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

TL;DR

Problem: conventional Trotterization faces large circuit depth and noise on near-term devices. The authors introduce a symmetry-based decomposition for the XXX Heisenberg model that compresses a three-site block into a two-qubit effective Hamiltonian $H_{eff}$ using an encoder $U_{enc}$ so that $exp(-i H_3 Delta t') = U_{enc}^dagger exp(-i H_{eff} Delta t') U_{enc}$. The key contributions are a residual-error reduction by about a factor of four at equal iterations, a reduction in two-qubit gate count, and validation via nine-site numerics and three-site IBM experiments achieving fidelities up to around 0.98 with quantum error mitigation. The work demonstrates a practical route toward noise-resilient quantum dynamics simulation and lays groundwork for applying similar symmetry-based encodings to other symmetric mappings such as those from Jordan-Wigner transformations to electronic structure problems.

Abstract

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.

Figures (12)

• Figure 1: The schematic illustration of the proposed framework. In simulating the time evolution of a given Hamiltonian, we exploit its symmetric structure to construct Trotter blocks with a faster convergence rate and fewer CNOT gates based on the effective Hamiltonian.
• Figure 2: The quantum circuit of the unitary operator in Eq. \ref{['eq:unitprop']}.
• Figure 3: The quantum circuit of the time evolution operator using the Trotter decomposition in Eq. \ref{['eq:Suzuki_Trotter']} for the $5$-site system. The operation corresponding to the propagation of each single time step $\Delta t$ is enclosed by a dashed box.
• Figure 4: (a) The schematic illustration of the conventional Trotter decomposition that takes non-commutative Trotter blocks with propagator $\hat{u}(\Delta t)$ according to the native edge structure of the given Hamiltonian. (b) The schematic illustration of the proposed Trotter decomposition that takes non-commutative Trotter blocks with propagator $\hat{U}_{\mathrm{enc}}^{\dagger}\exp\left(-\mathrm{i}\hat{H}_{\mathrm{eff}}\Delta t^{\prime}\right)\hat{U}_{\mathrm{enc}}$ according to the hyper-edge of the set with three neighboring vertices in the given Hamiltonian.
• Figure 5: The quantum circuit to realize the encoder $\hat{U}_{\mathrm{enc}}$.