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At least 235 records · Page 13

Techniques for correcting transmission errors in video adaptive delta modulation channels

We investigated the effects of channel errors on an adaptive delta modulator used to encode video signals. The investigation revealed that channel errors caused a permanent shift in the dc level of the delta modulator's estimate. Errors in the step size, on the other hand, were transitory and had no noticeable effect on the received pictures. We then presented three error correction schemes to minimize the visibility of the channel errors in the received picture. The first scheme required the transmitter to periodically send the correct dc level of the estimate to the receiver. The second method employed a leaky integrator, and the third method used line-to-line interpolation

Scheinberg, N.↗

Low-overhead transversal fault tolerance for universal quantum computation

Fast, reliable logical operations are essential for realizing useful quantum computers. By redundantly encoding logical qubits into many physical qubits and using syndrome measurements to detect and correct errors, we can achieve low logical error rates. However, for many practical quantum error correction codes such as the surface code, owing to syndrome measurement errors, standard constructions require multiple extraction rounds—of the order of the code distance d—for fault-tolerant computation, particularly considering fault-tolerant state preparation. Here we show that logical operations can be performed fault-tolerantly with only a constant number of extraction rounds for a broad class of quantum error correction codes, including the surface code with magic state inputs and feedforward, to achieve ‘transversal algorithmic fault tolerance’. Through the combination of transversal operations7 and new strategies for correlated decoding, despite only having access to partial syndrome information, we prove that the deviation from the ideal logical measurement distribution can be made exponentially small in the distance, even if the instantaneous quantum state cannot be made close to a logical codeword because of measurement errors. We supplement this proof with circuit-level simulations in a range of relevant settings, demonstrating the fault tolerance and competitive performance of our approach. Furthermore, our work sheds new light on the theory of quantum fault tolerance and has the potential to reduce the space–time cost of practical fault-tolerant quantum computation by over an order of magnitude.

Zhou, Hengyun [QuEra Computing, Boston, MA (United↗

Multispin Clifford codes for angular momentum errors in spin systems

The physical symmetries of a system play a central role in quantum error correction. Here, in this work we encode a qubit in a collection of systems with angular momentum symmetry (spins), extending the tools developed by Gross for single large spins. By considering large spins present in atomic systems and focusing on their collective symmetric subspace, we develop codes with octahedral symmetry capable of correcting errors up to second order in angular momentum operators. These errors include the most physically relevant noise sources such as microwave control errors and optical pumping. We additionally explore qubit codes that exhibit distance scaling commensurate with the surface code while permitting transversal single-qubit Clifford operations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

30 years of adaptive neural networks - Perceptron, Madaline, and backpropagation

Fundamental developments in feedforward artificial neural networks from the past thirty years are reviewed. The history, origination, operating characteristics, and basic theory of several supervised neural-network training algorithms (including the perceptron rule, the least-mean-square algorithm, three Madaline rules, and the backpropagation technique) are described. The concept underlying these iterative adaptation algorithms is the minimal disturbance principle, which suggests that during training it is advisable to inject new information into a network in a manner that disturbs stored information to the smallest extent possible. The two principal kinds of online rules that have developed for altering the weights of a network are examined for both single-threshold elements and multielement networks. They are error-correction rules, which alter the weights of a network to correct error in the output response to the present input pattern, and gradient rules, which alter the weights of a network during each pattern presentation by gradient descent with the objective of reducing mean-square error (averaged over all training patterns).

Widrow, Bernard↗

System and method for transferring data on a data link

A system and method are provided for transferring a packet across a data link. The packet may include a stream of data symbols which is delimited by one or more framing symbols. Corruptions of the framing symbol which result in valid data symbols may be mapped to invalid symbols. If it is desired to transfer one of the valid data symbols that has been mapped to an invalid symbol, the data symbol may be replaced with an unused symbol. At the receiving end, these unused symbols are replaced with the corresponding valid data symbols. The data stream of the packet may be encoded with forward error correction information to detect and correct errors in the data stream.

Cole, Robert M.↗

Highly Reliable, High-Speed, Unidirectional Serial Data Links

Highly reliable, high-speed, unidirectional serial data-communication subsystems have been proposed to be installed in an upgrade of the computing systems aboard the space shuttles. The basic design concept of these serial data links is also adaptable to terrestrial use in applications in which there are requirements for highly reliable serial data communications. The hardware and software aspects of the architecture of the data links are dictated largely by a requirement, in the original space-shuttle application, for one computer to monitor the memory transactions and memory contents of other computers in real time with high reliability and without reliance on requests for retransmission. To minimize weight while affording a capability to transfer data at a required rate of 2.56 x 10(exp 8) bits per second, it was decided that the links would be serial ones of the fiber-channel type. [Fiber channel denotes a type of serial computer bus that is used to connect a computer (usually a supercomputer) with a high-speed data storage device. Depending on the specific application, the physical connection between the transmitter and receiver could be made via an optical fiber or a twisted pair of wires.] Heretofore, fiber-channel links have ordinarily been bidirectional and have operated under protocols that provide for receiving stations to detect errors and request retransmission when necessary. In the present case, the time taken by processing to request retransmission would conflict with the requirement for real-time transfer of data. To ensure reliability without retransmission, a link according to the proposal would utilize a modified version of the normal fiberchannel character set in conjunction with forward error correction by means of a Reed-Solomon code (see figure). The Reed-Solomon encoding and decoding and the translations between the normal and modified character sets would be effected by logic circuitry external to the fiber-channel transmitter and receiver, which would be commercial off-the-shelf units. The receiving end of the link could detect and correct errors at a rate as high as 4 million times per second, if necessary. The receiver detects uncorrectable double-byte errors. It has been estimated that uncorrectable-error rate would amount to one failure in about 10(exp 19) characters.

Cole, Robert M.↗

Majorana subsystem qubit codes that also correct odd-weight errors

Abstract A potential platform for topological quantum computation is the Majorana-based tetron architecture. Its building blocks are superconducting islands called tetrons, which host four Majorana zero modes. Existing error correcting codes can correct even-weight errors on tetrons. In a previous proposal by us, we had shown that incorporating tetrons in the stabilizer group allows us to correct a combination of odd-weight errors and even-weight errors on tetrons. In this work, we show that inclusion of tetrons in the gauge group lets us create subsystem codes from conventional Pauli stabilizer codes, which can correct both kinds of errors. Compared to the previous approach, the current approach lets us construct codes with fewer stabilizer generators. This leads to shorter fault-tolerant sequence length, and improves the fault-tolerant pseudothreshold by as much as 84%.

Physics↗

Mid-circuit correction of correlated phase errors using an array of spectator qubits

Scaling up invariably error-prone quantum processors is a formidable challenge. Although quantum error correction ultimately promises fault-tolerant operation, the required qubit overhead and error thresholds are daunting. In a complementary proposal, colocated, auxiliary “spectator” qubits act as in situ probes of noise and enable real-time, coherent corrections of data qubit errors. We used an array of cesium spectator qubits to correct correlated phase errors on an array of rubidium data qubits. By combining in-sequence readout, data processing, and feedforward operations, these correlated errors were suppressed within the execution of the quantum circuit. The protocol is broadly applicable to quantum information platforms and establishes key tools for scaling neutral-atom quantum processors: mid-circuit readout of atom arrays, real-time processing and feedforward, and coherent mid-circuit reloading of atomic qubits.

Science & Technology - Other Topics↗

Quantum annealing correction for random Ising problems

Here, we demonstrate that the performance of a quantum annealer on hard random Ising optimization problems can be substantially improved using quantum annealing correction (QAC). Our error correction strategy is tailored to the D-Wave Two device. We find that QAC provides a statistically significant enhancement in the performance of the device over a classical repetition code, improving as a function of problem size as well as hardness. Moreover, QAC provides a mechanism for overcoming the precision limit of the device, in addition to correcting calibration errors. Performance is robust even to missing qubits. We present evidence for a constructive role played by quantum effects in our experiments by contrasting the experimental results with the predictions of a classical model of the device. Our work demonstrates the importance of error correction in appropriately determining the performance of quantum annealers.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Encoding an Oscillator into Many Oscillators

An outstanding challenge for quantum information processing using bosonic systems is Gaussian errors such as excitation loss and added thermal noise errors. Thus, bosonic quantum error correction is essential. Most bosonic quantum error correction schemes encode a finite-dimensional logical qubit or qudit into noisy bosonic oscillator modes. In this case, however, the infinite-dimensional bosonic nature of the physical system is lost at the error-corrected logical level. On the other hand, there are several proposals for encoding an oscillator mode into many noisy oscillator modes. However, these oscillator-into-oscillators encoding schemes are in the class of Gaussian quantum error correction. Therefore, these codes cannot correct practically relevant Gaussian errors due to the established no-go theorems that state that Gaussian errors cannot be corrected by using only Gaussian resources. Here, we circumvent these no-go results and show that it is possible to correct Gaussian errors by using Gottesman-Kitaev-Preskill (GKP) states as non-Gaussian resources. In particular, we propose a non-Gaussian oscillator-into-oscillators code, namely the GKP two-mode squeezing code, and demonstrate that it can quadratically suppress additive Gaussian noise errors in both the position and momentum quadratures except for a small sublogarithmic correction. Furthermore, we demonstrate that our GKP two-mode squeezing code is near optimal in the weak noise limit by proving via quantum information theoretic tools that quadratic noise suppression is optimal when we use two physical oscillator modes. Lastly, in this work we show that our non-Gaussian oscillator encoding scheme can also be used to correct excitation loss and thermal noise errors, which are dominant error sources in many realistic bosonic systems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

The importance of matched poloidal spectra to error field correction in DIII-D

Optimal error field correction (EFC) is thought to be achieved when coupling to the least-stable “dominant” mode of the plasma is nulled at each toroidal mode number (n). The limit of this picture is tested in the DIII-D tokamak by applying superpositions of in- and ex-vessel coil set n = 1 fields calculated to be fully orthogonal to the n = 1 dominant mode. In co-rotating H-mode and low-density Ohmic scenarios, the plasma is found to be, respectively, 7× and 20× less sensitive to the orthogonal field as compared to the in-vessel coil set field. For the scenarios investigated, any geometry of EFC coil can thus recover a strong majority of the detrimental effect introduced by the n = 1 error field. Despite low sensitivity to the orthogonal field, its optimization in H-mode is shown to be consistent with minimizing the neoclassical toroidal viscosity torque and not the higher-order n = 1 mode coupling.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Radiometric correction of scatterometric wind measurements

Use of a spaceborne scatterometer to determine the ocean-surface wind vector requires accurate measurement of radar backscatter from ocean. Such measurements are hindered by the effect of attenuation in the precipitating regions over sea. The attenuation can be estimated reasonably well with the knowledge of brightness temperatures observed by a microwave radiometer. The NASA SeaWinds scatterometer is to be flown on the Japanese ADEOS2. The AMSR multi-frequency radiometer on ADEOS2 will be used to correct errors due to attenuation in the SeaWinds scatterometer measurements. Here we investigate the errors in the attenuation corrections. Errors would be quite small if the radiometer and scatterometer footprints were identical and filled with uniform rain. However, the footprints are not identical, and because of their size one cannot expect uniform rain across each cell. Simulations were performed with the SeaWinds scatterometer (13.4 GHz) and AMSR (18.7 GHz) footprints with gradients of attenuation. The study shows that the resulting wind speed errors after correction (using the radiometer) are small for most cases. However, variations in the degree of overlap between the radiometer and scatterometer footprints affect the accuracy of the wind speed measurements.

Source record↗

A NASA Perspective on Quantum Computing, with Ties to Operator Algebras

The talk will survey work done by the NASA Quantum Artificial Intelligence Laboratory (QuAIL), particularly algorithms and protocols in which operator algebras may play a role. The talk will focus on recent work advancing quantum error correction and error mitigation, and will touch on other topics related to quantum algorithms and funda- mental quantum physics.

Quantum Computing↗

Encoding Scheme Reduces Hardware Requirements

Shift register time-shared in proposed error-correcting code for tape-storage systems. Error-correcting code logic for blocks of 256-bit data words implemented by 14-stage-time-shared shift register, two 4,096bit RAM's and logic gates. Encoding and decoding logic implement generator polynomial that defines error-correcting code, and error correction based on algorithm also implemented by logic.

Sasnowitz, H.↗

The spectral basis of optimal error field correction on DIII-D

Here, experimental optimum error field correction (EFC) currents found in a wide breadth of dedicated experiments on DIII-D are shown to be consistent with the currents required to null the poloidal harmonics of the vacuum field which drive the kink mode near the plasma edge. This allows the identification of empirical metrics which predict optimal EFC currents with accuracy comparable to that of first- principles modeling which includes the ideal plasma response. While further metric refinements are desirable, this work suggests optimal EFC currents can be effectively fed-forward based purely on knowledge of the vacuum error field and basic equilibrium properties which are routinely calculated in real-time.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

A novel scheme for error field correction in permanent magnet stellarators

Stellarators offer a promising path towards fusion reactors, but their design and construction are complicated by stringent tolerance requirements on highly complex 3D coils. A potential way to simplify the engineering requirements for stellarators is to use simple planar toroidal field coils along with permanent magnet arrays to generate shaping fields. In order to ensure sufficient field accuracy while minimizing engineering complexity and system cost, new techniques are required to correct the field produced by the permanent magnet arrays to within requirements set by plasma physics. This work describes a novel correction method developed for this purpose. This analysis is applied to the design of a quasi-axisymmetric stellarator that employs a combination of permanent magnets and planar toroidal field coils to generate its magnetic field. Analysis techniques and initial results using the method for error correction on a proposed permanent magnet stellarator are shown, and it is demonstrated that the method successfully meets the design requirements of the project.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

On the Error Covariance Correction Step of an ESKF Attitude Update

The attitude states of an error-state Kalman filter (ESKF) behave differently than most other states in the system due to their multiplicative (rather than additive) nature. One way in which they differ is an error covariance correction step after an ESKF error reset, which is not required for, for example, position and velocity states. This covariance correction step is not intuitive, and it has only been recently derived for coordinate transform matrices. The author of this memo, however, found the provided derivation in [1] confusing due to a lack of clarity surrounding the invoked reference frames, and clarity is required as there are at least 4 different ways to parameterize small-angle attitude errors in an ESKF. Furthermore, while reproducing the work, the author of this memo found a more straightforward derivation that provides additional insight into the correction step. This memo offers a derivation of the attitude error covariance correction step of an ESKF, which pays specific attention to the coordinate reference frames.

97 MATHEMATICS AND COMPUTING↗