  Optimization of circuits is an essential task for both quantum and classical
computers to improve their efficiency. In contrast, classical logic
optimization is known to be difficult, and a lot of heuristic approaches have
been developed so far. In this study, we define and construct a quantum
algorithmic primitive called quantum circuit unoptimization, which makes a
given quantum circuit complex by introducing some redundancies while preserving
circuit equivalence, i.e., the inverse operation of circuit optimization. Using
quantum circuit unoptimization, we propose the quantum circuit equivalence
test, a decision problem contained both in the NP and BQP classes but is not
trivially included in the P class. Furthermore, as a practical application, we
construct concrete unoptimization recipes to generate compiler benchmarks and
evaluate circuit optimization performance using Qiskit and Pytket. Our
numerical simulations demonstrate that quantum circuit unoptimizer
systematically generates redundant circuits that are challenging for compilers
to optimize, which can be used to compare the performance of different
compilers and improve them. We also offer potential applications of quantum
circuit unoptimization, such as generating quantum advantageous machine
learning datasets and quantum computer fidelity benchmarks.
