Quantum State Preparation via Schmidt Spectrum Optimisation

TL;DR

This paper presents a novel algorithm using Schmidt spectrum optimization to efficiently prepare many-body quantum states as Matrix Product States with shallow circuits suitable for near-term quantum hardware.

Contribution

It introduces a systematic method for designing shallow-depth quantum circuits for MPS state preparation by optimizing local unitaries based on Schmidt spectra.

Findings

Achieves state-of-the-art accuracy in MPS ground state approximation

Reduces circuit depth while maintaining entanglement structure

Mitigates time-complexity scaling issues in disentangling approaches

Abstract

We introduce an efficient algorithm for the systematic design of shallow-depth quantum circuits capable of preparing many-body quantum states represented as Matrix Product States (MPS). The proposed method leverages Schmidt spectrum optimization (SSO) to minimize circuit depth while preserving the entanglement structure inherent to MPS representations, thereby enabling scalable state preparation on near-term quantum hardware. The core idea is to \textit{disentangle} the target MPS using a sequence of optimised local unitaries, and then reverse this process to obtain a state preparation circuit. Specifically, we define a loss function directly on the Schmidt spectra of intermediate states and use automatic differentiation to optimise each circuit layer so as to systematically reduce entanglement entropy. Once a disentangling sequence has been learned, we take the adjoints of the optimised unitaries to obtain a shallow-depth circuit that approximately reconstructs the target MPS from the computational all-zero state. We benchmark SSO across a range of MPS approximations to the ground states of local Hamiltonians and demonstrate state-of-the-art shallow-depth performance, improving accuracy by up to an order of magnitude over existing methods. Finally, we provide numerical evidence that SSO mitigates the adverse time-complexity scaling observed in previous disentangling-based approaches.