# No-Regret Learning and Equilibrium Computation in Quantum Games

arXiv: https://arxiv.org/abs/2310.08473 · HTML: https://mlsanity.com/paper/2310.08473/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Oct 2023.

## Built on by (most cited first, 5 of 5)

- [A Quadratic Speedup in Finding Nash Equilibria of Quantum Zero-Sum Games](https://mlsanity.com/paper/2311.10859/) (2023)
- [Optimistic Online Learning in Symmetric Cone Games](https://mlsanity.com/paper/2504.03592/) (2025)
- [Near-Optimal Quantum Algorithms for Computing (Coarse) Correlated Equilibria of General-Sum Games](https://mlsanity.com/paper/2510.16782/) (2025)
- [Coherent Swap Regret and Channel-Proof Learning](https://mlsanity.com/paper/2606.02655/) (2026)
- [Natural Invariant Measures for Chaotic Game Dynamics: Finding Order in Chaos](https://mlsanity.com/paper/2607.21805/) (2026)

## Abstract (arXiv)

As quantum processors advance, the emergence of large-scale decentralized systems involving interacting quantum-enabled agents is on the horizon. Recent research efforts have explored quantum versions of Nash and correlated equilibria as solution concepts of strategic quantum interactions, but these approaches did not directly connect to decentralized adaptive setups where agents possess limited information. This paper delves into the dynamics of quantum-enabled agents within decentralized systems that employ no-regret algorithms to update their behaviors over time. Specifically, we investigate two-player quantum zero-sum games and polymatrix quantum zero-sum games, showing that no-regret algorithms converge to separable quantum Nash equilibria in time-average. In the case of general multi-player quantum games, our work leads to a novel solution concept, that of the {separable} quantum coarse correlated equilibria (QCCE), as the convergent outcome of the time-averaged behavior no-regret algorithms, offering a natural solution concept for decentralized quantum systems. Finally, we show that computing QCCEs can be formulated as a semidefinite program and establish the existence of entangled (i.e., non-separable) QCCEs, which are unlearnable via the current paradigm of no-regret learning.