Efficient tensor network simulation of IBM's largest quantum processors

TL;DR

We address the challenge of classically simulating IBM's largest superconducting quantum processors by modeling a kicked Ising dynamics on heavy-hex lattices and applying graph-based PEPS. The main approach is to adapt gPEPS with simple update to finite lattices and the thermodynamic limit, enabling efficient real-time evolution with bond dimension $\chi$. The key findings are that gPEPS achieves high accuracy (often surpassing the native quantum hardware for certain observables at comparable sizes) and scales to 433, 1121 qubits and beyond, with long-time evolution showing convergence with $\chi$ due to the lattice's local structure. The significance lies in providing a scalable classical benchmark and a scalable tool for simulating lattice-based quantum processors, informing both hardware design and error mitigation strategies, with potential applicability to other architectures.

Abstract

We show how quantum-inspired 2d tensor networks can be used to efficiently and accurately simulate the largest quantum processors from IBM, namely Eagle (127 qubits), Osprey (433 qubits) and Condor (1121 qubits). We simulate the dynamics of a complex quantum many-body system -- specifically, the kicked Ising experiment considered recently by IBM in Nature 618, p. 500-505 (2023) -- using graph-based Projected Entangled Pair States (gPEPS), which was proposed by some of us in PRB 99, 195105 (2019). Our results show that simple tensor updates are already sufficient to achieve very large unprecedented accuracy with remarkably low computational resources for this model. Apart from simulating the original experiment for 127 qubits, we also extend our results to 433 and 1121 qubits, and for evolution times around 8 times longer, thus setting a benchmark for the newest IBM quantum machines. We also report accurate simulations for infinitely-many qubits. Our results show that gPEPS are a natural tool to efficiently simulate quantum computers with an underlying lattice-based qubit connectivity, such as all quantum processors based on superconducting qubits.

Figures (8)

• Figure 1: (Color online) Different heavy-hexagon lattices, corresponding to the topology of qubit connectivity of three IBM quantum processors: (a) Eagle, with 127 qubits; (b) Osprey, with 433 qubits; (c) Condor, with 1121 qubits. Every dot in the lattices corresponds to a superconducting qubit, and every link corresponds to a qubit-qubit coupling.
• Figure 2: (Color online) Comparing the gPEPS method in simulating the kicked transverse field Ising model against the 127-qubit IBM Eagle quantum processor and various other tensor network methods. The operator expectation values shown in (a) Average Magnetization, (b) Weight-10 observable, and (c) Weight-17 observable, are computed with respect to the state $|\psi(\theta_h,5)\rangle$. Each bottom plot shows the absolute difference between the light-cone based exact results and the results obtained through simulations (gPEPS and Eagle processor). Labelling of qubits is done sequentially, from left to right and top to bottom, starting with 0.
• Figure 3: (Color online) Comparison of the gPEPS simulation with higher number of trotter steps with the Eagle quantum processor and various other tensor network methods. (a) Weight-17 observable computed after 6 trotter steps with respect to the state $|\psi(\theta_h,6)\rangle$. The bottom plot shows the absolute difference between our simulation and the available exact result. (b) Weight-1 expectation value computed after 20 trotter steps with respect to the state $|\psi(\theta_h,20)\rangle$. Because of the absence of exact result for this simulation, we have computed the absolute difference between our simulation and the BP-approximation tensor network state approach with $\chi\rightarrow \infty$, presented in the bottom subplot. (c) Finite-entanglement scaling of Weight-1 observable expectation value $\langle \psi(\theta_h,20)| Z_{62} |\psi(\theta_h,20) \rangle$ with respect to the inverse of bond dimension ($1/\chi$) for two distinct $\theta_h$ values. Labeling of qubits is done sequentially, from left to right and top to bottom, starting with 0.
• Figure 4: (Color online) Results of simulating various IBM quantum chips with higher number of qubits using gPEPS: Eagle processor with 127 qubits, Osprey with 433 qubits, Condor with 1121 qubits, and the heavy-hexagon lattice in thermodynamic limit. (a) Average magnetization, (b) Weight-10 observable near the open edge, (c) Weight-17 observable deep inside the bulk. The structure of the Weight-10 and Weight-17 observables is discussed in (Appendix.\ref{['sec:weight-N']}).
• Figure 5: (Color online) Long time evolution of the magnetization for a site in the bulk at $\theta_h = 1.0$ and the three different sizes: (a) 127 qubits, up to $\chi = 560$ and 39 Trotter steps, (b) 433 qubits, up to $\chi = 370$ and 38 Trotter steps, (c) 1121 qubits, up to $\chi = 270$ and 37 Trotter steps. Lower panel shows relative errors with respect to the maximum achievable bond dimension.