arXiv subjects

Mahtab Yaghubi Rad

Publications and source records attributed to Mahtab Yaghubi Rad.

3 recordsLinked to original sources

arXiv2025

Computational complexity of the homology problem with orientable filtration: MA-completeness

We show the existence of an MA-complete homology problem for a certain subclass of simplicial complexes. The problem is defined through a new concept of orientability of simplicial complexes that we call a "uniform orientable filtration", which is related to sign-problem freeness in homology. The containment in MA is achieved through the design of new, higher-order random walks on simplicial complexes associated with the filtration. For the MA-hardness, we design a new gadget with which we can reduce from an MA-hard stoquastic satisfiability problem. Therefore, our result provides the first natural MA-complete problem for higher-order random walks on simplicial complexes, combining the concepts of topology, persistent homology, and quantum computing.

quant-ph↗

arXiv2025

Quantum Advantage in Learning Quantum Dynamics via Fourier coefficient extraction

One of the key challenges in quantum machine learning is finding relevant machine learning tasks with a provable quantum advantage. A natural candidate for this is learning unknown Hamiltonian dynamics. Here, we tackle the supervised learning version of this problem, where we are given random examples of the inputs to the dynamics as classical data, paired with the expectation values of some observable after the time evolution, as corresponding output labels. The task is to replicate the corresponding input-output function. We prove that this task can yield provable exponential classical-quantum learning advantages under common complexity assumptions in natural settings. To design our quantum learning algorithms, we introduce a new method, which we term \textit{\subroutine}~algorithm for parametrized circuit functions, and which may be of independent interest. Furthermore, we discuss the limitations of generalizing our method to arbitrary quantum dynamics while maintaining provable guarantees. We explain that significant generalizations are impossible under certain complexity-theoretic assumptions, but nonetheless, we provide a heuristic kernel method, where we trade-off provable correctness for broader applicability.

quant-ph↗

arXiv2024

Universal approximation of continuous functions with minimal quantum circuits

The conventional paradigm of quantum computing is discrete: it utilizes discrete sets of gates to realize bitstring-to-bitstring mappings, some of them arguably intractable for classical computers. In parameterized quantum approaches, the input becomes continuous and the output represents real-valued functions. While the universality of discrete quantum computers is well understood, basic questions remained open in the continuous case. We focus on universality on multivariate functions. Current approaches require either a number of qubits scaling linearly with the dimension of the input for fixed encodings, or a tunable encoding procedure in single-qubit circuits. The question of whether universality can be reached with a fixed encoding and sub-linearly many qubits remained open for the last five years. In this paper, we answer this question in the affirmative for arbitrary multivariate functions. We provide two methods: (i) a single-qubit circuit where each coordinate of the arguments to the function to represent is input independently, and (ii) a multi-qubit approach where all coordinates are input in one step, with number of qubits scaling logarithmically with the dimension of the argument of the function of interest. We view the first result of inherent and fundamental interest, whereas the second result opens the path towards representing functions whose arguments are densely encoded in a unitary operation, possibly encoding for instance quantum processes.

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