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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…
There are several models of quantum computation which exhibit shared fundamental fault-tolerance properties. This article makes commonalities explicit by presenting these different models in a unifying framework based on the ZX calculus. We…
As quantum computing moves toward fault-tolerant architectures, quantum error correction (QEC) decoder performance is increasingly critical for scalability. Understanding the impact of transitioning from floating-point software to…
We study a class of gauge fixings of the Bacon-Shor code at the circuit level, which includes a subfamily of generalized surface codes. We show that for these codes, fault tolerance can be achieved by direct measurements of the stabilizers.…
Practical large-scale quantum computation requires both efficient error correction and robust implementation of logical operations. Three-dimensional (3D) color codes are a promising candidate for fault-tolerant quantum computation due to…
Extensive quantum error correction is necessary in order to scale quantum hardware to the regime of practical applications. As a result, a significant amount of decoding hardware is necessary to process the colossal amount of data required…
We use the quasienergy structure that emerges when a fluxonium superconducting circuit is driven periodically to encode quantum information with dynamically induced flux-insensitive sweet spots. The framework of Floquet theory provides an…
Current quantum technology is approaching the system sizes and fidelities required for quantum error correction. It is therefore important to determine exactly what is needed for proof-of-principle experiments, which will be the first major…
We discuss how the presence of gauge sub-systems in the Bacon-Shor code [D. Bacon, Phys. Rev. A 73, 012340 (2006)] leads to remarkably simple and efficient methods for fault-tolerant error correction (FTEC). Most notably, FTEC does not…
We show an equivalence relation between fault-tolerant circuits for a stabilizer code and fault-tolerant adiabatic processes for holonomic quantum computation (HQC), in the case where quantum information is encoded in the degenerated ground…
The constituent parts of a quantum computer are inherently vulnerable to errors. To this end we have developed quantum error-correcting codes to protect quantum information from noise. However, discovering codes that are capable of a…
We consider an approach to fault tolerant quantum computing based on a simple error detecting code operating as the substrate for a conventional surface code. We develop a customised decoder to process the information about the likely…
Quantum low-density parity-check codes are promising candidates towards scalable fault-tolerant quantum computation. Among these, bivariate bicycle (BB) codes offer superior encoding rates and large code distance compared to surface codes.…
Quantum networks serve as the means to transmit information, encoded in quantum bits or qubits, between quantum processors that are physically separated. Given the instability of qubits, the design of such networks is challenging,…
We describe a qubit encoded in continuous quantum variables of an rf superconducting quantum interference device. Since the number of accessible states in the system is infinite, we may protect its two-dimensional subspace from small errors…
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 technological development of hardware heading toward universal fault-tolerant quantum computation requires a large-scale processing unit with high performance. While fluxonium qubits are promising with high coherence and large…
The construction of a quantum computer remains a fundamental scientific and technological challenge, in particular due to unavoidable noise. Quantum states and operations can be protected from errors using protocols for fault-tolerant…
Quantum error correction is an important ingredient for scalable quantum computing. Stabilizer codes are one of the most promising and straightforward ways to correct quantum errors, are convenient for logical operations, and improve…
We present a fault-tolerant semi-global control strategy for universal quantum computers. We show that N-dimensional array of qubits where only (N-1)-dimensional addressing resolution is available is compatible with fault-tolerant universal…