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As current experiments already realize small quantum circuits on error corrected qubits, it is important to fully understand the effect of physical errors on the logical error channels of these fault-tolerant circuits. Here, we investigate…
Quantum error correction is necessary to perform large-scale quantum computations in the presence of noise and decoherence. As a result, several aspects of quantum error correction have already been explored. These have been primarily…
Quantum state teleportation is commonly used in designs for large-scale fault-tolerant quantum computers. Using Quantinuum's H2 trapped-ion quantum processor, we implement the first demonstration of a fault-tolerant state teleportation…
Quantum error correction codes (QECCs) play a central role in both quantum communications and quantum computation. Practical quantum error correction codes, such as stabilizer codes, are generally structured to suit a specific use, and…
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…
Here we present the cuLGT code for gauge fixing in lattice gauge field theories with graphic processing units (GPUs). Implementations for SU(3) Coulomb, Landau and maximally Abelian gauge fixing are available and the overrelaxation,…
The quantum logic gates used in the design of a quantum computer should be both universal, meaning arbitrary quantum computations can be performed, and fault-tolerant, meaning the gates keep errors from cascading out of control. A number of…
We give an introduction to the theory of quantum error correction using stabilizer codes that is geared towards the working computer scientists and mathematicians with an interest in exploring this area. To this end, we begin with an…
Many current quantum error-correcting codes that achieve full fault tolerance suffer from having low ratios of logical to physical qubits and significant overhead. This makes them difficult to implement on current noisy intermediate-scale…
Quantum computers can be protected from noise by encoding the logical quantum information redundantly into multiple qubits using error correcting codes. When manipulating the logical quantum states, it is imperative that errors caused by…
The stabiliser fragment of quantum theory is a foundational building block for quantum error correction and the fault-tolerant compilation of quantum programs. In this article, we develop a sound, universal and complete denotational…
Photonics provides a viable path to a scalable fault-tolerant quantum computer. The natural framework for this platform is measurement-based quantum computation, where fault-tolerant graph states supersede traditional quantum…
The yield of physical qubits fabricated in the laboratory is much lower than that of classical transistors in production semiconductor fabrication. Actual implementations of quantum computers will be susceptible to loss in the form of…
Steane code is one of the most widely studied quantum error-correction codes, which is a natural choice for fault-tolerant quantum computation (FTQC). However, the original Steane code is not fault-tolerant because the CNOT gates in an…
The path-integral approach to topological quantum error correction provides a unified way to construct and analyze fault-tolerant circuits in spacetime. In this work, we demonstrate its utility and versatility at hand of a simple example:…
Quantum error correction (QEC) enables reliable computation on noisy hardware by encoding logical information across many physical qubits and periodically measuring parities to detect errors. A decoder is the classical algorithm that uses…
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 correction allows to actively correct errors occurring in a quantum computation when the noise is weak enough. To make this error correction competitive information about the specific noise is required. Traditionally, this…
We propose a family of surface codes with general lattice structures, where the error-tolerances against bit and phase errors can be controlled asymmetrically by changing the underlying lattice geometries. The surface codes on various…
In fault-tolerant quantum computing, quantum algorithms are implemented through quantum circuits capable of error correction. These circuits are typically constructed based on specific quantum error correction codes, with consideration…