Andris Ambainis

Mārtiņš Kālis, Andris Locāns, Rolands Šikovs et al.

Boltzmann machine is a powerful machine learning model with many real-world applications, for example by constructing deep belief networks. Statistical inference on a Boltzmann machine can be carried out by sampling from its posterior distribution. However, uniform sampling from such a model is not trivial due to an extremely multi-modal distribution. Quantum computers have the promise of solving some non-trivial problems in an efficient manner. We explored the application of a D-Wave quantum annealer to generate samples from a restricted Boltzmann machine. The samples are further improved by Markov chains in a hybrid quantum-classical setup. We demonstrated that quantum annealer samples can improve the performance of Gibbs sampling compared to random initialization. The hybrid setup is considerably more efficient than a pure classical sampling. We also investigated the impact of annealing parameters (temperature) to improve the quality of samples. By increasing the amount of classical processing (Gibbs updates) the benefit of quantum annealing vanishes, which may be justified by the limited performance of today's quantum computers compared to classical.

Andris Ambainis, Joao F. Doriguello, Debbie Lim

We propose novel classical and quantum online algorithms for learning finite-horizon and infinite-horizon average-reward Markov Decision Processes (MDPs). Our algorithms are based on a hybrid exploration-generative reinforcement learning (RL) model wherein the agent can, from time to time, freely interact with the environment in a generative sampling fashion, i.e., by having access to a "simulator". By employing known classical and new quantum algorithms for approximating optimal policies under a generative model within our learning algorithms, we show that it is possible to avoid several paradigms from RL like "optimism in the face of uncertainty" and "posterior sampling" and instead compute and use optimal policies directly, which yields better regret bounds compared to previous works. For finite-horizon MDPs, our quantum algorithms obtain regret bounds which only depend logarithmically on the number of time steps $T$, thus breaking the $O(\sqrt{T})$ classical barrier. This matches the time dependence of the prior quantum works of Ganguly et al. (arXiv'23) and Zhong et al. (ICML'24), but with improved dependence on other parameters like state space size $S$ and action space size $A$. For infinite-horizon MDPs, our classical and quantum bounds still maintain the $O(\sqrt{T})$ dependence but with better $S$ and $A$ factors. Nonetheless, we propose a novel measure of regret for infinite-horizon MDPs with respect to which our quantum algorithms have $\operatorname{poly}\log{T}$ regret, exponentially better compared to classical algorithms. Finally, we generalise all of our results to compact state spaces.

Andris Ambainis, Ansis Rosmanis, Dominique Unruh

Quantum zero-knowledge proofs and quantum proofs of knowledge are inherently difficult to analyze because their security analysis uses rewinding. Certain cases of quantum rewinding are handled by the results by Watrous (SIAM J Comput, 2009) and Unruh (Eurocrypt 2012), yet in general the problem remains elusive. We show that this is not only due to a lack of proof techniques: relative to an oracle, we show that classically secure proofs and proofs of knowledge are insecure in the quantum setting. More specifically, sigma-protocols, the Fiat-Shamir construction, and Fischlin's proof system are quantum insecure under assumptions that are sufficient for classical security. Additionally, we show that for similar reasons, computationally binding commitments provide almost no security guarantees in a quantum setting. To show these results, we develop the "pick-one trick", a general technique that allows an adversary to find one value satisfying a given predicate, but not two.