arXiv subjects

Mikhail Mints

Publications and source records attributed to Mikhail Mints.

3 recordsLinked to original sources

arXiv2026

The Quantum Overlap Gap Property and Algorithmic Hardness for the Quantum Hypergraph Max-Cut Problem

In this work, we analyze the average-case hardness of approximation for the Quantum Hypergraph Max-Cut problem using the theoretical framework of the Quantum Overlap Gap Property (QOGP). We establish two main results. Our first result applies to a wide class of stable quantum algorithms, satisfying a Lipschitz property with respect to the quantum Wasserstein distance of order $2$. We show a weak hardness result, demonstrating that for any Lipschitz constant $L$, there is some $k$ such that $L$-stable algorithms cannot approximate the optimal solution to Quantum Hypergraph Max-Cut on $k$-uniform hypergraphs in the average case. Additionally, we establish a strong hardness result where $k$ is independent of $L$, but only for a more restricted class of local quantum algorithms defined using the quantum Wasserstein distance of order $\infty$. We apply these results to establish concrete depth lower bounds for popular quantum algorithms for preparing near-optimal states for this problem.

quant-ph↗

arXiv2025

Fragmentation is Efficiently Learnable by Quantum Neural Networks

In certain classes of physical quantum systems, the exponentially large state space "fragments" into many low-dimensional, dynamically disconnected subspaces. We introduce a learning problem known as fragment classification, where given a quantum state input, one is interested in classifying to which subspace the state belongs. We prove that solving this learning problem is efficient on a quantum computer when the fragmentation phenomenon satisfies certain conditions. Furthermore, we give evidence supporting the classical hardness of this task by demonstrating that known dequantization techniques fail for the fragment classification problem. Consequently, this work provides a rare example of a physically motivated quantum machine learning task that is both efficient for quantum computers to perform and admits no known classical dequantization.

quant-ph↗

arXiv2025

Compositional Quantum Control Flow with Efficient Compilation in Qunity

Most existing quantum programming languages are based on the quantum circuit model of computation, as higher-level abstractions are particularly challenging to implement - especially ones relating to quantum control flow. The Qunity language, proposed by Voichick et al., offered such an abstraction in the form of a quantum control construct, with great care taken to ensure that the resulting language is still realizable. However, Qunity lacked a working implementation, and the originally proposed compilation procedure was very inefficient, with even simple quantum algorithms compiling to unreasonably large circuits. In this work, we focus on the efficient compilation of high-level quantum control flow constructs, using Qunity as our starting point. We introduce a wider range of abstractions on top of Qunity's core language that offer compelling trade-offs compared to its existing control construct. We create a complete implementation of a Qunity compiler, which converts high-level Qunity code into the quantum assembly language OpenQASM 3. We develop optimization techniques for multiple stages of the Qunity compilation procedure, including both low-level circuit optimizations as well as methods that consider the high-level structure of a Qunity program, greatly reducing the number of qubits and gates used by the compiler.

cs.PL↗