Related papers: Fault-tolerant gates via homological product 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…

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…

Error detectable and error correctable coding in Hamming space was researched to discover possible fault tolerant coding constellations, which can implement Boolean logic with fault tolerant property. Basic logic operators of the Boolean…

We review an approach to fault-tolerant holonomic quantum computation on stabilizer codes. We explain its workings as based on adiabatic dragging of the subsystem containing the logical information around suitable loops along which the…

To run large-scale algorithms on a quantum computer, error-correcting codes must be able to perform a fundamental set of operations, called logic gates, while isolating the encoded information from…

The preparation of a quantum state using a noisy quantum computer (gate noise strength $\delta$), will necessarily affect an O($\delta$)-fraction of the qubits, no matter which protocol is used. Here, we show that fault-tolerant quantum…

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…

The color code has been invaluable for the development of the theory of fault-tolerant logic gates using transversal rotations. Three-dimensional examples of the color code have shown us how its structure, specifically the intersection of…

Performing entangling gates between physical qubits is necessary for building a large-scale universal quantum computer, but in some physical implementations - for example, those that are based on linear optics or networks of ion traps -…

Fault-tolerant quantum computation critically depends on architectures uniting high encoding rates with physical implementability. Quantum low-density parity-check (qLDPC) codes, including bivariate bicycle (BB) codes, achieve dramatic…

Steane's 7-qubit quantum error-correcting code admits a set of fault-tolerant gates that generate the Clifford group, which in itself is not universal for quantum computation. The 15-qubit Reed-Muller code also does not admit a universal…

Code-switching offers a route to universal, fault-tolerant quantum computation by circumventing the limitation implied by the Eastin-Knill theorem against a universal transversal gate set within a single quantum code. Here, we present a…

We explain how to combine holonomic quantum computation (HQC) with fault tolerant quantum error correction. This establishes the scalability of HQC, putting it on equal footing with other models of computation, while retaining the inherent…

In certain approaches to quantum computing the operations between qubits are non-deterministic and likely to fail. For example, a distributed quantum processor would achieve scalability by networking together many small components;…

Despite the evident necessity of topological protection for realizing scalable quantum computers, the conceptual underpinnings of topological quantum logic gates had arguably remained shaky, both regarding their physical realization as well…

A major goal for fault-tolerant quantum computation (FTQC) is to reduce the overhead needed for error correction. One approach is to use block codes that encode multiple qubits, which can achieve significantly higher rates for the same code…

It has been known that quantum error correction via concatenated codes can be done with exponentially small failure rate if the error rate for physical qubits is below a certain accuracy threshold. Other, unconcatenated codes with their own…

The path-integral approach to topological quantum error correction provides a unified way to construct and analyze fault-tolerant circuits in spacetime. In this work, we demonstrate its utility and versatility at hand of a simple example:…

The standard approach to universal fault-tolerant quantum computing is to develop a general purpose quantum error correction mechanism that can implement a universal set of logical gates fault-tolerantly. Given such a scheme, any quantum…

Quantum error correction protects fragile quantum information by encoding it into a larger quantum system. These extra degrees of freedom enable the detection and correction of errors, but also increase the operational complexity of the…