Large-scale NMR simulation on a trapped-ion quantum computer

AI summary

Overview

Research area: Quantum simulation of chemistry — specifically digital quantum simulation of liquid-state nuclear magnetic resonance (NMR) spectra on trapped-ion hardware.

Technical level: Advanced. The paper assumes familiarity with spin Hamiltonians, Trotterization, Pauli decomposition, and trapped-ion gate sets, though the spectroscopic goal is stated plainly.

Scope: An end-to-end demonstration on Quantinuum's H2-1 trapped-ion device that computes the proton NMR spectrum of the 22-spin molecule 1,2-di-tert-butyl-diphosphane using a reduced 21-spin Hamiltonian, 70 Trotter steps, and a tailored error-suppression stack.

What This Paper Is About

NMR spectroscopy reveals molecular structure by probing how nuclear spins interact, but predicting a full spectrum classically becomes exponentially hard as the number of coupled spins grows — even though optimized classical methods exploit approximations that scale linearly or polynomially with spin count. The authors ask whether a present-day quantum computer can reproduce a classically challenging benchmark spectrum accurately enough to capture chemically meaningful features. They target diphosphane, a heteronuclear 22-spin system (two ³¹P and twenty ¹H nuclei) whose proton spectrum previously could not be fully reproduced on quantum hardware.

Key Contributions

1. An end-to-end large-scale NMR simulation on trapped-ion hardware. The authors run a complete workflow on Quantinuum H2-1 in which time-domain correlation functions are generated on the device and then processed with standard Fourier-based NMR analysis to produce a liquid-state proton spectrum.

2. A hardware-efficient reduction of the spin Hamiltonian. The two-phosphorus subsystem is transformed into the singlet–triplet basis and projected onto the {|S⟩, |T₀⟩} subspace, replacing two phosphorus spins with one effective qubit. This reduces the model from 22 to 21 effective spins and cuts the two-qubit gate count per Trotter step from 69 (full model, 23 isotropic Heisenberg couplings) to 20 effective X̂₀Ẑⱼ couplings. The reduction is performed at the operator level, without constructing the full Hilbert space.

3. A three-part error-suppression strategy for deep circuits. Pauli twirling implemented as echo compiling (Trotter steps deterministically cycled through Î, X̂, Ŷ, Ẑ variants), server-side dynamical decoupling with the default 0.03 s idle threshold, and leakage-detection gadgets using one ancilla qubit per system qubit with post-selection.

4. Reproduction of a spectral feature that earlier hardware missed. The H2-1 spectrum captures the weaker double-peak structure in the 3.9–4.3 ppm region, which the authors state was not observed in previous quantum hardware demonstrations or in simple classical clustering approaches.

Main Findings

• The double-peak structure near 4.1 ppm is reproduced. The authors emphasize that this agreement is not merely a byproduct of line broadening: benchmarking against the Spinach software package indicates that reproducing the double-peak structure, even without resolving full multiplet fine structure, requires coupled-spin correlation effects up to fourth order.

• The dominant methyl peak near 1.35 ppm is reproduced, along with the overall shape of the classical reference spectrum when compared at matched (limited) resolution.

• Two sharp peaks are missing. Because the H2-1 simulation uses the projected Hamiltonian while the classical reference uses the full 22-spin Hamiltonian, the hardware spectrum lacks two sharp peaks in the proton region from 3.3 to 4.9 ppm, which originate from spectral contributions removed by the projection.

• Resolution is finite-time limited. With 70 Trotter steps at Δt = 0.42 ms, the maximum sampled free-induction-decay duration is 29.4 ms, giving roughly 0.07 ppm resolution at 500 MHz — too coarse to resolve the ~0.01 ppm fine structure visible in the classical reference. Resolving it would need T_max ∼ 200 ms and over 500 Trotter steps.

• Memory error is the dominant noise channel. Emulator studies identified coherent phase accumulation and decoherence during idle periods as the leading error source on the H2-1 device, motivating the dynamical decoupling and twirling.

• Circuit scale. The experiment used 21 system qubits plus 21 ancilla qubits, 70 Trotter steps (plus an initial t = 0 step), 10 initial states, and X/Y-basis measurements, for 1420 circuits (71 × 10 × 2) and 35,500 total shots (500 per Trotter step before leakage post-selection; 25 shots per circuit). The largest circuits reached a two-qubit gate depth of 1442, which the authors describe as among the deepest circuits yet executed for an NMR simulation on quantum hardware.

• Shot noise is comparatively benign. Parameter sweeps over 37 ≤ N_t ≤ 82 and 20 ≤ N_shot ≤ 100 on the H2-1E emulator indicated it was better to reduce shots and increase Trotter steps, since the spectrum was relatively robust to shot noise; the noiseless benchmark used N_t = 100 and N_shot = 1000 and was described as not fully converged.

Methodology in Plain English

The team started from the known spin Hamiltonian of diphosphane, with chemical shifts and coupling constants taken from the Spinach library and evaluated at a 500 MHz ¹H spectrometer field (B₀ ≈ 11.74 T). Rather than map all 22 nuclei onto qubits, they rewrote the two phosphorus spins in a singlet–triplet basis and kept only the two states with antiparallel spin alignment, collapsing that pair into a single effective qubit. This discards the parallel configurations, whose peaks can be estimated analytically, in exchange for a much shallower circuit.

To get an NMR spectrum, they prepared initial states corresponding to the transverse magnetization produced by a radiofrequency pulse on the protons, evolved the system in time using a first-order Lie–Trotter decomposition, and measured the x and y quadratures. Combining these into a complex free-induction decay and Fourier transforming gives the spectrum. Because the exact sum over initial states is exponentially large, they sampled 10 initial states with positive transverse magnetization, which proved sufficient given the molecule's symmetry and many equivalent protons.

Before running on hardware, they tuned the number of Trotter steps and shots using a noise-model emulator, then added echo-based Pauli twirling, dynamical decoupling during idle periods, and ancilla-based leakage detection with post-selection. Spectra from hardware were compared against classical references and against emulator runs with and without error suppression, with a ±2σ bootstrap band derived from 2000 resamples of the measurement counts.

Why This Matters

Research impact. The work moves digital quantum simulation of NMR from small textbook spin systems — such as the four-qubit acetonitrile simulations cited — to a 21-spin effective model with chemically meaningful output, and it establishes a concrete accuracy benchmark against optimized classical software. It also shows that a purely error-suppression approach (twirling, decoupling, post-selection) can carry very deep circuits without the shot overhead of zero-noise extrapolation or probabilistic error cancellation.

Real-world applications:

• Chemical analysis and structure determination, where NMR is a standard analytical tool.
• Drug discovery workflows, where NMR is used routinely.
• Battery materials research, cited by the authors as an area of industrial relevance.
• Materials science and chemistry more broadly, where local atomic structure and chemical environments are probed via coupled nuclear-spin dynamics.

Industry relevance. The paper is a joint academic–industry effort (HQS Quantum Simulations and Quantinuum) and frames NMR simulation as a candidate route toward practical quantum utility, given NMR's widespread use in industrial research.

Future Directions

• Longer evolution times. Reaching T_max ∼ 200 ms and over 500 Trotter steps would resolve the ~0.01 ppm fine structure and, the authors expect, bring the intensity of the double-peak structure closer to the classical reference. This requires circuit depths beyond current hardware.
• Removing the projection approximation. Running the full 22-spin Hamiltonian would recover the two missing sharp peaks in the 3.3–4.9 ppm region.
• Further circuit-depth reduction. The authors note that circuit gadgets for reducing NMR simulation depth exist and could be combined with the present approach.
• Extending to harder NMR regimes. The introduction identifies zero- to ultralow-field (ZULF) settings and solid-state environments governed by dipolar interactions as regimes where classical methods are less favorable and quantum simulation could matter more.

Target Audience

Quantum-computing researchers working on applications and benchmarks, especially those in quantum simulation of chemistry and spin dynamics; quantum-chemistry and NMR method developers interested in where hardware stands relative to classical tools like Spinach; and hardware teams evaluating error-suppression strategies for deep circuits on trapped-ion QCCD architectures. Readers need a working grasp of spin Hamiltonians and Trotterization to follow the methodology sections, though the results and their significance are accessible to chemists familiar with NMR.

Authors’ abstract

Simulating nuclear magnetic resonance (NMR) spectra is a promising application of quantum simulation. Using Quantinuum's System Model H2, a trapped-ion quantum computer, we demonstrate an end-to-end, large-scale digital NMR simulation of a classically challenging benchmark molecule, 1,2-di-tert-butyl-diphosphane. We implement a hardware-efficient reduction of the nuclear-spin Hamiltonian, enabling Trotterized real-time evolution of an effective 21-spin model with tailored error suppression to reduce the effects of device noise. The reconstructed liquid-state proton NMR spectrum agrees with classical reference calculations and reproduces key spectroscopic features that previous quantum hardware demonstrations did not capture. Given the widespread use of NMR in chemical analysis and industrial research, these results advance digital quantum simulation of NMR spectra towards practical quantum utility.