Related papers: Error Channels and the Threshold for Fault-toleran…

This paper proves the threshold result, which asserts that quantum computation can be made robust against errors and inaccuracies, when the error rate, $\eta$, is smaller than a constant threshold, $\eta_c$. The result holds for a very…

We have previously (quant-ph/9608012) shown that for quantum memories and quantum communication, a state can be transmitted over arbitrary distances with error $\epsilon$ provided each gate has error at most $c\epsilon$. We discuss a…

Here we revisit one of the prototypical tasks for characterizing the structure of noise in quantum devices: estimating every eigenvalue of an $n$-qubit Pauli noise channel to error $\epsilon$. Prior work [14] proved no-go theorems for this…

Channel capacities quantify the optimal rates of sending information reliably over noisy channels. Usually, the study of capacities assumes that the circuits which sender and receiver use for encoding and decoding consist of perfectly…

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…

The error threshold for fault tolerant quantum computation with concatenated encoding of qubits is penalized by internal communication overhead. Many quantum computation proposals rely on nearest-neighbour communication, which requires…

In fault-tolerant quantum computing schemes, the overhead is often dominated by the cost of preparing codewords reliably. This cost generally increases quadratically with the block size of the underlying quantum error-correcting code. In…

One of the major challenges in realizing fault-tolerant quantum computers (FTQCs) is the requirement for a large number of physical qubits. To address this issue, high-rate quantum error correcting codes, which efficiently embed logical…

Fundamental limits on communication rates over quantum channels are given by mathematical expressions involving entropic formulas. Often, it is unclear if these expressions are computable. This thesis describes contributions to the study of…

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…

We consider the problem of fault-tolerant quantum computation in the presence of slow error diagnostics, either caused by measurement latencies or slow decoding algorithms. Our scheme offers a few improvements over previously existing…

Quantum error correction methods use processing power to combat noise. The noise level which can be tolerated in a fault-tolerant method is therefore a function of the computational resources available, especially the size of computer and…

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…

The states needed in a quantum computation are extremely affected by decoherence. Several methods have been proposed to control error spreading. They use two main tools: fault-tolerant constructions and concatenated quantum error correcting…

A scheme for linear optical implementation of fault-tolerant quantum computation is proposed, which is based on an error-detecting code. Each computational step is mediated by transfer of quantum information into an ancilla system embedding…

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…

The hopes for scalable quantum computing rely on the "threshold theorem": once the error per qubit per gate is below a certain value, the methods of quantum error correction allow indefinitely long quantum computations. The proof is based…

Usual scenarios of fault-tolerant computation are concerned with the fault-tolerant realization of quantum algorithms that compute classical functions, such as Shor's algorithm for factoring. In particular, this means that input and output…

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…

Fault-tolerant quantum computing will require accurate estimates of the resource overhead, but standard metrics such as gate fidelity and diamond distance have been shown to be poor predictors of logical performance. We present a scalable…