Tensor Network enhanced Dynamic Multiproduct Formulas

Abstract

Tensor networks and quantum computation are two of the most powerful tools for the simulation of quantum many-body systems. Rather than viewing them as competing approaches, here we consider how these two methods can work in tandem. We introduce a novel algorithm that combines tensor networks and quantum computation to produce results that are more accurate than what could be achieved by either method used in isolation. Our algorithm is based on multiproduct formulas (MPF) - a technique that linearly combines Trotter product formulas to reduce algorithmic error. Our algorithm uses a quantum computer to calculate the expectation values and tensor networks to calculate the coefficients used in the linear combination. We present a detailed error analysis of the algorithm and demonstrate the full workflow on a one-dimensional quantum simulation problem on $50$ qubits using two IBM quantum computers: $ibm\_torino$ and $ibm\_kyiv$.

References in corpus (4)

• The density-matrix renormalization group in the age of matrix product states
• The Future of Quantum Computing with Superconducting Qubits
• Time-evolving a matrix product state with long-ranged interactions
• Fast convergence of imaginary time evolution tensor network algorithms by recycling the environment

Cited by in corpus (5)

• Dynamical simulations of many-body quantum chaos on a quantum computer
• Deep Circuit Compression for Quantum Dynamics via Tensor Networks
• Realization of Two-dimensional Discrete Time Crystals with Anisotropic Heisenberg Coupling
• Tensor-based phase difference estimation on time series analysis
• Time evolution of controlled many-body quantum systems with matrix product operators