Related papers: Fault-tolerant fidelity based on few-qubit codes: …

Typically, fault-tolerant operations and code concatenation are reserved for quantum error correction due to their resource overhead. Here, we show that fault tolerant operations have a large impact on the performance of symmetry based…

We use density matrix simulations to study the performance of three distance three quantum error correcting codes in the context of the rare-earth-ion-doped crystal (RE) platform for quantum computing. We analyze pseudothresholds for these…

Fault-tolerant quantum error correction is essential for implementing quantum algorithms of significant practical importance. In this work, we propose a highly effective use of the surface-GKP code, i.e., the surface code consisting of…

Topological quantum error correction codes are currently among the most promising candidates for efficiently dealing with the decoherence effects inherently present in quantum devices. Numerically, their theoretical error threshold can be…

In this short review, I draw attention to new developments in the theory of fault tolerance in quantum computation that may give concrete direction to future work in the development of superconducting qubit systems. The basics of quantum…

Various quantum applications can be reduced to estimating expectation values, which are inevitably deviated by operational and environmental errors. Although errors can be tackled by quantum error correction, the overheads are far from…

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…

Topological color codes defined by the 4.8.8 semiregular lattice feature geometrically local check operators and admit transversal implementation of the entire Clifford group, making them promising candidates for fault-tolerant quantum…

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…

We present a simple method for constructing optimal fault-tolerant approximations of arbitrary unitary gates using an arbitrary discrete universal gate set. The method presented is numerical and scales exponentially with the number of gates…

In order to solve problems of practical importance, quantum computers will likely need to incorporate quantum error correction, where a logical qubit is redundantly encoded in many noisy physical qubits. The large physical-qubit overhead…

We present a method of concatenated quantum error correction in which improved classical processing is used with existing quantum codes and fault-tolerant circuits to more reliably correct errors. Rather than correcting each level of a…

There are well known necessary and sufficient conditions for a quantum code to correct a set of errors. We study weaker conditions under which a quantum code may correct errors with probabilities that may be less than one. We work with…

Large-scale quantum computation will only be achieved if experimentally implementable quantum error correction procedures are devised that can tolerate experimentally achievable error rates. We describe a quantum error correction procedure…

We introduce heterogeneous quantum error-correcting codes composed of qubit types with distinct error channels and study their performance in the code-capacity regime using maximum-likelihood tensor network decoding. In the regime where…

Quantum error correction offers a promising path for performing quantum computations with low errors. Although a fully fault-tolerant execution of a quantum algorithm remains unrealized, recent experimental developments, along with…

Fast, reliable logical operations are essential for realizing useful quantum computers. By redundantly encoding logical qubits into many physical qubits and using syndrome measurements to detect and correct errors, one can achieve low…

The quantum paradigm presents a phenomenon known as degeneracy that should improve the performance of quantum error correcting codes. However, the effects of this mechanism are sometimes ignored when evaluating the performance of sparse…

Color code is a promising topological code for fault-tolerant quantum computing. Insufficient research on the color code has delayed its practical application. In this work, we address several key issues to facilitate practical…

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…