Quantum Computing with Very Noisy Devices

There are quantum algorithms that can efficiently simulate quantum physics, factor large numbers and estimate integrals. As a result, quantum c omputers can solve otherwise intractable computational problems. One of the main problems of experimental quantum computing is to preserve fragile quantum states in the prese nce of errors. It is known that if the needed elementary operations (gates) can be implemen t d with error probabilities below a threshold, then it is possible to efficiently quantum compute with arbitrary accuracy. Here we give evidence that for independent errors the theore tical threshold is well above3 %, which is a significant improvement over that of earlier calculations. However, the resources required at such high error probabilities are excessive. Fo rtunately, they decrease rapidly with decreasing error probabilities. If we had quantum resources comparable to the considerable resources available in today’s digital computer s, we could implement non-trivial quantum algorithms at error probabilities as high as1 % per gate. Research in quantum computing is motivated by the great incr ease in computational power offered by quantum computers. 1–3 There is a large and still growing number of experimental eff orts whose ultimate goal is to demonstrate scalable quantum comp uting. Scalable quantum computing requires that arbitrarily large computations can be efficie ntly 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 ph ysical gates is sufficiently low. The type of noise affecting the gat es in a given implementation is called the “error model”. A scheme for scalable quantum computing i n the presence of noise is called a “fault-tolerant architecture”. In view of the criterion ab ove, studies of scalable quantum computing involve constructing fault-tolerant architectures and pr oviding answers to questions such as the following: Q1: Is scalable quantum computing possible for e rror modelE? Q2: Can fault-tolerant architectureA 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 modelE? To obtain broadly applicable results, fault-tolerant arch itectures are constructed for generic error models. Here, the error model is parametrized by an err or p obability per gate (or simply error per gate, EPG), where the errors are unbiased and indep e nt. The fundamental theorem of scalable quantum computing is the threshold theorem and a nswers question Q1 as follows: If