Tensor-network-assisted variational quantum algorithm

TL;DR

This paper introduces a tensor-network-assisted variational quantum algorithm that enhances the expressivity of shallow quantum circuits, enabling efficient solutions to complex quantum many-body problems on near-term devices.

Contribution

It proposes a novel framework combining tensor networks with quantum circuits, significantly improving their expressivity without increasing circuit depth.

Findings

Enhanced circuit expressivity demonstrated through numerical simulations.

Efficient implementation of tensor-network-assisted circuits for specific models.

Outperforms conventional shallow quantum circuit methods in experiments.

Abstract

Near-term quantum devices generally suffer from shallow circuit depth and hence limited expressivity due to noise and decoherence. To address this, we propose tensor-network-assisted parametrized quantum circuits, which concatenate a classical tensor-network operator with a quantum circuit to effectively increase the circuit's expressivity without requiring a physically deeper circuit. We present a framework for tensor-network-assisted variational quantum algorithms that can solve quantum many-body problems using shallower quantum circuits. We demonstrate the efficiency of this approach by considering two examples of unitary matrix-product operators and unitary tree tensor networks, showing that they can both be implemented efficiently. Through numerical simulations, we show that the expressivity of these circuits is greatly enhanced with the assistance of tensor networks. We apply our method to two-dimensional Ising models and one-dimensional time-crystal Hamiltonian models with up to 16 qubits and demonstrate that our approach consistently outperforms conventional methods using shallow quantum circuits.