Noisy Quantum Simulation: Performance and Resource Considerations for the Tavis-Cummings and Heisenberg Models

TL;DR

The paper benchmarks zero-noise extrapolation (ZNE) and incremental structural learning (ISL) for digital quantum simulation of Trotterized dynamics in the Tavis–Cummings model and Heisenberg spin chain on a simulated NISQ backend. It shows that ISL typically offers superior accuracy for the Heisenberg spin chain, while ZNE provides more reliable improvements for the Tavis–Cummings model, though ISL incurs substantially higher circuit-execution overhead. The findings reveal a strong dependence of performance on Hamiltonian structure, interaction strength, and hardware connectivity, suggesting that no single mitigation strategy is universally optimal for near-term quantum simulation. The work highlights a trade-off between the deeper circuit resilience of ISL and the lower resource demands of ZNE, motivating hybrid approaches and improved optimization for scalable NISQ quantum simulations.

Abstract

Fault-tolerant quantum computers promise the simulation of complex quantum systems beyond the reach of classical computation. In contrast, current noisy intermediate-scale quantum (NISQ) devices are constrained by hardware noise. Consequently, quantum simulation methods remain limited in their near-term applicability. Two prominent techniques addressing these challenges are zero-noise extrapolation (ZNE) and incremental structural learning (ISL). In this work, ZNE and ISL are benchmarked for simulating the Trotterized time evolution of two models: the Tavis-Cummings model (TCM) and the Heisenberg spin chain (HSC), using a classically simulated noisy hardware backend. The methods are evaluated on the basis of the accuracy of expectation values relative to noiseless simulations and their resource demands such as circuit depths and shot counts. The impact of noise on optimization routines in ISL, previously underexplored, is also investigated. Results indicate that ISL performs more favorably in HSC systems, consistently surpassing ZNE in expectation value accuracy. Conversely, for the TCM, ISL generally yields lower accuracies despite reduced Trotter circuit depths, with weak interactions often leading to pronounced phase lags or flat expectation curves. Notably, when performing ISL optimization under noiseless conditions, the protocol is generally able to reduce dephasing errors, but average accuracies still vary on the simulated Hamiltonian. Our findings highlight the sensitivity of quantum simulation protocols to the structure of the Hamiltonian encoding system dynamics. Trends across systems suggest that ISL optimization benefits from Trotter circuits with stronger interactions, and that ansatz construction favors isotropic couplings. Moreover, although ISL introduces approximation errors, it demonstrates greater robustness than ZNE in systems with deeper Trotter circuits.

Figures (28)

• Figure 1: Qubit connectivity graph for the ibm_nairobi backend. Nodes represent qubits and edges indicate pairs that can perform native $\mathrm{CNOT}$ gates without $\mathrm{SWAP}$ routing.
• Figure 2: Time evolution of $\mathbb{P}(\ket{\varphi_0})$ for (a) $N = 1$, (b) $N = 2$, and (c) $N = 3$. Plain denotes plain Trotterization; other columns show results with noise reduction protocols. Each method uses $k$ shots per circuit evaluation (darker lines: higher $k$). The dotted line is the noiseless reference curve (evaluated with $k=k_\mathrm{max}$ shots).
• Figure 3: Median of the absolute error $\tilde{\varepsilon}$ over all time steps as a function of system size $N$, for the studied methods and experimental setup as in Fig. \ref{['fig:time-evolution']}. Vertical bars show the range (minimum to maximum) of absolute error observed across all time steps for each $k$.
• Figure 4: ISL recompilation cost at the end of each layer, for the main TCM parameterization, evaluated at $k_\mathrm{max}$. The rows correspond to sampled individual recompilations performed with the cost thresholds: (a) $C_{-2}$ and (b) $C_{-4}$. The color scale represents the corresponding time step. The dashed horizontal line marks the cost $C_{-2}$.
• Figure 5: Time evolution of $\mathbb{P}(|\varphi_0\rangle)$ for plain Trotterization, ZNE and ISL, for different coupling strengths and system sizes. Columns (left to right) correspond to $g=1$, $g=5$ and $g=20$, and the system sizes are (a) $N=1$ (b) $N=2$ and (c) $N=3$. The dotted line denotes the noiseless time curve. All algorithms are evaluated with $k=k_\mathrm{max}$. For ZNE reference curves, points outside the interval $[0, 1]$ have been clipped.