The impact of noise on the simulation of NMR spectroscopy on NISQ devices

TL;DR

The paper addresses the challenge of simulating NMR spectroscopy on NISQ devices, framing the problem as a digital quantum simulation of spin-1/2 Hamiltonians and introducing a Trotterized time-evolution scheme to obtain the spin correlation function whose Fourier transform yields the spectrum. A key contribution is the effective decoherence rate $\Gamma_{\rm eff}$, which ties gate-errors and fidelities to the resolvable energy scales and provides a practical error budget for NMR simulations on noisy hardware. Experimental results on IBM Perth and IonQ Aria show noise-induced peak broadening and motivate circuit-depth reductions (e.g., nearest-neighbor truncations) and coherent-noise modeling to align simulations with observed spectra. The work offers a concrete framework for assessing and guiding application-driven quantum tasks on public cloud processors, illustrating how noise-aware circuit design can extend the usefulness of NISQ devices while outlining clear paths for future improvements as hardware fidelity improves.

Abstract

With the surge of quantum computing platforms that continue to push the boundaries of capabilities of noisy intermediate-scale quantum computers, there is a growing interest in finding relevant applications and quantifying the corresponding error budgets. We present a simulation of nuclear magnetic resonance (NMR) spectroscopy of small organic molecules on publicly available cloud quantum computers. We are using two quantum computing platforms, namely IBM's quantum processors based on superconducting qubits and IonQ's Aria trapped ion quantum computer addressed via Amazon Braket. We analyze the impact of noise on the obtained NMR spectra, and we formulate an effective decoherence rate that quantifies the threshold noise that our proposed algorithm can tolerate. We show that the effective decoherence rate can be calculated using simple fidelity metrics that are available by cloud quantum computing providers. Our investigation paves the way to better employ such application-driven quantum tasks on current noisy quantum devices.

Figures (18)

• Figure 1: NMR spectrum of the non-exchangeable protons of cis-3-chloroacrylic acid simulated on NISQ devices. The solid orange curve depicts the simulation using IBM Perth, the dash-dotted blue curve is the simulation using IonQ Aria via Amazon Braket, and the solid black curve shows the results from exact diagonalization. We have performed a time evolution for the spin Hamiltonian Eq. (\ref{['eq:2spin_ham']}) at $B=11.7~T$ with Trotter step-size of $\tau=0.01$ and 81 and 61 Trotter-steps for IBM Perth and IonQ Aria via Amazon Braket, respectively.
• Figure 2: Circuit corresponding to one Trotter step ($\tau=0.01$) of the Trotterized time evolution of the Hamiltonian Eq. (\ref{['eq:2spin_ham']}) for IBM devices with native gates CNOT, $X$, $\sqrt{X}$, and virtual $R_z$. For the 2-spin molecule, the interaction can be decomposed into three CNOT gates in the second-order Trotter expansion.
• Figure 3: (a) Spectrum of 1,2,4-trichlorobenzene ($C_6H_3Cl_3$) from experimental NMR spectroscopy NMR_data. The marked peak at approx. 7.26 ppm is known to be caused by the solvent. (b) Comparison of the simulation with exact diagonalization, shown by the solid black curve, with noise-free simulation illustrated by the dashed blue curve. For the noise-free simulation, we have used the algorithm presented in the Method section with 1000 Trotter steps of the size $\tau=0.005$.
• Figure 4: Comparison of the NMR spectrum of 1,2,4-trichlorobenzene ($C_6H_3Cl_3$) simulated on IBM Perth on two different days, depicted as the orange and green curves, with the exact results shown as the black curve. For the simulations on IBM, we have performed a time evolution with 21 Trotter steps of the size $\tau=0.005$.
• Figure 5: Comparison of the NMR spectrum of cis-3-chloroacrylic acid simulated on IBM Perth device for a varying Trotter step size, with fixed number of Trotter steps (81). The shaded area depicts the effective decoherence rate Eq. (\ref{['eq:effective_decoherence_rate']}) in ppm units.