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A test set for integration of data compression/ error correction encoding techniques. II - Error correction encoding considerations
Error correction coding/decoding techniques integration, discussing convolutional and block coding and Viterbi, Sequential and Threshold decoding algorithms
The battle of clean and dirty qubits in the era of partial error correction
When error correction becomes possible it will be necessary to dedicate a large number of physical qubits to each logical qubit. Error correction allows for deeper circuits to be run, but each additional physical qubit can potentially contribute an exponential increase in computational space, so there is a trade-off between using qubits for error correction or using them as noisy qubits. In this work we look at the effects of using noisy qubits in conjunction with noiseless qubits (an idealized model for error-corrected qubits), which we call the "clean and dirty" setup. We employ analytical models and numerical simulations to characterize this setup. Numerically we show the appearance of Noise-Induced Barren Plateaus (NIBPs), i.e., an exponential concentration of observables caused by noise, in an Ising model Hamiltonian variational ansatz circuit. We observe this even if only a single qubit is noisy and given a deep enough circuit, suggesting that NIBPs cannot be fully overcome simply by error-correcting a subset of the qubits. On the positive side, we find that for every noiseless qubit in the circuit, there is an exponential suppression in concentration of gradient observables, showing the benefit of partial error correction. Finally, our analytical models corroborate these findings by showing that observables concentrate with a scaling in the exponent related to the ratio of dirty-to-total qubits.
The battle of clean and dirty qubits in the era of partial error correction
When error correction becomes possible it will be necessary to dedicate a large number of physical qubits to each logical qubit. Error correction allows for deeper circuits to be run, but each additional physical qubit can potentially contribute an exponential increase in computational space, so there is a trade-off between using qubits for error correction or using them as noisy qubits. In this work, we look at the effects of using noisy qubits in conjunction with noiseless qubits (an idealized model for error-corrected qubits), which we call the “clean and dirty” setup. We employ analytical models and numerical simulations to characterize this setup. Numerically we show the appearance of Noise-Induced Barren Plateaus (NIBPs), i.e., an exponential concentration of observables caused by noise, in an Ising model Hamiltonian variational ansatz circuit. We observe this even if only a single qubit is noisy and given a deep enough circuit, suggesting that NIBPs cannot be fully overcome simply by error-correcting a subset of the qubits. On the positive side, we find that for every noiseless qubit in the circuit, there is an exponential suppression in the concentration of gradient observables, showing the benefit of partial error correction. Finally, our analytical models corroborate these findings by showing that observables concentrate with a scaling in the exponent related to the ratio of dirty-to-total qubits.
Error-Correcting Codes for Code-Division Multiplexed TES Detectors
Transition edge sensors (TESs) have proven to be highly sensitive and versatile X-ray spectrometers. Upcoming missions, including Athena X-IFU, will rely on highly multiplexed focal planes where more than 32 TES pixels are read out using a single SQUID amplifier channel. We have implemented an error correction algorithm for code-division multiplexed TES signals that can compensate for potential failures of individual SQUID readout channels and that is both scalable and easily implemented in hardware. We present this algorithm for error correction and show results of laboratory tests to assess algorithm performance at recovering TES channels after a SQUID failure.
Error-correcting codes for high-speed digital computers
Published document discusses method for correcting errors. According to this method, computer operation becomes fault-tolerant, i.e., its operation is error-free in spite of single hardware element malfunction. Also, method provides for detection and correction of repetitive and spurious processing and transmission errors.
Error correction method and apparatus for electronic timepieces
A method and apparatus for correcting errors in an electronic digital timepiece that includes an oscillator which has a 2 in. frequency output, an n-stage frequency divider for reducing the oscillator output frequency to a time keeping frequency, and means for displaying the count of the time keeping frequency. In first and second embodiments of the invention the timepiece is synchronized with a time standard at the beginning of the period of time T. In the first embodiment of the invention the timepiece user observes E (the difference between the time standard and the timepiece time at the end of the period T) and then operates a switch to correct the time of the timepiece and to obtain a count for E. In the second embodiment of the invention, the user operates a switch at the beginning of T and at the end of T and a count for E is obtained electronically.
Adding Stale-Data Flag to and Error-Correcting Code
A suitable constant "exclusive-Ored" with ECC to flag data without impairing detection of correctable errors.
CaliQEC: In-situ Qubit Calibration for Surface Code Quantum Error Correction
Quantum Error Correction (QEC) is essential for fault-tolerant, large-scale quantum computation. However, error drift in qubits undermines QEC performance during long computations, necessitating frequent calibration. Conventional calibration methods disrupt quantum states, requiring system downtime and rendering in situ calibration impractical. To address this challenge, we propose QECali, a novel framework that enables in situ calibration for surface codes. Our evaluation demonstrates that QECali introduces modest qubit overhead and negligible increases in execution time, offering the first practical solution for in situ calibration in surface code based quantum computation.
Simultaneous error-correction and burst-error detection using binary linear cyclic codes.
Simultaneous error correction and burst error detection, using binary linear cyclic codes
Enhancing quantum memory lifetime with measurement-free local error correction and reinforcement learning
Reliable quantum computation requires systematic identification and correction of errors that occur and accumulate in quantum hardware. To diagnose and correct such errors, standard quantum error-correcting protocols utilize global error information across the system obtained by mid-circuit readout of ancillary qubits. We investigate circuit-level error-correcting protocols that are measurement-free and based on local error information. Such a local error correction (LEC) circuit consists of faulty multi-qubit gates to perform both syndrome extraction and ancilla-controlled error removal. We develop and implement a reinforcement learning framework that takes a fixed set of faulty gates as inputs and outputs an optimized LEC circuit. To evaluate this approach, we quantitatively characterize an extension of logical qubit lifetime by a noisy LEC circuit. For the two-dimensional (2D) classical Ising model and four-dimensional toric code, our optimized LEC circuit performs better at extending a memory lifetime compared with a conventional LEC circuit based on Toom's rule in a subthreshold gate error regime. We further show that such circuits can be used to reduce the rate of mid-circuit readouts to preserve a 2D toric code memory. Lastly, we discuss the application of the LEC protocol on dissipative preparation of quantum states with topological phases.
Ancilla-Free Quantum Error Correction Codes for Quantum Metrology
Quantum error correction has recently emerged as a tool to enhance quantum sensing under Markovian noise. It works by correcting errors in a sensor while letting a signal imprint on the logical state. This approach typically requires a specialized error-correcting code, as most existing codes correct away both the dominant errors and the signal. To date, however, few such specialized codes are known, among which most require noiseless, controllable ancillas. We show here that such ancillas are not needed when the signal Hamiltonian and the error operators commute, a common limiting type of decoherence in quantum sensors. We give a semidefinite program for finding optimal ancilla-free sensing codes in general, as well as closed-form codes for two common sensing scenarios: qubits undergoing dephasing, and a lossy bosonic mode. Lastly, we analyze the sensitivity enhancement offered by the qubit code under arbitrary spatial noise correlations, beyond the ideal limit of orthogonal signal and noise operators.
Error correction in multi-fidelity molecular dynamics simulations using functional uncertainty quantification
We use functional, Fréchet, derivatives to quantify how thermodynamic outputs of a molecular dynamics (MD) simulation depend on the potential used to compute atomic interactions. Our approach quantifies the sensitivity of the quantities of interest with respect to the input functions as opposed to its parameters as is done in typical uncertainty quantification methods. We show that the functional sensitivity of the average potential energy and pressure in isothermal, isochoric MD simulations using Lennard–Jones two-body interactions can be used to accurately predict those properties for other interatomic potentials (with different functional forms) without re-running the simulations. This is demonstrated under three different thermodynamic conditions, namely a crystal at room temperature, a liquid at ambient pressure, and a high pressure liquid. The method provides accurate predictions as long as the change in potential can be reasonably described to first order and does not significantly affect the region in phase space explored by the simulation. The functional uncertainty quantification approach can be used to estimate the uncertainties associated with constitutive models used in the simulation and to correct predictions if a more accurate representation becomes available.
Distributed Quantum Error Correction for Chip-Level Catastrophic Errors
Quantum error correction holds the key to scaling up quantum computers. Cosmic ray events severely impact the operation of a quantum computer by causing chip-level catastrophic errors, essentially erasing the information encoded in a chip. Here, in this work, we present a distributed error correction scheme to combat the devastating effect of such events by introducing an additional layer of quantum erasure error correcting code across separate chips. We show that our scheme is fault tolerant against chip-level catastrophic errors and discuss its experimental implementation using superconducting qubits with microwave links. Our analysis shows that in state-of-the-art experiments, it is possible to suppress the rate of these errors from 1 per 10 s to less than 1 per month.
Universal Optimization and Tighter Fidelity Bounds for Approximate Quantum Error Correction
Approximate quantum error correction (AQEC) not only dictates the performance of discrete- and continuous-variable quantum error correction codes but also serves as a unifying framework across various physical disciplines. Identifying the optimal recovery channel to maximize the entanglement fidelity via standard semidefinite programming is computationally bottlenecked by the exponentially growing number of Kraus operators with system size, rendering large-scale optimization prohibitive. While analytical near-optimal maps exist, they typically work only when the Knill-Laflamme conditions are nearly satisfied. In this Letter, we establish an efficient framework by leveraging the duality between recovery and environment decoupling. This framework yields a tighter analytical lower bound on entanglement fidelity than the conventional limit set by the transpose channel. Furthermore, by exploiting the decayed weights of noise Kraus operators, we introduce a framework based on principal component analysis to reduce the dimension. In thermal loss channels where the weights decay exponentially, our approach achieves a 33-fold computational speedup while maintaining rigorous accuracy. Our approach enables high-precision optimization for AQEC codes that were previously intractable due to the curse of dimensionality.
New double-byte error-correcting codes for memory systems
Error-correcting or error-detecting codes have been used in the computer industry to increase reliability, reduce service costs, and maintain data integrity. The single-byte error-correcting and double-byte error-detecting (SbEC-DbED) codes have been successfully used in computer memory subsystems. There are many methods to construct double-byte error-correcting (DBEC) codes. In the present paper we construct a class of double-byte error-correcting codes, which are more efficient than those known to be optimum, and a decoding procedure for our codes is also considered.
Approximate symmetries and quantum error correction
Abstract Quantum error correction (QEC) is a key concept in quantum computation as well as many areas of physics. There are fundamental tensions between continuous symmetries and QEC. One vital situation is unfolded by the Eastin–Knill theorem, which forbids the existence of QEC codes that admit transversal continuous symmetry actions (transformations). Here, we systematically study the competition between continuous symmetries and QEC in a quantitative manner. We first define a series of meaningful measures of approximate symmetries motivated from different perspectives, and then establish a series of trade-off bounds between them and QEC accuracy utilizing multiple different methods. Remarkably, the results allow us to derive general quantitative limitations of transversally implementable logical gates, an important topic in fault-tolerant quantum computation. As concrete examples, we showcase two explicit types of quantum codes, obtained from quantum Reed–Muller codes and thermodynamic codes, respectively, that nearly saturate our bounds. Finally, we discuss several potential applications of our results in physics.
Exact determination of probability of bit error for perfect single error correcting codes
Bit error probability after decoding for binary perfect single error correcting codes