measurement in the cardinal bases of the Bloch sphere, and a universal set of single-qubit gates. For each type of operation, we observe higher performance for fault-tolerant variants over non-fault-tolerant variants, and quantify the difference through detailed characterization. In particular, we demonstrate process tomography of logical gates, using the notion of a logical Pauli transfer matrix. This integration of high-fidelity logical operations with a scalable scheme for repeated stabilization is a milestone on the road to quantum error correction with higher-distance superconducting surface codes.

scholarly journals Exponential suppression of bit or phase errors with cyclic error correction

Nature ◽  
2021 ◽  
Vol 595 (7867) ◽  
pp. 383-387
Author(s):  
◽  
Zijun Chen ◽  
Kevin J. Satzinger ◽  
Juan Atalaya ◽  
Alexander N. Korotkov ◽  
...  
Keyword(s):  
Error Correction ◽  
Error Detection ◽  
Fault Tolerant ◽  
Error Rates ◽  
Quantum Error Correction ◽  
Superconducting Qubits ◽  
Two Dimensional ◽  
Logical Error ◽  
Quantum Error ◽  
Logical Qubit

AbstractRealizing the potential of quantum computing requires sufficiently low logical error rates1. Many applications call for error rates as low as 10−15 (refs. 2–9), but state-of-the-art quantum platforms typically have physical error rates near 10−3 (refs. 10–14). Quantum error correction15–17 promises to bridge this divide by distributing quantum logical information across many physical qubits in such a way that errors can be detected and corrected. Errors on the encoded logical qubit state can be exponentially suppressed as the number of physical qubits grows, provided that the physical error rates are below a certain threshold and stable over the course of a computation. Here we implement one-dimensional repetition codes embedded in a two-dimensional grid of superconducting qubits that demonstrate exponential suppression of bit-flip or phase-flip errors, reducing logical error per round more than 100-fold when increasing the number of qubits from 5 to 21. Crucially, this error suppression is stable over 50 rounds of error correction. We also introduce a method for analysing error correlations with high precision, allowing us to characterize error locality while performing quantum error correction. Finally, we perform error detection with a small logical qubit using the 2D surface code on the same device18,19 and show that the results from both one- and two-dimensional codes agree with numerical simulations that use a simple depolarizing error model. These experimental demonstrations provide a foundation for building a scalable fault-tolerant quantum computer with superconducting qubits.

scholarly journals Fault-tolerant detection of a quantum error

Science ◽  
2018 ◽  
Vol 361 (6399) ◽  
pp. 266-270 ◽  
Author(s):  
S. Rosenblum ◽  
P. Reinhold ◽  
M. Mirrahimi ◽  
Liang Jiang ◽  
L. Frunzio ◽  
...  
Keyword(s):  
Error Detection ◽  
Fault Tolerant ◽  
Critical Component ◽  
Detection Scheme ◽  
Dephasing Time ◽  
Order Of Magnitude ◽  
Quantum Error ◽  
Specific Error ◽  
Logical Qubit

A critical component of any quantum error–correcting scheme is detection of errors by using an ancilla system. However, errors occurring in the ancilla can propagate onto the logical qubit, irreversibly corrupting the encoded information. We demonstrate a fault-tolerant error-detection scheme that suppresses spreading of ancilla errors by a factor of 5, while maintaining the assignment fidelity. The same method is used to prevent propagation of ancilla excitations, increasing the logical qubit dephasing time by an order of magnitude. Our approach is hardware-efficient, as it uses a single multilevel transmon ancilla and a cavity-encoded logical qubit, whose interaction is engineered in situ by using an off-resonant sideband drive. The results demonstrate that hardware-efficient approaches that exploit system-specific error models can yield advances toward fault-tolerant quantum computation.

Determination of Resistance to Abrasive Wear. VIII. Influence of Softeners in Tests with the Akron-Croydon and Du Pont Machines

1949 ◽  
Vol 22 (1) ◽  
pp. 259-262
Author(s):  
J. F. Morley
Keyword(s):  
Unit Area ◽  
Published Data ◽  
The Road ◽  
Abrasive Surface ◽  
Abrasive Power ◽  
The Difference ◽  
On The Road ◽  
The Right ◽  
Abrasion Testing

Abstract These experiments indicate that softeners can influence abrasion resistance, as measured by laboratory machines, in some manner other than by altering the stress-strain properties of the rubber. One possible explanation is that the softener acts as a lubricant to the abrasive surface. Since this surface, in laboratory abrasion-testing machines, is relatively small, and comes repeatedly into contact with the rubber under test, it seems possible that it may become coated with a thin layer of softener that reduces its abrasive power. It would be interesting in this connection to try an abrasive machine in which a long continuous strip of abrasive material was used, no part of it being used more than once, so as to eliminate or minimize this lubricating effect. The fact that the effect of the softener is more pronounced on the du Pont than on the Akron-Croydon machine lends support to the lubrication hypothesis, because on the former machine the rate of wear per unit area of abrasive is much greater. Thus in the present tests the volume of rubber abraded per hr. per sq. cm. of abrasive surface ranges from 0.03 to 0.11 cc. on the du Pont machine and from 0.0035 to 0.0045 cc. on the Akron-Croydon machine. On the other hand, if the softener acts as a lubricant, it would be expected to reduce considerably the friction between the abrasive and the rubber and hence the energy used in dragging the rubber over the abrasive surface. The energy figures given in the right-hand columns of Tables 1 and 3, however, show that there is relatively little variation between the different rubbers. As a test of the lubrication hypothesis, it would be of interest to vary the conditions of test so that approximately the same amount of rubber per unit area of abrasive is abraded in a given time on both machines; this should show whether the phenomena observed under the present test conditions are due solely to the difference in rate of wear or to an inherent difference in the type of wear on the two machines. This could most conveniently be done by considerably reducing the load on the du Pont machine. In the original work on this machine the load was standardized at 8 pounds, but no figures are quoted to show how abrasion loss varies with the load. As an addition to the present investigation, it is proposed to examine the effect of this variation with special reference to rubbers containing various amounts and types of softener. Published data on the influence of softeners on the road wear of tire rubbers do not indicate anything like such large effects as are shown by the du Pont machine. This throws some doubt on the value of this machine for testing tire tread rubbers, a conclusion which is confirmed by information obtained from other workers.

scholarly journals Demonstration of qubit operations below a rigorous fault tolerance threshold with gate set tomography

2017 ◽  
Vol 8 (1) ◽  
Author(s):  
Robin Blume-Kohout ◽  
John King Gamble ◽  
Erik Nielsen ◽  
Kenneth Rudinger ◽  
Jonathan Mizrahi ◽  
...  
Keyword(s):  
Quantum Information ◽  
Fault Tolerance ◽  
Error Correction ◽  
Error Rate ◽  
Fault Tolerant ◽  
Fast Algorithms ◽  
Quantum Error Correction ◽  
Qubit Operations ◽  
Quantum Error ◽  
Qubit Operation

Abstract Quantum information processors promise fast algorithms for problems inaccessible to classical computers. But since qubits are noisy and error-prone, they will depend on fault-tolerant quantum error correction (FTQEC) to compute reliably. Quantum error correction can protect against general noise if—and only if—the error in each physical qubit operation is smaller than a certain threshold. The threshold for general errors is quantified by their diamond norm. Until now, qubits have been assessed primarily by randomized benchmarking, which reports a different error rate that is not sensitive to all errors, and cannot be compared directly to diamond norm thresholds. Here we use gate set tomography to completely characterize operations on a trapped-Yb+-ion qubit and demonstrate with greater than 95% confidence that they satisfy a rigorous threshold for FTQEC (diamond norm ≤6.7 × 10−4).

Vehicle Association and Tracking in Image Sequences Using Feature-Based Similarity Comparison

2014 ◽  
Vol 536-537 ◽  
pp. 176-179 ◽  
Author(s):  
Du Hyung Cho ◽  
M. Naushad Ali ◽  
Seok Ju Chun ◽  
Seok Lyong Lee
Keyword(s):  
Image Sequences ◽  
Similarity Comparison ◽  
Current Frame ◽  
The Road ◽  
Multiple Vehicles ◽  
Feature Based ◽  
The Difference ◽  
On The Road ◽  
Difference Operation ◽  
Object Association

Object association and tracking have attracted great attention in the computer vision. In this paper, we present an object association and tracking method for monitoring multiple vehicles on the road based on objects' visual features and the similarity comparison between them. First, we identify vehicles using the difference operation between the current frame in CCTV image sequences and the referential images that are stored in a database, and then extract various features from the vehicles identified. Finally, we associate the objects in the current frame with those in the next frames using similarity comparison, and track multiple objects over a sequence of CCTV image frames. Empirical study using CCTV images shows that our method has achieved the considerable effectiveness in tracking vehicles on the road.

scholarly journals The surface code with a twist

Quantum ◽  
2017 ◽  
Vol 1 ◽  
pp. 2 ◽  
Author(s):  
Theodore J. Yoder ◽  
Isaac H. Kim
Keyword(s):  
Quantum Error Correction ◽  
New Variety ◽  
Near Surface ◽  
Topological Quantum ◽  
Clifford Group ◽  
Logical Qubits ◽  
Surface Code ◽  
Quantum Error ◽  
Qubit Efficiency ◽  
Logical Qubit

The surface code is one of the most successful approaches to topological quantum error-correction. It boasts the smallest known syndrome extraction circuits and correspondingly largest thresholds. Defect-based logical encodings of a new variety called twists have made it possible to implement the full Clifford group without state distillation. Here we investigate a patch-based encoding involving a modified twist. In our modified formulation, the resulting codes, called triangle codes for the shape of their planar layout, have only weight-four checks and relatively simple syndrome extraction circuits that maintain a high, near surface-code-level threshold. They also use 25% fewer physical qubits per logical qubit than the surface code. Moreover, benefiting from the twist, we can implement all Clifford gates by lattice surgery without the need for state distillation. By a surgical transformation to the surface code, we also develop a scheme of doing all Clifford gates on surface code patches in an atypical planar layout, though with less qubit efficiency than the triangle code. Finally, we remark that logical qubits encoded in triangle codes are naturally amenable to logical tomography, and the smallest triangle code can demonstrate high-pseudothreshold fault-tolerance to depolarizing noise using just 13 physical qubits.

scholarly journals Fault-tolerant ancilla preparation and noise threshold lower bounds for the 23-qubit Golay code

2012 ◽  
Vol 12 (11&12) ◽  
pp. 1034-1080
Author(s):  
Adam Paetznick ◽  
Ben W. Reichardt
Keyword(s):  
Error Propagation ◽  
Fault Tolerant ◽  
Error Correcting Code ◽  
Block Size ◽  
Golay Code ◽  
Important Target ◽  
Noise Threshold ◽  
The Cost ◽  
Quantum Error ◽  
Logical Qubit

In fault-tolerant quantum computing schemes, the overhead is often dominated by the cost of preparing codewords reliably. This cost generally increases quadratically with the block size of the underlying quantum error-correcting code. In consequence, large codes that are otherwise very efficient have found limited fault-tolerance applications. Fault-tolerant preparation circuits therefore are an important target for optimization. We study the Golay code, a $23$-qubit quantum error-correcting code that protects the logical qubit to a distance of seven. In simulations, even using a na{\"i}ve ancilla preparation procedure, the Golay code is competitive with other codes both in terms of overhead and the tolerable noise threshold. We provide two simplified circuits for fault-tolerant preparation of Golay code-encoded ancillas. The new circuits minimize error propagation, reducing the overhead by roughly a factor of four compared to standard encoding circuits. By adapting the malignant set counting technique to depolarizing noise, we further prove a threshold above $\threshOverlap$ noise per gate.

scholarly journals In Situ Measurement of Discomfort Curves for Seated Subjects in a Car on the Four-Post Rig

2014 ◽  
Vol 2014 ◽  
pp. 1-14
Author(s):  
T. Ibicek ◽  
A. N. Thite
Keyword(s):  
Predictive Models ◽  
Dynamic Behaviour ◽  
Rate Of Change ◽  
Test Results ◽  
Vehicle Dynamic ◽  
The Road ◽  
Perceived Intensity ◽  
The Difference ◽  
On The Road

The aim of this study is to measure and quantify perceived intensity of discomfort due to vibration in a vehicle in situ considering complete vehicle dynamic behaviour. The shaker table based discomfort curves or the road test results may not accurately and universally indicate the true level of human discomfort in a vehicle. A new experimental method, using a seated human in a car on the four-post rig simulator, is proposed to quantify discomfort. The intensity of perception to vibration decreased with decreasing input and increasing frequency; the rate of change is different from the published literature; the difference is large for angular modes of inputs. Vehicle dynamic response is used to inform and analyse the results. The repeatability of the method and the fact that they are in situ measurements may eventually help reduce reliance on the road tests. Furthermore, discomfort curves obtained, subsequently, can be used in predictive models.

Safety Aspects of Sophisticated In-Vehicle Information Displays and Controls

1986 ◽  
Vol 30 (3) ◽  
pp. 256-260 ◽  
Author(s):  
Helmut T. Zwahlen ◽  
David P. DeBald
Keyword(s):  
Standard Deviation ◽  
Occlusion Time ◽  
The Road ◽  
Safety Aspects ◽  
Eyes Closed ◽  
Starting Point ◽  
Reading Text ◽  
Standard Deviations ◽  
The Difference ◽  
On The Road

Two groups of six young and healthy subjects were used in this study to investigate the lateral path deviations when driving in a straight path with the eyes fixated on the road ahead, when driving while reading information inside of the automobile, and when driving with the eyes closed. Each group of subjects drove a typical large car and a typical small car at a fixed speed of 30 mph. An unused 2000 foot long and 75 foot wide, level, concrete airport runway was used to conduct the experiment. Each subject made three runs under each of the three conditions with the large car and with the small car (18 runs total). The lateral path deviations from the longitudinal centerline of the car to the centerline of the runway were measured every 15 feet for a distance of 705 feet. A device which dripped liquid dye was attached to the center of the rear bumper of the automobiles to indicate their paths. The results of this study show that the average lateral standard deviations for driving with the eyes fixated upon the road ahead were between 5.5″ and 11.3″. The difference in the lateral standard deviations for large and small automobiles was statistically not significant for distances between 100 and 500 feet from the starting point for the three conditions tested. The lateral standard deviation was smaller for reading text within the automobile than for driving with the eyes closed, and was statistically significant after an occlusion distance of 225 feet or an occlusion time of about 5 seconds. Using a constant of 0.041, the fundamental relationship between the lateral standard deviation, the speed, and the occlusion distance developed by Zwahlen and Balasubramanian (1974) fits the data for reading text inside of the automobile while driving fairly well. This constant is approximately one half of that which has been used for driving with the eyes closed (0.076) in this study. Based upon the results of this study, the development and introduction of sophisticated in-vehicle displays and/or touch panels should be halted and their safety aspects with regard to information aquisition, information processing, and driver control actions should be critically evaluated.

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