Quantum Energetic Advantage before Computational Advantage in Boson Sampling

TL;DR

The paper investigates whether quantum energetic advantage can precede (and be observed before) quantum computational advantage in Boson Sampling by coupling hardware-level energy costs to a task-specific performance metric via the Metric-Noise-Resource framework. It derives both classical and quantum energy costs, identifies an energy-advantage regime around $M_0$ between 15 and 18, and proposes a near-term photonic architecture with a detailed noise and loss budget to experimentally demonstrate the effect. The results show that energetic efficiency can serve as a practical benchmark for quantum technologies, with photonic implementations offering orders-of-magnitude energy savings per sample compared to superconducting approaches. This work highlights energy-centric metrics as a critical design and evaluation criterion for near-term quantum devices and their potential advantage landscape.

Abstract

Understanding the energetic efficiency of quantum computers is essential for assessing their scalability and for determining whether quantum technologies can outperform classical computation beyond runtime alone. In this work, we analyze the energy required to solve the Boson Sampling problem, a paradigmatic task for quantum advantage, using a realistic photonic quantum computing architecture. Using the Metric-Noise-Resource methodology, we establish a quantitative connection between experimental control parameters, dominant noise processes, and energetic resources through a performance metric tailored to Boson Sampling. We estimate the energy cost per sample and identify operating regimes that optimize energetic efficiency. By comparing the energy consumption of quantum and state-of-the-art classical implementations, we demonstrate the existence of a quantum energetic advantage -- defined as a lower energy cost per sample compared to the best-known classical implementation -- that emerges before the onset of computational advantage, even in regimes where classical algorithms remain faster. Finally, we propose an experimentally feasible Boson Sampling architecture, including a complete noise and loss budget, that enables a near-term observation of quantum energetic advantage.

Figures (5)

• Figure 1: Proposed photonic Boson Sampling architecture for observing a quantum energetic advantage. Two quantum-dot single-photon sources operated at 3 K emit trains of single photons at a 1 GHz repetition rate. Active demultiplexers and fiber delays are used to inject up to 24 photons simultaneously into a 51-mode linear optical interferometer. The photons are detected using superconducting nanowire single-photon detectors (SNSPDs), with detection events processed by classical electronics. The architecture enables a full-stack estimation of the energy cost per generated sample, including cryogenic cooling, photon generation, interferometric processing, and detection. The end-to-end transmission and noise budget required to observe energetic advantage are detailed in Table\ref{['table:source-eff-target']}.
• Figure 2: Quantum energetic advantage preceding computational advantage in Boson Sampling. (a) Energy cost per sample for the photonic quantum device ($E^\text{Q}_\text{samples}$) and for classical simulation ($\langle E^\text{C}_\text{samples}\rangle$), shown as a function of the average performance metric $\langle M_0\rangle$. Quantum data points are colored according to the end-to-end transmission efficiency. (b) Corresponding time per sample for quantum ($t^\text{Q}_\text{samples}$ samples) and classical ($\langle t^\text{C}_\text{samples}\rangle$) implementations. The shaded region highlights the regime in which the quantum device consumes less energy per sample than the classical simulation, despite remaining slower in runtime. (c,d) Energy and time per sample as functions of the number of input photons for a realistic hardware configuration (Fig. \ref{['fig:circuit']}) with fixed per-component losses, illustrating the degradation of the metric at large system sizes when transmission is not improved.
• Figure 3: Relationship between indistinguishability and temperature. The blue dashed line represents the indistinguishability of the ZPL, given in Eq.\ref{['eq:ZPL']}, while the red line shows the effective indistinguishability considered in our model, given in Eq.\ref{['eq:ZPL-2qd']}, accounting for additional noise between distant sources.
• Figure 4: Top: Energy per sample for quantum ($E^\text{Q}_\text{samples}$) and classical ($E^\text{C}_\text{samples}$) computers as a function of the number of idealized photons $M_0$. The quantum energy per sample points are colored according to the transmission efficiency, as indicated by the color bar. Bottom: Time per sample for the quantum ($t^\text{Q}_\text{samples}$) and classical ($t^\text{C}_\text{samples}$) computers. The gray area shows the regime where the photonic quantum computer is slower but more energy efficient than the classical one.
• Figure 5: Histogram of the metrics obtained from 10,000 samples with an experimental setup of end-to-end transmission 60%, 61 modes, and 29 input photons.