Energetics of Rydberg-atom Quantum Computing

TL;DR

This paper investigates the energetics of quantum computation on a Rydberg-atom platform, focusing on Quantum Phase Estimation and the Quantum Fourier Transform. It introduces a four-term energy-cost model (Baseline, Preparation, Computation, Measurement) and combines experimental implementation details with a quantitative energy assessment of gate operations, repeated runs, and readout. The study finds that while gate execution energy is modest, baseline components—especially optical traps—dominate total energy, and it derives scaling laws showing the QFT energy cost grows polynomially with the number of qubits, $O(n^3)$, in contrast to the exponential scaling of classical FFT energy. A comparative analysis with classical supercomputers suggests a potential quantum energy advantage above a threshold (around $n\approx 39$ qubits), though realistic deployments will require error-correction overheads; the work provides a framework for energy-aware benchmarking and suggests directions to reduce energy through circuit optimizations and transport-management strategies.

Abstract

Quantum computing exploits the properties of Quantum Mechanics to solve problems faster than classical computers. The potential applications of this technology have been widely explored, and extensive research over the past decades has been dedicated to developing scalable quantum computers. However, the question of the energetic performance of quantum computation has only gained attention more recently, and its importance is now recognized. In fact, quantum computers can only be a viable alternative if their energy cost scales favorably, and some research has shown that there is even a potential quantum energy advantage. Rydberg atoms have emerged recently as one of the most promising platforms to implement a large-scale quantum computer, with significant advances made in recent years. This work aims at contributing first steps to understand the energy efficiency of this platform, namely by investigating the energy consumption of the different elements of a Rydberg atom quantum computer. First, an experimental implementation of the Quantum Phase Estimation algorithm is analyzed, and an estimation of the energetic cost of executing this algorithm is calculated. Then, a potential scaling of the energy cost of performing the Quantum Fourier Transform with Rydberg atoms is derived. This analysis facilitates a comparison of the energy consumption of different elements within a Rydberg atom quantum computer, from the preparation of the atoms to the execution of the algorithm, and the measurement of the final state, enabling the evaluation of the energy expenditure of the Rydberg platform and the identification of potential improvements. Finally, we used the Quantum Fourier Transform as an energetic benchmark, comparing the scaling we obtained to that of the execution of the Discrete Fourier Transform in two state-of-the-art classical supercomputers.

Figures (7)

• Figure 1: QFT circuit. Here $R_k =R_{z}(2\pi/2^k)$. Figure taken from Nielsen_Chuang_2010.
• Figure 2: First part of the Phase Estimation algorithm. Figure taken from Nielsen_Chuang_2010.
• Figure 3: Atomic level diagram of the Cesium atom, with the laser wavelengths used for gate implementations, trapping and cooling. Figure taken from phase_estimation_implementation.
• Figure 4: Rydberg blockade. When two atoms are within a distance smaller than the Rydberg radius and interact with a radiation pulse resonant with the $\left\lvert g \right\rangle \rightarrow \left\lvert r \right\rangle$ transition, only one atom will undergo the transition. This is because the atom that transitions to the Rydberg state will shift the energy levels of the nearby atom, causing the radiation source to no longer be in resonance with the transition of the second atom.
• Figure 5: Experimental setup used in the implementation under analysis. phase_estimation_implementation