12.9 Is NISQ worth it?

The bulk of this book covers algorithms using logical qubits, such as those by Grover (section 9.7.1) and Shor (section 10.7). Since we do not yet have logical qubits, we must make do with physical qubits with their noise and finite (and often short) coherence times. Unlike logical qubit algorithms that may have circuit depths and qubit counts in the thousands or millions, we must make do with a few dozen gates on a few dozen to a few hundred qubits. This situation defines the NISQ era as a prelude to the “Fault-Tolerant Quantum Computing” or “FTQC” era. FTQC logical qubit qubit$logical

Here are some reasons why the development of NISQ algorithms is a good idea:

• NISQ algorithms are a practical way to learn how to characterize quantum hardware systems and improve their control software.
• Improvements in optimizing quantum transpilers for NISQ quantum algorithms will be applicable for implementing...