Recently, a quantum computer has extensively been studied. In comparison with present computation (classical computation), in quantum computing, memory errors occur by decoherence, and a gate operation having high reliability is difficult. Accordingly, error-correction is extremely important. As to the theory of quantum error-correction, by using a quantum error-correcting code, a rapid rise of error probability of computing result with increase of computational complexity can be suppressed. In this way, computing with error-correction is called “fault tolerant computing”.
As a result, if the probabilities of fundamental errors (memory error, error of one-qubit gate, error of two-qubit gate, error of initialization of qubit, error of measurement of qubit) are lower than some value (it is called a threshold), error probability of final computing result can be lowered to any degree (Briefly, a long computing can be performed to any degree). This is called “a threshold theorem”, which is the most important result in quantum information science.
From a view point of the threshold theorem, the reason why realization of a quantum computer is difficult at present is that the probabilities of fundamental errors are difficult to be smaller than the threshold. Accordingly, if the threshold can be raised by contriving the error-correction method, realization of the quantum computer will be easier.
The threshold was estimated as a very small value such as 10−4˜10−6. Recently, it is known that the threshold can be raise to 10−2˜10−3. For example, this fact is disclosed in the following references.
[Non-patent reference 1] M. A. Steane, Phys. Rev. A68, 042322 (2003)
[Non-patent reference 2] E. Knill, Nature 434, 39 (2005).
[Non-patent reference 3] B. W. Reichardt, e-print arXiv:quant-ph/0406025
Such a value is still very low. In addition, the present approaches have a problem that a high threshold cannot be realized by few resources.