Tensor-network-assisted variational quantum algorithm

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.

12 pages, 8 figures, 37 references

References in corpus (5)

• Hybrid quantum-classical algorithms and quantum error mitigation
• Quantum Computation of Electronic Transitions using a Variational Quantum Eigensolver
• Hybrid-space density matrix renormalization group study of the doped two-dimensional Hubbard model
• Variational Quantum-Neural Hybrid Eigensolver
• Schrödinger-Heisenberg Variational Quantum Algorithms

Cited by in corpus (6)

• Measurement-based infused circuits for variational quantum eigensolvers
• Hybrid Tree Tensor Networks for quantum simulation
• Matrix product state ansatz for the variational quantum solution of the Heisenberg model on Kagome geometries
• Variational LOCC-assisted quantum circuits for long-range entangled states
• Utility-Scale Quantum State Preparation: Classical Training using Pauli Path Simulation
• A quantum eigenvalue solver based on tensor networks