Quantum simulation of many-body dynamics with noise-robust Trotter decomposition based on symmetric structures

The Suzuki-Trotter decomposition, which digitalizes quantum time evolution, provides a promising framework for simulating quantum dynamics on quantum hardware and exploring quantum advantage over classical computation. However, conventional Trotter circuits require a large number of non-local gates, lowering their faithfulness to the ideal dynamics when implemented on current noisy quantum hardware. While most previous studies have focused on circuit optimization, we instead propose a new Trotter decomposition that is intrinsically circuit-efficient for simulating quantum dynamics on near-term devices. Our method substantially reduces both the residual error by Trotter decomposition and the number of CNOT operations compared to conventional Trotter decompositions by exploiting the symmetry of the target model to construct an effective Hamiltonian with fewer two-qubit gates. We demonstrate the noise robustness of the proposed approach through numerical simulations of a nine-site Heisenberg model under realistic noise, and further validate its experimental practicality on the IBM superconducting device, achieving a state fidelity exceeding $0.98$ when combined with quantum error mitigation in the three-site case. The proposed circuit design is also compatible with existing circuit optimization techniques. Our results establish a practical route toward noise-resilient quantum simulation in many-body dynamics.

💡 Research Summary

The paper addresses a fundamental bottleneck in digital quantum simulation: the gate overhead and Trotter error inherent in conventional Suzuki‑Trotter decompositions. While prior work has largely focused on post‑hoc circuit optimization, the authors propose a new decomposition strategy that is intrinsically more efficient by exploiting the symmetry of the target Hamiltonian, specifically the XXX Heisenberg model.

First, the authors observe that the three‑site Heisenberg block H₃ = σ₁·σ₂ + σ₂·σ₃ possesses an SU(2) symmetry generated by s_μ = –σ₁^μ⊗σ₂^μ⊗σ₃^μ. Using this symmetry, they construct an encoder unitary U_enc that maps the three‑qubit Hilbert space into a tensor product of a single‑qubit register (holding the parity quantum number P = ±1) and a two‑qubit register (encoding the energy eigenvalue E). The encoder requires only three CNOT gates. In the encoded basis, H₃ is compressed to a two‑qubit effective Hamiltonian

 H_eff = √2 (h₁ + h₂) – (σ₁ᶻ⊗σ₂ˣ + σ₁ˣ⊗σ₂ᶻ),

where h_i = (σ_i^x + σ_i^z)/√2.

The authors then apply a second‑order Strang splitting to H_eff, yielding a decomposition with an O(Δt³) error term, which is higher order than the first‑order conventional Trotter step. By partitioning the full N‑site Hamiltonian into four alternating blocks (A₁, B₁, A₂, B₂) each composed of such three‑site hyper‑edges, a single Trotter iteration consists of four exponentials of the form exp(–iA_kΔt′) and exp(–iB_kΔt′). Because each block is realized via the encoder, a two‑qubit evolution, and a decoder, the total CNOT count per four‑qubit block is reduced from the naïve 32 to 28, i.e., an average of 7 CNOTs per qubit per iteration. Moreover, the convergence analysis shows that to achieve the same residual Trotter error, the new scheme requires only m ≈ n/4 iterations, where n is the number of steps in the conventional approach. Consequently, the overall CNOT budget is reduced by a factor of 0.583 (1.75 n versus 3 n).

Numerical simulations on a nine‑site XXX Heisenberg chain confirm the theoretical predictions: the process fidelity improves markedly for a given number of CNOT gates, and the error scales more favorably with the number of Trotter steps. To demonstrate hardware relevance, the authors implement a three‑site instance on IBM’s superconducting device ibmq_jakarta. By combining the symmetry‑based decomposition with quantum error mitigation (zero‑noise extrapolation and measurement error mitigation), they achieve a state fidelity exceeding 0.98, surpassing the conventional Trotter circuit under identical conditions.

The proposed method is compatible with existing compiler‑level optimizations (e.g., Qiskit transpiler passes), allowing further reductions in depth and gate count. Limitations include the reliance on explicit SU(2) symmetry; extending the approach to models lacking such clear symmetry (e.g., Hubbard models with on‑site disorder) will require new encoding strategies. Additionally, the encoder/decoder overhead may offset gains for very small systems.

In summary, the work introduces a symmetry‑driven Hamiltonian compression combined with higher‑order Trotter splitting, delivering substantial reductions in two‑qubit gate count and Trotter error. The experimental validation on real quantum hardware, together with compatibility with standard optimization toolchains, positions this approach as a practical pathway toward noise‑resilient quantum simulation of many‑body dynamics on near‑term devices. Future directions include generalizing to other symmetry groups, incorporating dynamical error correction, and applying the technique to larger, more complex quantum many‑body models.