Introduction to quantum error correction

Zachary P. Bradshaw, Jeffrey J. Dale, Ethan N. Evans

Dave Bacon

In Chapter 1 we saw that open quantum systems could interact with an environment and that this coupling could turn pure states into mixed states. This process will detrimentally impact any quantum computation, because it can lessen or destroy the interference effects that are vital to distinguishing a quantum computer from a classical computer. The problem of overcoming this effect is called the decoherence problem . Historically, the problem of overcoming decoherence was thought to be a major obstacle towards building a quantum computer. However, it was discovered that, under suitable conditions, the decoherence problem could be overcome. The main idea behind how this can be achieved is through the theory of quantum error correction (QEC). In this chapter we give an introduction into the way in which the decoherence problem can be overcome via the method of QEC. It is important to note that the scope of the introduction is not comprehensive, and focuses only on the basics of QEC without reference to the notion of fault-tolerant quantum computation, which is covered in Chapter 5. Quantum error correction should be thought of as a (major) tool in this larger theory of fault-tolerant quantum computing.

Stefano Olivares

Simon J. Devitt, William J. Munro, Kae Nemoto

Quantum error correction (QEC) and fault-tolerant quantum computation represent one of the most vital theoretical aspects of quantum information processing. It was well known from the early developments of this exciting field that the fragility of coherent quantum systems would be a catastrophic obstacle to the development of large-scale quantum computers. The introduction of quantum error correction in 1995 showed that active techniques could be employed to mitigate this fatal problem. However, quantum error correction and fault-tolerant computation is now a much larger field and many new codes, techniques, and methodologies have been developed to implement error correction for large-scale quantum algorithms. In response, we have attempted to summarize the basic aspects of quantum error correction and fault-tolerance, not as a detailed guide, but rather as a basic introduction. The development in this area has been so pronounced that many in the field of quantum information, specifically researchers who are new to quantum information or people focused on the many other important issues in quantum computation, have found it difficult to keep up with the general formalisms and methodologies employed in this area. Rather than introducing these concepts from a rigorous mathematical and computer science framework, we instead examine error correction and fault-tolerance largely through detailed examples, which are more relevant to experimentalists today and in the near future.

Ivan B. Djordjević

Rodriguez, Derek

The introduction of quantum computing has presented algorithmic solutions to computationally difficult challenges that are far more efficient than those of classical computers. These algorithms leverage the properties of quantum mechanics to manipulate the quantum properties of subatomic particles, requiring immense precision and stability. Current quantum hardware, however, is too noisy and introduces too many errors for these algorithms to be useful in practice, necessitating the use of error correction algorithms. This field survey seeks to introduce various principles of quantum mechanics relevant to quantum computing and quantum error correction (QEC), detail the implementation and motivations of a basic QEC algorithm, and provide insight into the current research direction.