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It is conjectured that quantum computers are able to solve certain problems more quickly than any deterministic or probabilistic computer. A quantum computer exploits the rules of quantum mechanics to speed up computations. However, it is a…
Quantum systems, in general, output data that cannot be simulated efficiently by a classical computer, and hence is useful for solving certain mathematical problems and simulating quantum many-body systems. This also implies, unfortunately,…
The potential of quantum computers to outperform classical ones in practically useful tasks remains challenging in the near term due to scaling limitations and high error rates of current quantum hardware. While quantum error correction…
A long-standing open question about Gaussian continuous-variable cluster states is whether they enable fault-tolerant measurement-based quantum computation. The answer is yes. Initial squeezing in the cluster above a threshold value of 20.5…
We propose a fault-tolerant quantum error correction architecture consisting of a linear array of emitters and delay lines. In our scheme, a resource state for fault-tolerant quantum computation is generated by letting the emitters interact…
Quantum Error Correction (QEC) codes are essential for achieving fault-tolerant quantum computing (FTQC). However, their implementation faces significant challenges due to disparity between required dense qubit connectivity and sparse…
A universal and fault tolerant scheme for quantum computation is proposed which utilizes a class of error correcting codes that is based on the detection of spontaneous emission (of, e.g., photons, phonons, and ripplons). The scheme is…
Quantum computing holds the promise of solving classically intractable problems. Enabling this requires scalable and hardware-efficient quantum processors with vanishing error rates. This perspective manuscript describes how bosonic codes,…
Quantum computing promises to provide exponential speed-ups to certain classes of problems. In many such algorithms, a classical vector $\mathbf{b}$ is encoded in the amplitudes of a quantum state $\left |b \right >$. However, efficiently…
In this paper we provide a basic introduction of the core ideas and theories surrounding fault-tolerant quantum computation. These concepts underly the theoretical framework of large-scale quantum computation and communications and are the…
Quantum computers are poised to radically outperform their classical counterparts by manipulating coherent quantum systems. A realistic quantum computer will experience errors due to the environment and imperfect control. When these errors…
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…
Quantum error correction plays a critical role in enabling fault-tolerant quantum computing by protecting fragile quantum information from noise. While general-purpose quantum error correction codes are designed to address a wide range of…
We exhibit a simple, systematic procedure for detecting and correcting errors using any of the recently reported quantum error-correcting codes. The procedure is shown explicitly for a code in which one qubit is mapped into five. The…
The failure susceptibility of the quantum hardware will force quantum computers to execute fault-tolerant quantum circuits. These circuits are based on quantum error correcting codes, and there is increasing evidence that one of the most…
The discovery of quantum error correction has greatly improved the long-term prospects for quantum computing technology. Encoded quantum information can be protected from errors that arise due to uncontrolled interactions with the…
Practical applications of quantum computing depend on fault-tolerant devices with error correction. Today, the most promising approach is a class of error-correcting codes called surface codes. We study the problem of compiling quantum…
The realization of large-scale quantum computers requires not only quantum error correction (QEC) but also fault-tolerant operations to handle errors that propagate into harmful errors. Recently, flag-based protocols have been introduced…
A major obstacle towards realizing a practical quantum computer is the noise that arises due to system-environment interactions. While it is very well known that quantum error correction (QEC) provides a way to protect against errors that…
The aim of this paper is to propose an alternative method to solve a Fault Tolerant Control problem. The model is a linear system affected by a disturbance term: this represents a large class of technological faulty processes. The goal is…