What Is Computational Capacity?

Introduction to Quantum Communication

Computational Capacity: Communication Over Noise Wires

When you are sending information using a noisy channel, the probability of error in transmitting the message is a function of the communication rate.  The communication channel capacity then, is the upper bound on the rate at which information can be reliably transmitted.  Thus, the channel capacity is the highest information rate that can be achieved with small error probability.

This concept has been central to the development of communication systems.  Using error correction coding mechanisms, performance very close to the limits of the channel can be achieved.  Thus, the best you can do to have a low probability of error is to transmit the information at a rate that is less than or equal to the channel capacity.  This recognizes that the faster the information is sent the higher the probability of error that will occur.

So, with regard to quantum computing and using the idea of communication channel capacity, computational capacity is referring to the transaction processing capability of the systems.  Thus, the computational capacity is the idea of using imperfect components or "noisy gates" to compute some function as if there was "no noise".  Further, if the error probability of a component is less than or equal to the computational capacity, then the error probability of the circuit can be exponentially close to zero.