Related papers: Flag Gadgets based on Classical Codes
Fault-tolerant (FT) computation by using quantum error correction (QEC) is essential for realizing large-scale quantum algorithms. Devices are expected to have enough qubits to demonstrate aspects of fault tolerance in the near future.…
Quantum error-correcting codes are a vital technology for demonstrating reliable quantum computation. They require data qubits for encoding quantum information and ancillary qubits for taking error syndromes necessary for error correction.…
Fault-tolerant (FT) preparation of diverse logical stabilizer states in quantum error-correcting (QEC) codes is essential for FT computation. Existing constructions of these FT circuits are often constrained by classical computational…
Quantum computers have the potential to change the way we solve computational problems. Due to the noisy nature of qubits, the need arises to correct physical errors occurring during computation. The surface code is a promising candidate…
We introduce homological measurement, a framework for measuring the logical Pauli operators encoded in CSS stabilizer codes. The framework is based on the algebraic description of such codes as chain complexes. Protocols such as lattice…
Characterizing how quantum error correction circuits behave under realistic hardware noise is essential for testing the premises that enable scalable fault tolerance. Logical error rates conditioned on syndrome outcomes are needed to enable…
Quantum error correction (QEC) is considered a deciding component in enabling practical quantum computing. Stabilizer codes, and in particular topological surface codes, are promising candidates for implementing QEC by redundantly encoding…
Typical stabilizer codes aim to solve the general problem of fault-tolerance without regard for the structure of a specific system. By incorporating a broader representation-theoretic perspective, we provide a generalized framework that…
Although qubit coherence times and gate fidelities are continuously improving, logical encoding is essential to achieve fault tolerance in quantum computing. In most encoding schemes, correcting or tracking errors throughout the computation…
The quest of demonstrating beneficial quantum error correction in near-term noisy quantum processors can benefit enormously from a low-resource optimization of fault-tolerant schemes, which are specially designed for a particular platform…
Fault-tolerant quantum computation allows quantum computations to be carried out while resisting unwanted noise. Several error-correcting codes have been developed to achieve this task, but none alone are capable of universal quantum…
Stabilizer states are extensively studied in quantum information theory for their structures based on the Pauli group. Calderbank-Shor-Steane (CSS) stabilizer states are of particular importance in their application to fault-tolerant…
Quantum error-correcting codes, such as subspace, subsystem, and Floquet codes, are typically constructed within the stabilizer formalism, which does not fully capture the idea of fault-tolerance needed for practical quantum computing…
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…
Fault-tolerant operations based on stabilizer codes are the state of the art in suppressing error rates in quantum computations. Most such codes do not permit a straightforward implementation of non-Clifford logical operations, which are…
Majorana-based quantum computation in nanowires and neutral atoms has gained prominence as a promising platform to encode qubits and protect them against noise. In order to run computations reliably on such devices, a fully fault-tolerant…
The color code is a topological quantum error-correcting code supporting a variety of valuable fault-tolerant logical gates. Its two-dimensional version, the triangular color code, may soon be realized with currently available…
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…
The hypergraph product creates a quantum stabilizer code from two input classical linear codes; a paradigmatic example being the surface code as a hypergraph product of two classical repetition codes. Many properties of the hypergraph…
Quantum computers will eventually reach a size at which quantum error correction becomes imperative. Quantum information can be protected from qubit imperfections and flawed control operations by encoding a single logical qubit in multiple…