Practical Log-Depth Quantum State Preparation and Circuit Verification via Tree Tensor Network Compilation

• URL: http://arxiv.org/abs/2605.06579v1
• Date: Thu, 07 May 2026 17:08:22 GMT
• Title: Practical Log-Depth Quantum State Preparation and Circuit Verification via Tree Tensor Network Compilation
• Abstract summary: Matrix product states provide efficient classical descriptions of quantum systems.<n>Shallow circuit constructions for loading matrix product states onto quantum computers is necessary for this to be practical on near-term hardware.<n>We present a decomposition of matrix product states to log-depth quantum circuits via a simple tree tensor network renormalisation procedure.
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• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Matrix product states provide efficient classical descriptions of quantum systems that may be useful as reference states for quantum algorithms such as quantum phase estimation and quantum-selected configuration interaction. Shallow circuit constructions for loading matrix product states onto quantum computers is necessary for this to be practical on near-term hardware. We present a decomposition of matrix product states to log-depth quantum circuits via a simple tree tensor network renormalisation procedure. Our method exposes an explicit parameter which can be used to trade a small amount of fidelity for large savings in circuit depth. We extend this decomposition to the case of matrix product operators allowing us to construct log-depth and ancilla-free circuits to calculate overlaps of the form $\left |\langleφ|U|ψ\rangle\right |^2$. In particular, we demonstrate an interpretation of these circuits as \emph{verifier circuits} with application to circuit-level device calibration.

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