![]() For instance, if we saw a bit string 10*00, then we would know that the third bit had been erased and we would also suspect that the first bit had suffered from the bit-flit error. Also, we can consider a scenario where both erasure and bit-flip errors happen. In general, erasure errors are easier to correct than bit-flip errors because we know which bits have been lost. For instance, as long as not all the bits are erased, we still preserve the value of the bit that we want to protect. We can then represent the value of this bit by a symbol *. A similar strategy would work if bits also suffered from erasure errors – when an erasure error happens, then the corresponding bit is irrevocably lost and we know it. It is easy to see that we would succeed as long as fewer than a half of the bits in the bit string suffered from the bit-flip errors and changed their values. Subsequently, we could reliably infer the value of the stored bit to be 0. Then, if we saw a bit string 01000, we could take the majority vote of the bit values and guess that the second bit might have suffered from the bit-flip error. ![]() Instead of keeping only one copy of the bit, either 0 or 1, we choose to store a bit string with, for instance, five copies of that bit, either 00000 or 11111, respectively. There is a simple error correction strategy that relies on using more resources and making multiple copies of the bit that we want to protect against bit-flip errors. We assume that bit-flip errors are not too likely, e.g., each bit flip happens independently with probability p=0.02, and that we do not know when they occur. One way in which noise can corrupt the stored information is through a bit-flip error, i.e., the value of the bit is changed from 0 to 1 or from 1 to 0. Let us consider a concrete example of storing one bit of information, either 0 or 1, in the presence of noise. In addition, we discuss how we can use so-called biased noise in quantum computers to our advantage in order to improve the performance of quantum error-correcting protocols.Įrror correction techniques strive to protect information from the detrimental effects of noise that may change or even completely destroy it. In this blog post, we explain the basic ideas behind error correction and how to apply it to quantum computing. These results allow us to give the first estimations of error correction thresholds for a universal non-Abelian quantum error correcting code.Have you ever heard about error correction? Without it, we could not obtain awe-inspiring pictures of Jupiter and its moons, conduct intelligible mobile phone calls, or have reliable computers. By simulating the effect of noise on this code, and the subsequent recovery processes, we obtain the logical error rate as a function of the intensity of the noise. We devise a set of measurement operators and the corresponding quantum circuits, which allow us to measure the charge of anyonic quasiparticles created by microscopic errors on physical qubits. Our focus is a particular topological quantum error correcting code, based on a modified version of what is known as the Fibonacci Levin-Wen string-net model. Hence, when a topological code is subjected to noise, the resulting state can be interpreted as containing clusters of anyonic excitations, which must be annihilated in pairs to recover the encoded information. One of the defining characteristics of such models is that their excited states contain anyons, quasiparticles that do not behave like bosons or fermions (the two main classifications of subatomic particles). In this approach, the logical quantum state that we wish to protect is encoded in the degenerate ground space of a 2D topological model. ![]() Here, we provide estimates on the performance of one of these codes.Ī very promising class of quantum error correcting codes are topological codes. Hence, one of the main challenges for achieving a universal quantum computer is the development of techniques, known as quantum error correcting codes, to protect quantum information against errors. Such quantum computers are, however, vulnerable to noise from the environment or imperfect hardware, as this destroys the coherence of the quantum states used in computations. ![]() The use of quantum states for computing purposes will enable computations that are intractable for classical computers, such as the simulation of quantum many-body systems. ![]()
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