Tensor Network enhanced Dynamic Multiproduct Formulas

• URL: http://arxiv.org/abs/2407.17405v3
• Date: Tue, 8 Oct 2024 14:14:53 GMT
• Title: Tensor Network enhanced Dynamic Multiproduct Formulas
• Authors: Niall F. Robertson, Bibek Pokharel, Bryce Fuller, Eric Switzer, Oles Shtanko, Mirko Amico, Adam Byrne, Andrea D'Urbano, Salome Hayes-Shuptar, Albert Akhriev, Nathan Keenan, Sergey Bravyi, Sergiy Zhuk,
• Abstract summary: We introduce a novel algorithm that combines tensor networks and quantum computation to produce results 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. 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.
• Score: 2.3249255788359813
• License: http://creativecommons.org/licenses/by/4.0/
• 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 $ibm\_kyiv$.

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