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.

arXiv comment12 pages, 8 figures, 37 references

References in corpus (31)

• Variational Quantum Algorithms
• Hardware-efficient Variational Quantum Eigensolver for Small Molecules and Quantum Magnets
• Solving the Quantum Many-Body Problem with Artificial Neural Networks
• Quantum computational chemistry
• Quantum Chemistry in the Age of Quantum Computing
• The power of quantum neural networks
• Quantum Monte Carlo methods for nuclear physics
• Quantum algorithms for quantum chemistry and quantum materials science
• Connecting ansatz expressibility to gradient magnitudes and barren plateaus
• Classical simulation of quantum many-body systems with a tree tensor network
• Tensor networks for complex quantum systems
• Variational ansatz-based quantum simulation of imaginary time evolution
• Hybrid quantum-classical algorithms and quantum error mitigation
• A class of ansatz wave functions for 1D spin systems and their relation to DMRG
• Variational quantum algorithms for nonlinear problems
• Towards Quantum Machine Learning with Tensor Networks
• Quantum Computation of Electronic Transitions using a Variational Quantum Eigensolver
• Accelerated Variational Quantum Eigensolver
• Lecture Notes of Tensor Network Contractions
• Parallel Quantum Simulation of Large Systems on Small Quantum Computers
• Hybrid-space density matrix renormalization group study of the doped two-dimensional Hubbard model
• Efficient variational diagonalization of fully many-body localized Hamiltonians
• Holographic quantum algorithms for simulating correlated spin systems
• A tensor network annealing algorithm for two-dimensional thermal states
• Quantum simulation with hybrid tensor networks
• Variational Quantum-Neural Hybrid Eigensolver
• Classical algorithms for quantum mean values
• Entanglement, quantum randomness, and complexity beyond scrambling
• Quantum State Complexity in Computationally Tractable Quantum Circuits
• Schrödinger-Heisenberg Variational Quantum Algorithms
• Optimization schemes for unitary tensor-network circuit

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