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 called "gates" that tend to destroy the fragile quantum states needed for computation. The goal of fault-tolerant quantum computing is to compute accurately even when gates have a high probability of error each time they are used. Here we give evidence that accurate quantum computing is possible with error probabilities above 3 % per gate, which is significantly higher than what was previously thought possible. However, the resources required for computing at such high error probabilities are excessive. Fortunately, they decrease rapidly with decreasing error probabilities. If we had quantum resources comparable to the considerable resources available in today's digital computers, we could implement non-trivial quantum computations at error probabilities as high as 1 % per gate.Research in quantum computing is motivated by the great increase in computational power offered by quantum computers. [1][2][3] There is a large and still growing number of experimental efforts whose ultimate goal is to demonstrate scalable quantum computing. Scalable quantum computing requires that arbitrarily large computations can be efficiently implemented with little error in the output. Criteria that need to be satisfied by devices used for scalable quantum computing have been specified by DiVincenzo. 4 One of the criteria is that the level of noise affecting the physical gates is sufficiently low. The type of noise affecting the gates in a given implementation is called the "error model". A scheme for scalable quantum computing in the presence of noise is called a "faulttolerant architecture". In view of the low-noise criterion, studies of scalable quantum computing involve constructing fault-tolerant architectures and providing answers to questions such as the following: Q1: Is scalable quantum computing possible for error model E? Q2: Can fault-tolerant architecture A be used for scalable quantum computing with error model E? Q3: What resources are required to implement quantum computation C using fault-tolerant architecture A with error model E?To obtain broadly applicable results, fault-tolerant architectures are constructed for generic error models. Here, the error model is parametrized by an error probability per gate (or simply error per gate, EPG), where the errors are unbiased and independent. The fundamental theorem of scalable quantum computing is the threshold theorem and answers question Q1 as follows: If 1