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I. This paper is devoted to the problem of error detection with quantum codes. In the first part we examine possible problem settings for quantum error detection. Our goal is to derive a functional that describes the probability of…
Quantum Error Mitigation (QEM) presents a promising near-term approach to reduce error when estimating expectation values in quantum computing. Here, we introduce QEM techniques tailored for quantum annealing, using Zero-Noise Extrapolation…
The analysis of noisy quantum states prepared on current quantum computers is getting beyond the capabilities of classical computing. Quantum neural networks based on parametrized quantum circuits, measurements and feed-forward can process…
Fault-tolerant quantum error correction provides a strategy to protect information processed by a quantum computer against noise which would otherwise corrupt the data. A fault-tolerant universal quantum computer must implement a universal…
Quantum error correcting code can diagnose potential errors and correct them based on measured outcomes by leveraging syndrome measurement. However, mid-circuit measurement has been technically challenging for early fault-tolerant quantum…
Mapping quantum error correcting codes to classical disordered statistical mechanics models and studying the phase diagram of the latter has proven a powerful tool to study the fundamental error robustness and associated critical error…
Quantum resources enable one to achieve quantum-enhanced estimation sensitivity beyond its classical counterpart. Many studies mainly focus on reducing statistical error, under the assumption that one can always set an unbiased estimator.…
The robustness of quantum memory against physical noises is measured by two methods: the exact and approximate quantum error correction (QEC) conditions for error recoverability, and the decoder-dependent error threshold which assesses if…
When neural networks (NeuralNets) are implemented in hardware, their weights need to be stored in memory devices. As noise accumulates in the stored weights, the NeuralNet's performance will degrade. This paper studies how to use error…
Quantum error correction (QEC) codes can tolerate hardware errors by encoding fault-tolerant logical qubits using redundant physical qubits and detecting errors using parity checks. Leakage errors occur in quantum systems when a qubit…
Quantum error correction (QEC) is critical for scalable fault-tolerant quantum computing. Topological codes, such as the toric code, offer hardware-efficient architectures but their Tanner graphs contain many girth-4 cycles that degrade the…
The problem of channel coding with the erasure option is revisited for discrete memoryless channels. The interplay between the code rate, the undetected and total error probabilities is characterized. Using the information spectrum method,…
Quantum error correction is believed to be a necessity for large-scale fault-tolerant quantum computation. In the past two decades, various constructions of quantum error-correcting codes (QECCs) have been developed, leading to many good…
The recently introduced Quantum Lego framework provides a powerful method for generating complex quantum error correcting codes (QECCs) out of simple ones. We gamify this process and unlock a new avenue for code design and discovery using…
Quantum error correction (QEC) is essential for quantum computers to perform useful algorithms, but large-scale fault-tolerant computation remains out of reach due to demanding requirements on operation fidelity and the number of…
Recent thousand-qubit processors represent a significant hardware advancement, but current limitations prevent effective quantum error correction (QEC), necessitating reliance on quantum error mitigation (QEM) to enhance result fidelity…
With fault-tolerant quantum computing (FTQC) on the horizon, it is critical to understand sources of logical error in plausible hardware implementations of quantum error-correcting codes (QECC). In this work, we consider logical error rates…
We consider the surface code under errors featuring both coherent and incoherent components and study the coherence of the corresponding logical noise channel and how this impacts information-theoretic measures of code performance, namely…
Quantum circuits with local particle number conservation (LPNC) restrict the quantum computation to a subspace of the Hilbert space of the qubit register. In a noiseless or fault-tolerant quantum computation, such quantities are preserved.…
The development and use of large-scale quantum computers relies on integrating quantum error-correcting (QEC) schemes into the quantum computing pipeline. A fundamental part of the QEC protocol is the decoding of the syndrome to identify a…