![]() ![]() One of the best performing QEC strategies is based on topological QEC codes, such as the surface code see Figure 1. With their seminal work, the field of QEC was born and many QEC strategies have been developed since then. In particular, they provided the very first quantum error correction (QEC) strategies. In the mid-nineties, Peter Shor and Andrew Steane gave an affirmative answer to this question. The surface code can be realized by placing qubits on the vertices of the square lattice and measuring Pauli X and Z parity checks associated with dark and light faces, respectively. We may then wonder whether, despite these challenges, it is possible to protect qubits from bit-flip and phase-flip errors simultaneously.įigure 1. We assume that bit-flip and phase-flip errors are not too likely to happen, e.g., each bit-flip and phase-flip error happens independently with probability p=0.02, and that we do not know when they occur. ![]() In addition to quantum noise being more complex than classical noise, we cannot learn the state of the qubit without drastically altering it. A phase-flip error, however, has no classical counterpart and it changes the qubit state α|0〉 + β|1〉 to α|0〉 – β|1〉. Similarly to its classical counterpart, a bit-flip error changes the qubit state from α|0〉 + β|1〉 to β|0〉 + α|1〉. A qubit may suffer not only from bit-flip noise, but also from phase-flip noise. Unlike a classical bit that is either 0 or 1, a qubit can be in any state α|0〉 + β|1〉, which is a superposition of two states |0〉 and |1〉 (where α and β are two complex numbers, such that the squares of their modules sum up to 1). This is due to quantum noise being more complex than classical noise and the no-cloning theorem, which asserts that it is impossible to make a copy of a qubit in an arbitrary unknown state. Perplexingly, the strategy that we just discussed is inadequate to protect quantum bits (or qubits for short). This, in turn, would allow us to infer the value of the stored bit to be 0. 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. ![]() 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. ![]()
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