Māris Ozols

Sofiene Jerbi, Arjan Cornelissen, Māris Ozols et al.

Understanding the power and limitations of quantum access to data in machine learning tasks is primordial to assess the potential of quantum computing in artificial intelligence. Previous works have already shown that speed-ups in learning are possible when given quantum access to reinforcement learning environments. Yet, the applicability of quantum algorithms in this setting remains very limited, notably in environments with large state and action spaces. In this work, we design quantum algorithms to train state-of-the-art reinforcement learning policies by exploiting quantum interactions with an environment. However, these algorithms only offer full quadratic speed-ups in sample complexity over their classical analogs when the trained policies satisfy some regularity conditions. Interestingly, we find that reinforcement learning policies derived from parametrized quantum circuits are well-behaved with respect to these conditions, which showcases the benefit of a fully-quantum reinforcement learning framework.

Liam J. Bond, Jiří Minář, Māris Ozols et al.

We investigate Permutation-Invariant (PI) quantum error-correcting codes encoding a logical qudit of dimension $\mathrm{d}_\mathrm{L}$ in PI states using physical qudits of dimension $\mathrm{d}_\mathrm{P}$. We extend the Knill--Laflamme (KL) conditions for $d-1$ deletion errors from qubits to qudits and investigate numerically both qubit ($\mathrm{d}_\mathrm{L} = \mathrm{d}_\mathrm{P} = 2$) and qudit ($\mathrm{d}_\mathrm{L} > 2$ or $\mathrm{d}_\mathrm{P} > 2$) PI codes. We analyze the scaling of the block length $n$ in terms of the code distance $d$, and compare to existing families of PI codes due to Ouyang, Aydin--Alekseyev--Barg (AAB) and Pollatsek--Ruskai (PR). Our three main findings are: (i) We conjecture that qubit PI codes correcting up to $d-1$ deletion errors have block length $n(d) \geq (3d^2 + 1) / 4$, which implies an upper bound $d \leq \sqrt{12n-3}/3$ on their code distance, and that PR codes can saturate this bound. (ii) For qudit PI codes encoding a single qudit we numerically observe that increasing $\mathrm{d}_\mathrm{P}$ results in $n$ monotonically decreasing and approaching the quantum Singleton bound $n(d) \geq 2d-1$. (iii) We propose a semi-analytic extension of the qubit AAB construction to qudits that finds explicit solutions by solving a linear program. Our results therefore provide key insights into lower bounds on the block length scaling of both qubit and qudit PI codes, and demonstrate the benefit of increased physical local dimension in the context of PI codes.