# Simulation-Based Evaluation of Energy-Constrained Quantum-Classical Competition

arXiv: https://arxiv.org/abs/2308.08025 · HTML: https://mlsanity.com/paper/2308.08025/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 1 of its 12 references that are in the map.
- First posted on arXiv 15 Aug 2023.

## Builds on (most cited first, 1 of 1)

- [Variational Quantum Algorithms](https://mlsanity.com/paper/2012.09265/) (2020)

## Built on by (most cited first, 1 of 1)

- [Towards identifying possible fault-tolerant advantage of quantum linear system algorithms in terms of space, time and energy](https://mlsanity.com/paper/2502.11239/) (2025)

## Abstract (arXiv)

This paper develops a simulation-based framework for evaluating the energy implications of quantum and classical computing firms competing in a market with limited energy resources. We model providers as differentiated Cournot competitors whose feasible service capacity is induced by technology-specific energy scaling laws: polylogarithmic for quantum algorithms that achieve an equivalent computational target and polynomial for classical emulation. For symmetric groups of quantum and classical firms, the equilibrium reduces to a tractable two-equation system that supports large scenario sweeps over market size, technology mix, and hardware coefficients. We characterize the capacity-constrained Nash equilibrium, prove the existence of a demand scale beyond which quantum service becomes more energy efficient, and report numerical experiments calibrated to trapped-ion and Rydberg platforms. The results identify when quantum energy advantage is only asymptotic and when it becomes operationally relevant.