Tensor Network-Based Continuous Variable Quantum Circuit Optimization for Preparation of GKP State

• Published in: 2023 IEEE International Conference on Quantum Computing and Engineering (QCE) Vol. 2; pp. 385 - 386
• Main Authors: Nagai, Ryutaro, Tomono, Takao
• Format: Conference Proceeding
• Language: English
• Published: IEEE 17-09-2023
• Subjects: Codes; Computers; CV quantum computing; Fault tolerance; Fault tolerant systems; FTQC; GKP state; Optimization methods; Quantum system; Tensor network; Tensors
• DOI: 10.1109/QCE57702.2023.10294

Tensor networks are highly promising methods for efficiently simulating quantum systems using classical computers. In recent years, the efficiency of tensor networks has been eagerly harnessed to simulate NISQ devices in the era of quantum supremacy. However, as of now, quantum advantage with NISQ devices has not been clearly demonstrated in practical applications. This provide impetus for us to intensify our effort in fault tolerant quantum computation (FTQC). Various physical systems and schemes for FTQC have been proposed, with GKP encoding in bosonic systems being one such example. The preparation of GKP states serves as an important building block for realizing FTQC with the GKP code. We introduce tensor networks for simulating and optimizing the GKP state preparation circuit. It is known that the generation of approximated GKP states is achievable through photon counting and post-selection applied to properly prepared multimode Gaussian states. However, it requires optimization of numerous circuit parameters, which is typically computationally challenging on classical computers due to the involvement of the photon counting measurement process. We attempt to utilize tensor networks for more efficient parameter optimization. Additionally, we explore further efficient approach in terms of tensor network structure. We propose a multi-cutoff dimension approach combined with a tree tensor network structure.