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We describe a quantum error correction scheme that can increase the effective absorption length of the communication channel. This device can play the role of a quantum transponder when placed in series, or a cyclic quantum memory when inserted in an optical loop.
We study the quantum error correction properties of the black hole interior in a toy model for an evaporating black hole: Jackiw-Teitelboim gravity entangled with a non-gravitational bath. After the Page time, the black hole interior degrees of freedom in this system are encoded in the bath Hilbert space. We use the gravitational path integral to show that the interior density matrix is correctable against the action of quantum operations on the bath which (i) do not have prior access to details of the black hole microstates, and (ii) do not have a large, negative coherent information with respect to the maximally mixed state on the bath, with the lower bound controlled by the black hole entropy and code subspace dimension. Thus, the encoding of the black hole interior in the radiation is robust against generic, low-rank quantum operations. For erasure errors, gravity comes within an O (1) distance of saturating the Singleton bound on the tolerance of error correcting codes. For typical errors in the bath to corrupt the interior, they must have a rank that is a large multiple of the bath Hilbert space dimension, with the precise coefficient set by the black hole entropy and code subspace dimension.
The cryptographic robustness of quantum key distribution (QKD) with phase–time coding against a photon number splitting (PNS) attack is analyzed. The line length up to which a secret key distribution is guaranteed is determined both by the protocol itself and by the efficiency of error correction in raw keys. The effect of different parameters of avalanche single-photon detectors on the length of the secret key distribution line is investigated. To correct errors, various versions of low-density parity-check (LDPC) codes are considered whose efficiency today is the closest to the Shannon theoretical limit.
Frame synchronization and error correction by pulse-code modulated systems
Quantum computers are growing in size, and design decisions are being made now that attempt to squeeze more computation out of these machines. In this spirit, we design a method to boost the computational power of near-term quantum computers by adapting protocols used in quantum error correction to implement "Approximate Quantum Error Correction (AQEC)." By approximating fully-fledged error correction mechanisms, we can increase the compute volume (qubits × gates, or "Simple Quantum Volume (SQV)") of near-term machines. The crux of our design is a fast hardware decoder that can approximately decode detected error syndromes rapidly. Specifically, we demonstrate a proof-of-concept that approximate error decoding can be accomplished online in near-term quantum systems by designing and implementing a novel algorithm in Single-Flux Quantum (SFQ) superconducting logic technology. This avoids a critical decoding backlog, hidden in all offline decoding schemes, that leads to idle time exponential in the number of T gates in a program. Our design utilizes one SFQ processing module per physical qubit. Employing state-of-the-art SFQ synthesis tools, we show that the circuit area, power, and latency are within the constraints of contemporary quantum system designs. Under pure dephasing error models, the proposed accelerator and AQEC solution is able to expand SQV by factors between 3,402 and 11,163 on expected near-term machines. The decoder achieves a 5% accuracy-threshold and pseudo-thresholds of ~ 5%,4.75%,4.5%, and 3.5% physical error-rates for code distances 3,5,7, and 9. Decoding solutions are achieved in a maximum of ~20 nanoseconds on the largest code distances studied. By avoiding the exponential idle time in offline decoders, we achieve a 10x reduction in required code distances to achieve the same logical performance as alternative designs.
Error correction for Mariner space probe high speed data transmission
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.
Kalman filtering applied to error correction of inertial navigators
Topologically ordered phases are stable to local perturbations, and topological quantum error-correcting codes enjoy thresholds to local errors. We connect the two notions of stability by constructing classical statistical mechanics models for decoding general Calderbank-Shor-Steane codes and classical linear codes. Our construction encodes correction success probabilities under uncorrelated bit-flip and phase-flip errors, and simultaneously describes a generalized ℤ 2 lattice-gauge theory with quenched disorder. We observe that the clean limit of the latter is precisely the discretized imaginary-time path integral of the corresponding quantum code Hamiltonian when the errors are turned into a perturbative 𝑋 or 𝑍 magnetic field. Motivated by error-correction considerations, we define general order parameters for all such generalized ℤ 2 lattice-gauge theories, and show that they are generally lower bounded by success probabilities of error correction. For CSS codes satisfying the low-density parity-check condition and with a sufficiently large code distance, we prove the existence of a low-temperature ordered phase of the corresponding lattice-gauge theories, particularly for those lacking Euclidean spatial locality and/or when there is a nonzero code rate. We further argue that these results provide evidence for stable phases in the corresponding perturbed quantum Hamiltonians, obtained in the limit of continuous imaginary time. To do so, we distinguish space- and timelike defects in the lattice-gauge theory. A high free-energy cost of spacelike defects corresponds to a successful “memory experiment” and suppresses the energy splitting among the ground states, while a high free-energy cost of timelike defects corresponds to a successful “stability experiment” and points to a nonzero gap to local excitations.
The eigenstate thermalization hypothesis (ETH) is a powerful conjecture for understanding how statistical mechanics emerges in a large class of many-body quantum systems. It has also been interpreted in a CFT context, and, in particular, holographic CFTs are expected to satisfy ETH. Recently, it was observed that the ETH condition corresponds to a necessary and sufficient condition for an approximate quantum error correcting code (AQECC), implying the presence of AQECCs in systems satisfying ETH. In this paper, we explore the properties of ETH as an error correcting code and show that there exists an explicit universal recovery channel for the code. Based on the analysis, we discuss a generalization that all chaotic theories contain error correcting codes. We then specialize to AdS/CFT to demonstrate the possibility of total bulk reconstruction in black holes with a well-defined macroscopic geometry. When combined with the existing AdS/CFT error correction story, this shows that black holes are enormously robust against erasure errors.
In this article, we study a model for error-correcting codes that comes from spin glass theory and leads to both new codes and a new decoding technique. Using the theory of spin glasses, it has been proven that a simple construction yields a family of binary codes whose performance asymptotically approaches the Shannon bound for the Gaussian channel. The limit is approached as the number of information bits per codeword approaches infinity while the rate of the code approaches zero. Thus, the codes rapidly become impractical. We present simulation results that show the performance of a few manageable examples of these codes. In the correspondence that exists between spin glasses and error-correcting codes, the concept of a thermal average leads to a method of decoding that differs from the standard method of finding the most likely information sequence for a given received codeword. Whereas the standard method corresponds to calculating the thermal average at temperature zero, calculating the thermal average at a certain optimum temperature results instead in the sequence of most likely information bits. Since linear block codes and convolutional codes can be viewed as examples of spin glasses, this new decoding method can be used to decode these codes in a way that minimizes the bit error rate instead of the codeword error rate. We present simulation results that show a small improvement in bit error rate by using the thermal average technique.
Processor register protection management is disclosed. In embodiments, a method of processor register protection management can include determining a sensitive logical register for executable code generated by a compiler, generating an error-correction table identifying the sensitive logical register, and storing the error-correction table in a memory accessible by a processor. The processor can be configured to generate a duplicate register of the sensitive logical register identified by the error-correction table.
The decoding and error-correction of data transmitted over a noisy channel is in principle equivalent to the operation of a neural network performing as a content-addressable memory. For a successful application, however, the neural network has to be capable of storing arbitrary words, and it has to be guaranteed that the stored words represent the only stable attractors of the memory. This paper presents a novel high-order neural network architecture that has these characteristics. The analog nature of the network can be used to perform soft-decision decoding with any block code. The performance in terms of postdecoding bit error rate versus SNR is demonstrated for two exemplary block codes. The comparison with a conventional decoding algorithm for a (15,5) cyclic redundancy code shows, for example, that the bit error rate at 7dB SNR can be decreased by two orders of magnitude.
The ambition of harnessing the quantum for computation is at odds with the fundamental phenomenon of decoherence. The purpose of quantum error correction (QEC) is to counteract the natural tendency of a complex system to decohere. This cooperative process, which requires participation of multiple quantum and classical components, creates a special type of dissipation that removes the entropy caused by the errors faster than the rate at which these errors corrupt the stored quantum information. Previous experimental attempts to engineer such a process faced an excessive generation of errors that overwhelmed the error-correcting capability of the process itself. Whether it is practically possible to utilize QEC for extending quantum coherence thus remains an open question. We answer it by demonstrating a fully stabilized and error-corrected logical qubit whose quantum coherence is significantly longer than that of all the imperfect quantum components involved in the QEC process, beating the best of them with a coherence gain of G=2.27±0.07. Here we achieve this performance by combining innovations in several domains including the fabrication of superconducting quantum circuits and model-free reinforcement learning.
Quantum Error Correction (QEC) codes are essential for achieving fault-tolerant quantum computing (FTQC). However, their implementation faces significant challenges due to disparity between required dense qubit connectivity and sparse hardware architectures. Current approaches often either underutilize QEC circuit features or focus on manual designs tailored to specific codes and architectures, limiting their capability and generality. In response, we introduce QECC-Synth, an automated compiler for QEC code implementation that addresses these challenges. We leverage the ancilla bridge technique tailored to the requirements of QEC circuits and introduces a systematic classification of its design space flexibilities. We then formalize this problem using the MaxSAT framework to optimize these flexibilities. Evaluation shows that our method significantly outperforms existing methods while demonstrating broader applicability across diverse QEC codes and hardware architectures.
Data compression and error correcting codes applied to digital transmission of real time, standard format TV, along with voice and other data from Apollo spacecraft
We construct a subsystem code in three dimensions that exhibits single-shot error correction in a user-friendly and transparent way. As this code is a subsystem version of coupled toric codes, we call it the intertwined toric code (ITC). Although previous codes share the property of single-shot error correction, the ITC is distinguished by its physically motivated origin, geometrically straightforward logical operators and errors, and a simple phase diagram. The code arises from three-dimensional (3D) stabilizer toric codes in a way that emphasizes the physical origin of the single-shot property. In particular, starting with two copies of the 3D toric code, we add check operators that provide for the confinement of pointlike excitations without condensing the loop excitations. Geometrically, the bare and dressed logical operators in the ITC derive from logical operators in the underlying toric codes, creating a clear relationship between errors and measurement outcomes. The syndromes of the ITC resemble the syndromes of the single-shot code by Kubica and Vasmer, allowing us to use their decoding schemes. We also extract the phase diagram corresponding to ITC and show that it contains the phases found in the Kubica-Vasmer code. Lastly, we suggest various connections to Walker-Wang models and measurement-based quantum computation.
Reed Solomon codes are powerful error correcting codes that include some of the best random and burst correcting codes currently known. It is well known that an (n,k) Reed Solomon code can correct up to (n - k)/2 errors. Many applications utilizing Reed Solomon codes require corrections of errors consisting primarily of bursts. In this paper, it is shown that the burst correcting ability of Reed Solomon codes can be increased beyond (n - k)/2 with an acceptable probability of miscorrect.