Classical optimization algorithms for diagonalizing quantum Hamiltonians

• URL: http://arxiv.org/abs/2506.17883v1
• Date: Sun, 22 Jun 2025 03:17:56 GMT
• Title: Classical optimization algorithms for diagonalizing quantum Hamiltonians
• Authors: Taehee Ko, Sangkook Choi, Hyowon Park, Xiantao Li,
• Abstract summary: This paper introduces classical optimization algorithms for diagonalization by simulating a Hamiltonian.<n>We pinpoint a class of Hamiltonians that highlights severe drawbacks of existing methods, including exponential per-iteration, exponential circuit depth, or convergence to optima.<n>Our approach overcomes these shortcomings, achieving cost-time efficiency while avoiding spurious points.<n>On the practical side, we also present a randomized-coordinate variant that achieves a more efficient per-iteration cost than the deterministic counterpart.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Diagonalizing a Hamiltonian, which is essential for simulating its long-time dynamics, is a key primitive in quantum computing and has been proven to yield a quantum advantage for several specific families of Hamiltonians. Yet, despite its importance, only a handful of diagonalization algorithms exist, and correspondingly few families of fast-forwardable Hamiltonians have been identified. This paper introduces classical optimization algorithms for Hamiltonian diagonalization by formulating a cost function that penalizes off-diagonal terms and enforces unitarity via an orthogonality constraint, both expressed in the Pauli operator basis. We pinpoint a class of Hamiltonians that highlights severe drawbacks of existing methods, including exponential per-iteration cost, exponential circuit depth, or convergence to spurious optima. Our approach overcomes these shortcomings, achieving polynomial-time efficiency while provably avoiding suboptimal points. As a result, we broaden the known realm of fast-forwardable systems, showing that quantum-diagonalizable Hamiltonians extend to cases generated by exponentially large Lie algebras. On the practical side, we also present a randomized-coordinate variant that achieves a more efficient per-iteration cost than the deterministic counterpart. We demonstrate the effectiveness of these algorithms through explicit examples and numerical experiments.

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