Related papers: Error mitigation for logical circuits using decode…
The realization of quantum error correction protocols whose logical error rates are suppressed far below physical error rates relies on an intricate combination: the error-correcting code's efficiency, the syndrome extraction circuit's…
Quantum computers now show the promise of surpassing any possible classical machine. However, errors limit this ability and current machines do not have the ability to implement error correcting codes due to the limited number of qubits and…
Noise remains one of the most significant challenges in the development of reliable and scalable quantum processors. While quantum error correction and mitigation techniques offer potential solutions, they are often limited by the…
In this paper we consider regular low-density parity-check codes over a binary-symmetric channel in the decoding regime. We prove that up to a certain noise threshold the bit-error probability of the bit-sampling decoder converges in mean…
When the environmental disturbace to a quantum system has a wavelength much larger than the system size, all qubits localized within a small area are under action of the same error operators. Noiseless subsystem and decoherence free…
Logical qubits can be protected from decoherence by performing QEC cycles repeatedly. Algorithms for fault-tolerant QEC must be compiled to the specific hardware platform under consideration in order to practically realize a quantum memory…
Concatenating quantum error correction codes scales error correction capability by driving logical error rates down double-exponentially across levels. However, the noise structure shifts under concatenation, making it hard to choose an…
Due to the low error tolerance of a qubit, detecting and correcting errors on it is essential for fault-tolerant quantum computing. Surface code (SC) associated with its decoding algorithm is one of the most promising quantum error…
Accurate decoding of quantum error-correcting codes is a crucial ingredient in protecting quantum information from decoherence. It requires characterizing the error channels corrupting the logical quantum state and providing this…
Practical large-scale quantum computation requires both efficient error correction and robust implementation of logical operations. Three-dimensional (3D) color codes are a promising candidate for fault-tolerant quantum computation due to…
We discuss the effects of imperfect photon detectors suffering from loss and noise on the reliability of linear optical quantum computers. We show that for a given detector efficiency, there is a maximum achievable success probability, and…
Quantum error correction methods use processing power to combat noise. The noise level which can be tolerated in a fault-tolerant method is therefore a function of the computational resources available, especially the size of computer and…
In Linear Programming (LP) decoding of a Low-Density-Parity-Check (LDPC) code one minimizes a linear functional, with coefficients related to log-likelihood ratios, over a relaxation of the polytope spanned by the codewords \cite{03FWK}. In…
Quantum Error Correction (QEC) decoding faces a fundamental accuracy-efficiency tradeoff. Classical methods like Minimum Weight Perfect Matching (MWPM) exhibit variable performance across noise models and suffer from polynomial complexity,…
Neural decoders for quantum error correction (QEC) rely on neural networks to classify syndromes extracted from error correction codes and find appropriate recovery operators to protect logical information against errors. Its ability to…
Noise is one of the central obstacles to building useful quantum computers, and quantum error correction (QEC) provides the framework for protecting quantum information against it. Unlike classical error correction, QEC must preserve…
Quantum Error Correction (QEC) protects qubits against bit- and phase-flip errors in the |0> or |1> subspace, but physical qubits can also leak into higher energy levels (e.g., |2>). Leakage is especially harmful, as it corrupts all…
Quantum Error Correction (QEC) is required in quantum computers to mitigate the effect of errors on physical qubits. When adopting a QEC scheme based on surface codes, error decoding is the most computationally expensive task in the…
Pre-fault tolerant quantum computers have already demonstrated the ability to estimate observable values accurately, at a scale beyond brute-force classical computation. This has been enabled by error mitigation techniques that often rely…
In most error correction coding (ECC) frameworks, the typical error metric is the bit error rate (BER) which measures the number of bit errors. For this metric, the positions of the bits are not relevant to the decoding, and in many noise…