Related papers: Checking the error correction strength of arbitrar…
Certain quantum codes allow logic operations to be performed on the encoded data, such that a multitude of errors introduced by faulty gates can be corrected. An important class of such operations are {\em transversal}, acting bitwise…
A fundamental question in the theory of quantum computation is to understand the ultimate space-time resource costs for performing a universal set of logical quantum gates to arbitrary precision. Here we demonstrate that non-Abelian anyons…
Due to the fragility of quantum mechanical effects, real quantum computers are plagued by frequent noise effects that cause errors during computations. Quantum error-correcting codes address this problem by providing means to identify and…
The potential of quantum computers to outperform classical ones in practically useful tasks remains challenging in the near term due to scaling limitations and high error rates of current quantum hardware. While quantum error correction…
Realizing large-scale quantum advantage is expected to require quantum error correction (QEC), making the compilation and optimization of logical operations a critical area of research. Logical computation imposes distinct constraints and…
Quantum computers are poised to radically outperform their classical counterparts by manipulating coherent quantum systems. A realistic quantum computer will experience errors due to the environment and imperfect control. When these errors…
High-fidelity logical \emph{T}-gate realization constitutes a core prerequisite for large-scale fault-tolerant quantum computing. However, conventional magic state distillation requires massive physical qubit overhead across successive…
A common assumption in analyses of error thresholds and quantum computing in general is that one applies fault-tolerant quantum error correction (FTQEC) after every gate. This, however, is known not to always be optimal if the FTQEC…
Quantum error correction is a critical technique for transitioning from noisy intermediate-scale quantum (NISQ) devices to fully fledged quantum computers. The surface code, which has a high threshold error rate, is the leading quantum…
We introduce a new graphical framework for designing quantum error correction codes based on classical principles. A key feature of this graphical language, over previous approaches, is that it is closely related to that of factor graphs or…
Fault tolerance is a prerequisite for scalable quantum computing. Architectures based on 2D topological codes are effective for near-term implementations of fault tolerance. To obtain high performance with these architectures, we require a…
Homological quantum error correction uses tools of algebraic topology and homological algebra to derive Calderbank-Shor-Steane quantum error correcting codes from cellulations of topological spaces. This work is an exploration of the…
Self-correction has achieved impressive results in enhancing the style and security of the generated output from large language models (LLMs). However, recent studies suggest that self-correction might be limited or even counterproductive…
Quantum error correction in general is experimentally challenging as it requires significant expansion of the size of quantum circuits and accurate performance of quantum gates to fulfill the error threshold requirement. Here we propose a…
Quantum computers hold the promise of solving computational problems which are intractable using conventional methods. For fault-tolerant operation quantum computers must correct errors occurring due to unavoidable decoherence and limited…
Quantum error correction is indispensable for scalable quantum computation. Although encoding logical qubits substantially enhances noise resilience, achieving logical error rates low enough for practical algorithms remains challenging on…
We report on the fault-tolerant operation of logical qubits on a neutral atom quantum computer, with logical performance surpassing physical performance for multiple circuits including Bell states (12x error reduction), random circuits…
Stabilizer codes are a simple and successful class of quantum error-correcting codes. Yet this success comes in spite of some harsh limitations on the ability of these codes to fault-tolerantly compute. Here we introduce a new metric for…
We describe a linear quantum optical circuit capable of demonstrating a simple quantum error correction code in a four photon experiment.
Transversal Pauli $Z$ rotations provide a natural route to fault-tolerant logical diagonal gates in quantum CSS codes, but their capability is inherently constrained. We develop a homological framework that organizes transversal diagonal…