[Paper Review] Efficient tensor network simulation of IBM's Eagle kicked Ising experiment

Joseph Tindall, Matthew Fishman+2 more|arXiv (Cornell University)|Jun 26, 2023

Quantum many-body systems43 references15 citations

TL;DR

The authors perform a highly accurate classical simulation of the kicked Ising model on a heavy-hex lattice using belief-propagation-approximated tensor networks, achieving far higher accuracy than the 127-qubit IBM Eagle experiment for several observables and circuit depths.

ABSTRACT

We report an accurate and efficient classical simulation of a kicked Ising quantum system on the heavy-hexagon lattice. A simulation of this system was recently performed on a 127 qubit quantum processor using noise mitigation techniques to enhance accuracy (Nature volume 618, p.~500-505 (2023)). Here we show that, by adopting a tensor network approach that reflects the geometry of the lattice and is approximately contracted using belief propagation, we can perform a classical simulation that is significantly more accurate and precise than the results obtained from the quantum processor and many other classical methods. We quantify the tree-like correlations of the wavefunction in order to explain the accuracy of our belief propagation-based approach. We also show how our method allows us to perform simulations of the system to long times in the thermodynamic limit, corresponding to a quantum computer with an infinite number of qubits. Our tensor network approach has broader applications for simulating the dynamics of quantum systems with tree-like correlations.

Motivation & Objective

• Motivate and benchmark classical simulation against a noisy quantum device performing a kicked Ising dynamics on a heavy-hex lattice.
• Develop and apply a BP-approximated tensor network ansatz that respects lattice geometry and reflects tree-like correlations.
• Explore finite-size and infinite (thermodynamic limit) dynamics to long times, assessing the role of loop structures in accuracy.
• Quantify edge-environment separability and validate the approach against exact or high-accuracy benchmarks (where available).
• Demonstrate scalability and potential applicability of the method to other systems with locally tree-like correlations.

Proposed method

• Adopt a tensor network state (TNS) that mirrors the heavy-hex connectivity of the IBM Eagle lattice.
• Evolve the TNS via Trotterized gates using the simple-update scheme, truncating bond dimensions to a fixed χ.
• Regauge and contract the network efficiently with belief propagation, exploiting Vidal gauge with diagonal bond tensors.
• Measure observables by absorbing neighbor tensors and contracting to obtain expectation values within the Vidal gauge.
• Extend measurements to higher-weight observables using extended time evolution and Clifford circuit properties to reduce to single-site measurements under suitable evolutions.
• Investigate infinite lattice dynamics by constructing a 5-site unit cell with periodic boundary conditions and applying BP to estimate thermodynamic-limit behavior.
• Validate and compare results against exact state vector simulations on small lattices, boundary MPS methods, and independent MPS simulations when possible.

Experimental results

Research questions

• RQ1 Can belief-propagation-based tensor networks accurately simulate the dynamics of a kicked Ising model on a heavy-hex lattice with large qubit counts?
• RQ2 How does the BP approximation’s accuracy depend on system size, circuit depth, and lattice topology (loops vs. tree-like correlations)?
• RQ3 Is it feasible to extend the simulation to the thermodynamic limit (infinite lattice) and long times while maintaining accuracy?
• RQ4 How do BP-based results compare to the IBM Eagle quantum processor and other classical tensor-network methods for both low- and high-weight observables?

Key findings

• The BP-approximated TNS achieves near-exact agreement with exact simulations for small lattices and remains highly accurate for the 127-qubit problem, outperforming the quantum processor for several observables.
• For the 127-qubit system after five Trotter steps, the average magnetization can be reproduced with absolute error on the order of 1e-14, with the computation completing in under 10 seconds on a laptop.
• Higher-weight observables (weight-10 and weight-17) are recovered with substantially higher accuracy than the quantum processor, with computations completing in under 4 minutes on a laptop and requiring at most ~0.3 GB memory.
• The BP edge-environment separability improves with larger system sizes, supporting the premise that the lattice’s loops have a diminishing effect on local properties as the system grows.
• The method can simulate the infinite (thermodynamic) heavy-hex lattice, showing long-time entanglement growth that saturates in certain regimes, indicating feasibility of long-time dynamics in the thermodynamic limit.
• Cross-method validation with boundary MPS and independent MPS calculations shows strong agreement where MPS errors are small, reinforcing confidence in the BP-based results.