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Efficient high-performance decoding of topological stabilizer codes has the potential to crucially improve the balance between logical failure rates and the number and individual error rates of the constituent qubits. High-threshold…
Topological quantum error-correcting codes are defined by geometrically local checks on a two-dimensional lattice of quantum bits (qubits), making them particularly well suited for fault-tolerant quantum information processing. Here, we…
A quantum computer needs the assistance of a classical algorithm to detect and identify errors that affect encoded quantum information. At this interface of classical and quantum computing the technique of machine learning has appeared as a…
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…
Quantum computers could solve problems beyond the reach of classical devices, but this potential depends on quantum error correction (QEC) to protect fragile quantum states from noise. A central challenge in QEC is decoding: inferring…
Quantum computers have the potential to solve certain complex problems in a much more efficient way than classical computers. Nevertheless, current quantum computer implementations are limited by high physical error rates. This issue is…
We propose a new tensor renormalization group algorithm, Anisotropic Tensor Renormalization Group (ATRG), for lattice models in arbitrary dimensions. The proposed method shares the same versatility with the Higher-Order Tensor…
We investigate a novel class of quantum error correcting codes to correct errors on both qubits and higher-state quantum systems represented as qudits. These codes arise from an original graph-theoretic representation of sets of quantum…
Surface code error correction offers a highly promising pathway to achieve scalable fault-tolerant quantum computing. When operated as stabilizer codes, surface code computations consist of a syndrome decoding step where measured stabilizer…
Quantum errors are primarily detected and corrected using the measurement of syndrome information which itself is an unreliable step in practical error correction implementations. Typically, such faulty or noisy syndrome measurements are…
Fast, reliable decoders are pivotal components for enabling fault-tolerant quantum computation (FTQC). Neural network decoders like AlphaQubit have demonstrated potential, achieving higher accuracy than traditional human-designed decoding…
Efficient and high-performance quantum error correction is essential for achieving fault-tolerant quantum computing. Low-depth random circuits offer a promising approach to identifying effective and practical encoding strategies. In this…
The Density Matrix Renormalization Group (DMRG) algorithm is a powerful tool for solving eigenvalue problems to model quantum systems. DMRG relies on tensor contractions and dense linear algebra to compute properties of condensed matter…
Current approaches for building quantum computing devices focus on two-level quantum systems which nicely mimic the concept of a classical bit, albeit enhanced with additional quantum properties. However, rather than artificially limiting…
Lookup table decoding is fast and distance-preserving, making it attractive for near-term quantum computer architectures with small-distance quantum error-correcting codes. In this work, we develop several optimization tools that can…
Topological color codes defined by the 4.8.8 semiregular lattice feature geometrically local check operators and admit transversal implementation of the entire Clifford group, making them promising candidates for fault-tolerant quantum…
Quantum error correction and symmetry arise in many areas of physics, including many-body systems, metrology in the presence of noise, fault-tolerant computation, and holographic quantum gravity. Here we study the compatibility of these two…
Quantum error correction becomes a practical possibility only if the physical error rate is below a threshold value that depends on a particular quantum code, syndrome measurement circuit, and decoding algorithm. Here we present an…
We present a classical enhancement to improve the accuracy of the Hybrid variant (Hybrid HHL) of the quantum algorithm for solving linear systems of equations proposed by Harrow, Hassidim, and Lloyd (HHL). We achieve this by using higher…
We describe a computationally-efficient heuristic algorithm based on a renormalization-group procedure which aims at solving the problem of finding minimal surface given its boundary (curve) in any hypercubic lattice of dimension $D>2$. We…