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

TL;DR

This paper introduces a method to decompose matrix product states into log-depth quantum circuits using tree tensor networks, enabling efficient state preparation and verification on near-term quantum hardware.

Contribution

It presents a novel decomposition technique for matrix product states into shallow circuits and extends it to matrix product operators for overlap calculations.

Findings

Enables log-depth, ancilla-free circuits for quantum state loading.

Provides a method to trade fidelity for circuit depth savings.

Demonstrates applications in circuit verification and device calibration.

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 $\left |\langle\phi|U|\psi\rangle\right |^2$. In particular, we demonstrate an interpretation of these circuits as \emph{verifier circuits} with application to circuit-level device calibration.