Density matrix representation of hybrid tensor networks for noisy quantum devices

TL;DR

This paper extends hybrid tensor network methods to noisy quantum states by introducing a density matrix framework, enabling analysis of noise effects and paving the way for noise-resilient quantum simulations.

Contribution

It introduces a density matrix approach for hybrid tensor networks, allowing explicit representation and analysis of noise in quantum states.

Findings

Expectation values decay exponentially with tensor contractions

Framework enables explicit noise propagation analysis

Supports development of noise-resilient quantum algorithms

Abstract

The hybrid tensor network (HTN) method is a general framework allowing for the construction of an effective wavefunction with the combination of classical tensors and quantum tensors, i.e., amplitudes of quantum states. In particular, hybrid tree tensor networks (HTTNs) are very useful for simulating larger systems beyond the available size of the quantum hardware. However, while the realistic quantum states in NISQ hardware are highly likely to be noisy, this framework is formulated for pure states. In this work, as well as discussing the relevant methods, i.e., Deep VQE and entanglement forging under the framework of HTTNs, we investigate the noisy HTN states by introducing the expansion operator for providing the description of the expansion of the size of simulated quantum systems and the noise propagation. This framework enables the general tree HTN states to be explicitly represented and their physicality to be discussed. We also show that the expectation value of a measured observable exponentially vanishes with the number of contracted quantum tensors. Our work will lead to providing the noise-resilient construction of HTN states.