## Issues in Scalable Quantum Computation

### Charanjit S. Jutla

**Abstract:**

A celebrated theorem of Shor states that if quantum gates can be built to a certain constant reliability, then quantum error-correction codes can be devised that lead to scalable quantum computation. However, we argue that as opposed to classical circuits, it can not be assured that gates deeper in the quantum circuit have the same reliability as shallower gates. We introduce the notion of carrier-fidelity, which is the fidelity of the carriers of the qu-bits. For example, the qu-bit representing the spin of an electron has as it's carrier the position wave-function of the electron itself, and the polarity of a photon has its spectral-width as its carrier. As opposed to the customary notion of fidelity of the quantum state, which can be controlled using quantum error-correction, we argue that carrier-fidelity degrades with each gate and fundamentally cannot be controlled - a form of uncertainty principle. Since the reliability of a gate depends on the carrier-fidelity of the qu-bits being operated on, viable scalable quantum computation needs to address these issues. The talk will cover some aspects of quantum mechanics.