  Energy consumption in solving computational problems has been gaining growing
attention as a part of the performance measures of computers. Quantum
computation is known to offer advantages over classical computation in terms of
various computational resources; however, its advantage in energy consumption
has been challenging to analyze due to the lack of a theoretical foundation to
relate the physical notion of energy and the computer-scientific notion of
complexity for quantum computation with finite computational resources. To
bridge this gap, we introduce a general framework for studying the energy
consumption of quantum and classical computation based on a computational model
that has been conventionally used for studying query complexity in
computational complexity theory. With this framework, we derive an upper bound
for the achievable energy consumption of quantum computation. We also develop
techniques for proving a nonzero lower bound of energy consumption of classical
computation based on the energy-conservation law and Landauer's principle. With
these general bounds, we rigorously prove that quantum computation achieves an
exponential energy-consumption advantage over classical computation for solving
a specific computational problem, Simon's problem. Furthermore, we clarify how
to demonstrate this energy-consumption advantage of quantum computation in an
experimental setting. These results provide a fundamental framework and
techniques to explore the physical meaning of quantum advantage in the
query-complexity setting based on energy consumption, opening an alternative
way to study the advantages of quantum computation.
