Learning the Complexity of Weakly Noisy Quantum States
Authors: Yusen Wu, Bujiao Wu, Yanqi Song, Xiao Yuan, Jingbo Wang
ICLR 2025 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Here, we demonstrate how to use the proposed learning method to benchmark the capabilities of noisy state computation, providing numerical evidence to support our theoretical findings. Specifically, we address the fundamental question: Does the complexity of weakly noisy quantum states grow linearly with circuit depth? We consider to simulate the time dynamics of the Hamiltonian... In the numerical simulation, we demonstrated our algorithm on a server with 64 v CPUs and 128 Gi B of memory, where the density matrix ρTI( R, p) and classical shadow set are prepared by the Pennylane package (Bergholm et al., 2018). Figure 2: (a) Visualization of the 2D transverse field Ising model. (b)-(d) illustrate the trend of the function min β LR as it varies with the circuit depth R of QCA set. |
| Researcher Affiliation | Academia | 1 School of Artificial Intelligence, Beijing Normal University, Beijing, 100875, China 2 Department of Physics, The University of Western Australia, Perth, WA 6009, Australia 3 Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China 4 International Quantum Academy, Shenzhen 518048, China 5 Dahlem Center for Complex Quantum Systems, Freie Universit at Berlin, 14195 Berlin, Germany 6 Center on Frontiers of Computing Studies, Peking University, Beijing 100871, China 7 China Academy of Information and Communications Technology, Beijing, 100191, China EMAIL, EMAIL |
| Pseudocode | Yes | Details are provided in Alg. 1. Algorithm 1: Quantum Learning Algorithm for Limited-Structured Complexity Prediction Input : Noisy quantum state ρun, ϵ; Output: The minimum depth R (R < log n) such that Clim,A ϵ (ρun) LR (True); False if such R does not exist; Or return True/False arbitrarily for invalid cases; 1 Initialize R 1, s log(n); 2 while s R > 1 do ... (Algorithm steps continue) Algorithm 2: Bayesian Maximize Subroutine, BMax S(ρun, ˆρQCA(R, A, N), T, ϵ) |
| Open Source Code | No | This work is essentially a theoretical research, and the algorithm has not yet been explicitly tested on these practical platforms. |
| Open Datasets | No | We consider to simulate the time dynamics of the Hamiltonian H = J P i,j Zi Zj + h P i Xi on a two-dimensional grid with (a b) size... We focus on a small-scale scenario studied in Ref. (Kim et al., 2023), where the system size is 3 × 4, angle rotations 2Jδt = π/2, hδt {π/8, π/4, π/2, 3π/4, π} and each quantum gate is affected by a local depolarizing channel Ei with strength p = 10-3. |
| Dataset Splits | No | The paper describes generating a weakly noisy quantum state through simulation and numerically evaluating it. It does not refer to a static dataset that would require train/test/validation splits. Instead, it describes parameters for generating quantum states and simulating their dynamics. |
| Hardware Specification | Yes | In the numerical simulation, we demonstrated our algorithm on a server with 64 v CPUs and 128 Gi B of memory, where the density matrix ρTI( R, p) and classical shadow set are prepared by the Pennylane package (Bergholm et al., 2018). |
| Software Dependencies | No | In the numerical simulation, we demonstrated our algorithm on a server with 64 v CPUs and 128 Gi B of memory, where the density matrix ρTI( R, p) and classical shadow set are prepared by the Pennylane package (Bergholm et al., 2018). |
| Experiment Setup | Yes | We consider to simulate the time dynamics of the Hamiltonian H = J P i,j Zi Zj + h P i Xi on a two-dimensional grid with (a b) size... where the system size is 3 × 4, angle rotations 2Jδt = π/2, hδt {π/8, π/4, π/2, 3π/4, π} and each quantum gate is affected by a local depolarizing channel Ei with strength p = 10-3. Let R = τ/δt , then we denote the output quantum weakly noisy state as ρTI( R, p) = R r=1 [Ep UZZ Ep UX] (|0n 0n|)... To estimate the lower bound, we thus set a small error (ϵ = 10-2)7 and randomly generate N = n2R quantum circuits with varying circuit depths R {2, 3, 4, 5} based on the architecture A. Precisely, we tune the linear coefficient β to minimize the metric functions outlined in Lemma 2, as depicted in Figure 2, where each point represents the mean value of min β LR by repeating 10 independent experiments, and the error bar represents the standard variance. |