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Quantum computers face significant challenges from quantum deviations or coherent noise, particularly during gate operations, which pose a complex threat to the efficacy of quantum error correction (QEC) protocols. In this study, we…
Fault-tolerant quantum computing in systems composed of both Majorana fermions and topologically unprotected quantum systems, e.g. superconducting circuits or quantum dots, is studied in this paper. Errors caused by topologically…
Active quantum error correction using qubit stabilizer codes has emerged as a promising, but experimentally challenging, engineering program for building a universal quantum computer. In this review we consider the formalism of qubit…
Using quantum systems with more than two levels, or qudits, can scale the computation space of quantum processors more efficiently than using qubits, which may offer an easier physical implementation for larger Hilbert spaces. However,…
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…
With gate error rates in multiple technologies now below the threshold required for fault-tolerant quantum computation, the major remaining obstacle to useful quantum computation is scaling, a challenge greatly amplified by the huge…
Quantum information can be protected from decoherence and other errors, but only if these errors are sufficiently rare. For quantum computation to become a scalable technology, practical schemes for quantum error correction that can…
As quantum devices scale toward practical machine learning applications, the binary qubit paradigm faces expressivity and resource efficiency limitations. Multi-level quantum systems, or qudits, offer a promising alternative by harnessing a…
We analyze surface codes, the topological quantum error-correcting codes introduced by Kitaev. In these codes, qubits are arranged in a two-dimensional array on a surface of nontrivial topology, and encoded quantum operations are associated…
Quantum states are very delicate, so it is likely some sort of quantum error correction will be necessary to build reliable quantum computers. The theory of quantum error-correcting codes has some close ties to and some striking differences…
Sensitivity to noise makes most of the current quantum computing schemes prone to error and nonscalable, allowing only for small proof-of-principle devices. Topologically-protected quantum computing aims at solving this problem by encoding…
Quantum error correction becomes a practical possibility only if the physical error rate is below a threshold value that depends on a particular quantum code, syndrome measurement circuit, and decoding algorithm. Here we present an…
Quantum circuits implementing fault-tolerant quantum error correction (QEC) for the three qubit bit-flip code and five-qubit code are studied. To describe the effect of noise, we apply a model based on a generalized effective Hamiltonian…
Qudits can be described by a state vector in a $q$-dimensional Hilbert space, enabling a more extensive encoding and manipulation of information compared to qubits. This implies that conducting fault-tolerant quantum computations using…
A promising approach to overcome decoherence in quantum computing schemes is to perform active quantum error correction using topology. Topological subsystem codes incorporate both the benefits of topological and subsystem codes, allowing…
Scalable quantum computing can only be achieved if qubits are manipulated fault-tolerantly. Topological error correction - a novel method which combines topological quantum computing and quantum error correction - possesses the highest…
Symmetric extendibility of quantum states has recently drawn attention in the context of quantum cryptography to judge whether quantum states shared between two distant parties can be purified by means of one-way error correction protocols.…
We estimate and analyze the error rates and the resource overheads of the repetition cat qubit approach to universal and fault-tolerant quantum computation. The cat qubits stabilized by two-photon dissipation exhibit an extremely biased…
Topological quantum computing promises intrinsic fault tolerance by encoding quantum information in non-Abelian anyons, where quantum gates are implemented via braiding. While braiding operations are robust against local perturbations, a…
Quantum computing becomes viable when a quantum state can be preserved from environmentally-induced error. If quantum bits (qubits) are sufficiently reliable, errors are sparse and quantum error correction (QEC) is capable of identifying…