  In the race to build scalable quantum computers, minimizing the resource
consumption of their full stack to achieve a target performance becomes
crucial. It mandates a synergy of fundamental physics and engineering: the
former for the microscopic aspects of computing performance, and the latter for
the macroscopic resource consumption. For this we propose a holistic
methodology dubbed Metric-Noise-Resource (MNR) able to quantify and optimize
all aspects of the full-stack quantum computer, bringing together concepts from
quantum physics (e.g., noise on the qubits), quantum information (e.g.,
computing architecture and type of error correction), and enabling technologies
(e.g., cryogenics, control electronics, and wiring). This holistic approach
allows us to define and study resource efficiencies as ratios between
performance and resource cost. As a proof of concept, we use MNR to minimize
the power consumption of a full-stack quantum computer, performing noisy or
fault-tolerant computing with a target performance for the task of interest.
Comparing this with a classical processor performing the same task, we identify
a quantum energy advantage in regimes of parameters distinct from the commonly
considered quantum computational advantage. This provides a previously
overlooked practical argument for building quantum computers. While our
illustration uses highly idealized parameters inspired by superconducting
qubits with concatenated error correction, the methodology is universal -- it
applies to other qubits and error-correcting codes -- and provides
experimenters with guidelines to build energy-efficient quantum processors. In
some regimes of high energy consumption, it can reduce this consumption by
orders of magnitudes. Overall, our methodology lays the theoretical foundation
for resource-efficient quantum technologies.
