Efficient quantum state preparation of multivariate functions using tensor networks

TL;DR

This paper introduces tensor network algorithms for efficient high-dimensional quantum state preparation, optimizing circuits with hardware-native gates and error considerations, demonstrated on Gaussian functions up to 17 dimensions.

Contribution

It presents a novel tensor network approach that addresses the barren plateau problem and enables accurate preparation of multivariate functions on quantum computers.

Findings

Successfully prepared a 17-dimensional Gaussian state in simulations.

Experimentally realized a 9-dimensional Gaussian on Quantinuum's H2 quantum processor.

Optimized circuits considering hardware-native gates and gate errors.

Abstract

For the preparation of high-dimensional functions on quantum computers, we introduce tensor network algorithms that are efficient with regard to dimensionality, optimize circuits composed of hardware-native gates and take gate errors into account during the optimization. To avoid the notorious barren plateau problem of vanishing gradients in the circuit optimization, we smoothly transform the circuit from an easy-to-prepare initial function into the desired target function. We show that paradigmatic multivariate functions can be accurately prepared such as, by numerical simulations, a 17-dimensional Gaussian encoded in the state of 102 qubits and, through experiments, a 9-dimensional Gaussian realized using 54 qubits on Quantinuum's H2 quantum processor.