Speaker
Description
Classical simulation of current noisy intermediate-scale quantum (NISQ) devices forwards the development of all the research directions in near-term quantum computing. While the simulation algorithms based on tensor network states can efficiently simulate a NISQ device with around 100 qubits, restricted by the real-space sequential nature of these algorithms, efficiently simulating a NISQ device with hundreds, or even thousands, of qubits remains elusive. One of the approaches to releasing this limitation is developing real-space parallelizable algorithms.
In this presentation, I will introduce a newly developed real-space parallelizable matrix-product state (MPS) compression method [1] that can efficiently compress all the virtual dimensions of the MPS in a constant time against increasing the system size and simultaneously stabilize the wavefunction norm [see Fig. 1(a)] without triggering sequential renormalization procedures. Moreover, the deviated canonical form is partially recovered by appended parallel regauging steps. Based on this method, we propose the parallel time-evolving block-decimation (pTEBD) algorithm for the simulation of unitary quantum circuits. After benchmarking the pTEBD algorithm with extensive simulations of typical one- and two-dimensional quantum circuits containing up to over 1000 qubits on Supercomputer Fugaku, we demonstrate that the pTEBD algorithm achieves the same simulation precision as compared with the current state-of-the-art MPS algorithm using a polynomially shorter time [see Fig. 1(b)], exhibiting a nearly perfect performance weak scaling [see Fig. 1(c)].
![(Adapted from [1]) Simulations of one-dimensional random quantum circuits using a sequential MPS algorithm (open circles) and the pTEBD algorithm (crosses): (a) wavefunction norm n versus circuit depth D in the simulations with a fixed number of qubits, (b) wavefunction fidelity F (representing simulation precision) versus elapsed time in the simulations with a fixed number of qubits, and (c) elapsed time versus number of qubits N in the simulations with a fixed circuit depth. \chi denotes the MPS bond dimension.](https://i.ibb.co/CBG68tF/in-talk-abst.jpg)
Reference
[1] Rong-Yang Sun, Tomonori Shirakawa, and Seiji Yunoki. "Improved real-space parallelizable matrix-product state compression and its application to unitary quantum dynamics simulation." arXiv preprint arXiv:2312.02667 (2023).
