Related papers: Learning to Decode the Surface Code with a Recurre…
This is an expository article aiming to introduce the reader to the underlying mathematics and geometry of quantum error correction. Information stored on quantum particles is subject to noise and interference from the environment. Quantum…
Surface codes exploit topological protection to increase error resilience in quantum computing devices and can in principle be implemented in existing hardware. They are one of the most promising candidates for active error correction, not…
The surface code is a promising candidate for fault-tolerant quantum computation and has been implemented in many quantum hardware platforms. In this work, we propose a new non-local unitary circuit to encode a surface code state based on a…
Reliable communication over noisy channels requires the design of specialized error-correcting codes (ECCs) tailored to specific system requirements. Recently, neural network-based decoders have emerged as promising tools for enhancing ECC…
Recent developments in the field of deep learning have motivated many researchers to apply these methods to problems in quantum information. Torlai and Melko first proposed a decoder for surface codes based on neural networks. Since then,…
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…
A common approach to studying the performance of quantum error correcting codes is to assume independent and identically distributed single-qubit errors. However, the available experimental data shows that realistic errors in modern…
Recent work on approximate quantum error correction (QEC) has opened up the possibility of constructing subspace codes that protect information with high fidelity in scenarios where perfect error correction is impossible. Motivated by this,…
We develop novel protocols for generating loss-tolerant quantum codes; these are central for safeguarding information against qubit losses, with most crucial applications in quantum communications. Contrary to current proposals, our method…
Practical quantum computing will require error rates that are well below what is achievable with physical qubits. Quantum error correction offers a path to algorithmically-relevant error rates by encoding logical qubits within many physical…
Quantum computers have the potential to provide exponential speedups over their classical counterparts. Quantum principles are being applied to fields such as communications, information processing, and artificial intelligence to achieve…
Quantum error correction promises a viable path to fault-tolerant computations, enabling exponential error suppression when the device's error rates remain below the protocol's threshold. This threshold, however, strongly depends on the…
This is a comprehensive review on fault-tolerant topological quantum computation with the surface codes. The basic concepts and useful tools underlying fault-tolerant quantum computation, such as universal quantum computation, stabilizer…
We estimate the resource requirements for the quantum simulation of the ground state energy of the one dimensional quantum transverse Ising model (TIM), based on the surface code implementation of a fault tolerant quantum computer. The…
We present a semidefinite program optimization approach to quantum error correction that yields codes and recovery procedures that are robust against significant variations in the noise channel. Our approach allows us to optimize the…
The typical model for measurement noise in quantum error correction is to randomly flip the binary measurement outcome. In experiments, measurements yield much richer information - e.g., continuous current values, discrete photon counts -…
Fast decoders that achieve strong error suppression are essential for fault-tolerant quantum computation (FTQC) from both practical and theoretical perspectives. The union-find (UF) decoder for the surface code is widely regarded as a…
Deep learning and quantum computing have achieved dramatic progresses in recent years. The interplay between these two fast-growing fields gives rise to a new research frontier of quantum machine learning. In this work, we report the first…
Quantum error correction offers a promising path for performing quantum computations with low errors. Although a fully fault-tolerant execution of a quantum algorithm remains unrealized, recent experimental developments, along with…
Surface codes are one of the most important topological stabilizer codes in the theory of quantum error correction. In this paper, we provide an efficient way to obtain surface codes through Measurement-based quantum computation (MBQC)…