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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…
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…
Large-scale quantum computation requires to be performed in the fault-tolerant manner. One crucial challenge of fault-tolerant quantum computing (FTQC) is reducing the overhead of implementing logical gates. Recently work proposed…
Compared to the more widely studied Pauli errors, coherent errors present several new challenges in quantum computing and quantum error correction (QEC). For example, coherent errors may interfere constructively over a long circuit and…
Magic states are a foundational resource for universal quantum computation. To survive in a realistic noisy environment, magic states must be prepared fault-tolerantly and protected by a quantum error-correcting code. The recent discovery…
The stabilization of a quantum computer by repeated error correction can be reduced almost entirely to repeated preparation of blocks of qubits in quantum codeword states. These are multi-particle entangled states with a high degree of…
Measurement-based quantum computing is a promising paradigm of quantum computation, where universal computing is achieved through a sequence of local measurements. The backbone of this approach is the preparation of multipartite…
Concatenation of a bosonic code with a qubit code is one of the promising ways to achieve fault-tolerant quantum computation. As one of the most important bosonic codes, Gottesman-Kitaev-Preskill (GKP) code is proposed to correct small…
Current noisy quantum computers have multiple types of errors, which can occur in the state preparation, measurement/readout, and gate operation, as well as intrinsic decoherence and relaxation. Partly motivated by the booming of…
Noise and errors are inevitable parts of any practical implementation of a quantum computer. As a result, large-scale quantum computation will require ways to detect and correct errors on quantum information. Here, we present such a quantum…
We construct a fault-tolerant quantum error-correcting protocol based on a qubit encoded in a large spin qudit using a spin-cat code, analogous to the continuous variable cat encoding. With this, we can correct the dominant error sources,…
We study the robustness of a fault-tolerant quantum computer subject to Gaussian non-Markovian quantum noise, and we show that scalable quantum computation is possible if the noise power spectrum satisfies an appropriate "threshold…
The Gottesman-Kitaev-Preskill (GKP) code was proposed in 2001 by Daniel Gottesman, Alexei Kitaev, and John Preskill as a way to encode a qubit in an oscillator. The GKP codewords are coherent superpositions of periodically displaced…
We show how to perform measurement-based quantum computing on qudits (high-dimensional quantum systems) using alternative resource states beyond the cluster state. Estimating overheads for gate decomposition, we find that generalizing…
A quantum computer with low-error, high-speed quantum operations and capability for interconnections is required for useful quantum computations. A logical qubit called Gottesman-Kitaev-Preskill (GKP) qubit in a single Bosonic harmonic…
We introduce fault-tolerant (FT) architectures for error correction with the XZZX cluster state based on performing measurements of two-qubit Pauli operators $Z\otimes Z$ and $X\otimes X$, or fusions, on a collection of few-body entangled…
We discuss the potential and limitations of Gaussian cluster states for measurement-based quantum computing. Using a framework of Gaussian projected entangled pair states (GPEPS), we show that no matter what Gaussian local measurements are…
Robust quantum computation requires encoding delicate quantum information into degrees of freedom that are hard for the environment to change. Quantum encodings have been demonstrated in many physical systems by observing and correcting…
We present a hybrid scheme for quantum computation that combines the modular structure of elementary building blocks used in the circuit model with the advantages of a measurement-based approach to quantum computation. We show how to…
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…