Near-Optimal Quantum Time Evolution Circuits via Provably Convergent Compression

• URL: http://arxiv.org/abs/2605.17067v1
• Date: Sat, 16 May 2026 16:35:09 GMT
• Title: Near-Optimal Quantum Time Evolution Circuits via Provably Convergent Compression
• Abstract summary: Variational compression can significantly lower implementation overheads for encoding the time evolution of Hamiltonians into quantum circuits.<n>We provide a recipe for choosing the initial point of such variational optimizations that guarantees convergence to a quantum circuit.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Variational compression can significantly lower implementation overheads for encoding the time evolution of Hamiltonians into quantum circuits. However, they usually lack global convergence guarantees and well-established scaling behavior. In this work, we provide a recipe for choosing the initial point of such variational optimizations that guarantees convergence to a quantum circuit with near-optimal gate complexity $\mathcal{O}\left( N \, t \, \text{polylog}(N \, t/ε) \right)$ for all local and translationally invariant Hamiltonians. We demonstrate our method by encoding the globally controlled time evolution of a Heisenberg antiferromagnet on a Kagome lattice. For $N = 48$ sites, evolution time $t=0.1$ and infidelity $ε\approx1\%$, the controlled time-evolution circuit requires 960 two-qubit B gates, for which we propose a straightforward implementation scheme for ion-trap setups. Thereby, our recipe extends digital quantum simulators toward system sizes and geometries that are challenging for classical computation.

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