Related papers: Fault-Tolerant Quantum Computation With Constant E…
Fault-tolerant quantum computation traditionally incurs substantial resource overhead, with both qubit and time overheads scaling polylogarithmically with the size of the computation. While prior work by Gottesman showed that constant qubit…
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…
Quantum information processors promise fast algorithms for problems inaccessible to classical computers. But since qubits are noisy and error-prone, they will depend on fault-tolerant quantum error correction (FTQEC) to compute reliably.…
We prove that quantum expander codes can be combined with quantum fault-tolerance techniques to achieve constant overhead: the ratio between the total number of physical qubits required for a quantum computation with faulty hardware and the…
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;…
The goal of this paper is to review the theoretical basis for achieving a faithful quantum information transmission and processing in the presence of noise. Initially encoding and decoding, implementing gates and quantum error correction…
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…
With the intense interest in small, noisy quantum computing devices comes the push for larger, more accurate -- and hence more useful -- quantum computers. While fully fault-tolerant quantum computers are, in principle, capable of achieving…
It is not so well-known that measurement-free quantum error correction protocols can be designed to achieve fault-tolerant quantum computing. Despite the potential advantages of using such protocols in terms of the relaxation of accuracy,…
In theory, quantum computers can efficiently simulate quantum physics, factor large numbers and estimate integrals, thus solving otherwise intractable computational problems. In practice, quantum computers must operate with noisy devices…
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…
Designing encoding and decoding circuits to reliably send messages over many uses of a noisy channel is a central problem in communication theory. When studying the optimal transmission rates achievable with asymptotically vanishing error…
As there is no quantum error correction code with universal set of transversal gates, several approaches have been proposed which, in combination of transversal gates, make universal fault-tolerant quantum computation possible. Magic state…
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,…
Quantum error correction and fault-tolerance make it possible to perform quantum computations in the presence of imprecision and imperfections of realistic devices. An important question is to find the noise rate at which errors can be…
Quantum computers have advanced rapidly in qubit count and gate fidelity. However, large-scale fault-tolerant quantum computing still relies on quantum error correction code (QECC) to suppress noise. Manually or experimentally verifying the…
Quantum computation holds the promise of solving certain complex problems exponentially faster than classical computers. However, the high prevalent noise in current quantum devices impedes the accurate execution of even basic algorithms.…
A major challenge in practical quantum computation is the ineludible errors caused by the interaction of quantum systems with their environment. Fault-tolerant schemes, in which logical qubits are encoded by several physical qubits, enable…
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…
In this paper, we place bounds on when it is impossible to purify a noisy two-qubit state if all the gates used in the purification protocol are subject to adversarial local, independent, noise. It is found that the gate operations must be…