Beyond Ansätze: Learning Quantum Circuits as Unitary Operators

2022/03/01 by Bálint Máté, Máté, Bálint, Bertrand Le Saux +3
Computer Science · Mathematics · #Algebraic structures and combinatorial models #FOS: Computer and information sciences #FOS: Physical sciences #Machine Learning (cs.LG) #Quantum Computing Algorithms and Architecture #Quantum Physics (quant-ph) #Stochastic Gradient Optimization Techniques

paper · pdf · doi:10.48550/arxiv.2203.00601

openalex publication_date 2022/03/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper explores the advantages of optimizing quantum circuits on N wires as operators in the unitary group U(2^N). We run gradient-based optimization in the Lie algebra \mathfrak u(2^N) and use the exponential map to parametrize unitary matrices. We argue that U(2^N) is not only more general than the search space induced by an ansatz, but in ways easier to work with on classical computers. The resulting approach is quick, ansatz-free and provides an upper bound on performance over all ansätze on N wires.

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