NMR Spectroscopy Advances with Quantum Hardware from IBM & IonQ

Artemiy Burov, Julien Baglio, and Clément Javerzac have demonstrated the quantum Hamiltonian simulation of liquid-state one-dimensional (1D) nuclear magnetic resonance (NMR) spectra using commercially available superconducting-qubit computers from IBM and trapped-ion quantum computers from IonQ. This work, conducted at the School of Life Sciences, University of Applied Sciences Northwestern Switzerland (FHNW), and other affiliated institutions, achieved simulations for spin systems up to 34 spins, exceeding the 32-spin limit of classical Liouville-space simulations. By employing advanced error mitigation and suppression techniques from Q-CTRL, the pipeline improved mean square error by a factor of 22, representing a step toward near-term quantum utility in NMR spectroscopy for material sciences and pharmaceutical investigations. Quantum Simulation of NMR Spectroscopy Researchers have successfully performed quantum Hamiltonian simulations of liquid-state 1D NMR spectra for systems up to 34 spins, exceeding the classical “Liouville limit” of 32 spins. This was achieved using both a 156-qubit superconducting computer from IBM and a trapped-ion computer from IonQ. The simulations focused on three classically hard spin systems: DFH (16 spins), symm H/symm P (22 spins), and a phosphorous cluster (34 spins), demonstrating the potential to study molecules challenging for traditional methods. The approach utilizes Trotterization of the NMR Hamiltonian, simulating the free induction decay (FID) signal necessary to reconstruct the 1D NMR spectrum. A key element of this work is the implementation of an advanced error suppression pipeline from Q-CTRL, significantly reducing quantum circuit depth and improving accuracy. This resulted in a 12x to 22x improvement in the simulation of the FID, highlighting the importance of error mitigation in NISQ-era quantum computing. Comparisons with restricted classical simulations using the SPINACH package confirm that the quantum simulations reproduce the key features of the 1D NMR spectra. This work represents a step towards demonstrating near-term quantum utility in NMR spectroscopy, offering a potential advantage over classical methods for increasingly complex molecular systems and extending the boundaries of what’s computationally feasible. NISQ Era and Quantum Utility Recent advances are shifting quantum computing from the noisy intermediate-scale quantum (NISQ) era toward an age of quantum utility. Researchers are tackling problems previously intractable with classical methods, such as simulating one-dimensional (1D) nuclear magnetic resonance (NMR) spectra. This work demonstrates quantum Hamiltonian simulation of liquid-state 1D NMR spectra for spin systems up to 34 spins – exceeding the classical “Liouville limit” of 32 spins – using both IBM superconducting qubits and IonQ trapped-ion technology. The research team achieved simulations for molecules with 16, 22, and 34 spins—including anti-3,4-difluoroheptane, a symmetric P-H molecule, and a phosphorous cluster. Utilizing advanced error mitigation and suppression techniques from Q-CTRL’s Fire Opal, they significantly reduced quantum circuit depth and improved mean square error by a factor of 22. These simulations, compared to classical methods using SPINACH, successfully reproduce key features of the 1D NMR spectra. This work represents a step toward near-term quantum utility in NMR spectroscopy, a practical application where quantum advantages may first become apparent. Classical simulations of NMR dynamics become increasingly challenging as spin system size grows, hitting a limit around 20 spins (raised to 32 with tensor networks). The ability to simulate systems beyond this limit – as demonstrated with the 34-spin system – highlights the potential of quantum computing to address complex molecular simulations. Logical transpilation The first step is the transpilation of the logical circuit to the physical device, ensuring an optimal mapping to the native gate of the target hardware. Challenges in Classical NMR Simulation Classical simulations of NMR spectra face limitations as the size of the spin system increases. The source details a “Liouville limit” of around 20 spins for full classical simulations, extended to 32 spins using advanced tensor network methods. Researchers addressed this by employing restricted Liouville space techniques within the SPINACH package to make a 34-spin simulation tractable, highlighting the computational challenges inherent in simulating larger molecular systems with classical methods. This work successfully performed quantum Hamiltonian simulations of liquid-state 1D NMR spectra for systems up to 34 spins—exceeding the classical limit. Simulations were conducted on both IBM’s superconducting-qubit computer and IonQ’s trapped-ion system, utilizing error suppression techniques from Q-CTRL’s Fire Opal. This error suppression pipeline improved simulation accuracy by a factor of 12 to 22, demonstrating a path toward tackling complex systems beyond the reach of classical computation. Researchers simulated three specific molecules: anti-3,4-difluoroheptane (16 spins), a symmetric P-H molecule (22 spins), and a phosphorous cluster (34 spins). These were chosen as “classically hard spin systems.” By comparing quantum simulations to restricted classical simulations using SPINACH, the team reproduced key features of the 1D NMR spectra, supporting the potential of quantum computing for NMR spectroscopy and demonstrating results beyond the classical Liouville limit. Liouville Limit of NMR Simulations The classical limit for simulating NMR spectra, known as the Liouville limit, has historically been around 20 spins for a full simulation. Advanced classical methods, specifically those utilizing tensor networks like matrix product states, have extended this limit to 32 spins. Researchers in this study successfully performed a restricted classical simulation of a 34-spin system using the SPINACH package, demonstrating a push beyond the previously established Liouville limit with specific computational techniques. This work focuses on simulating NMR spectra for systems up to 34 spins, exceeding the classical Liouville limit. The researchers simulated three molecules: anti-3,4-difluoroheptane (16 spins), a symmetric P-H molecule (22 spins), and a phosphorous cluster (34 spins). These molecules were chosen as “classically hard” systems, meaning they pose a significant computational challenge for traditional methods, highlighting the potential of quantum simulation for complex systems. The simulations were conducted using both a 156-qubit superconducting computer (IBM Aachen) and a trapped-ion computer (IonQ Forte Enterprise). Employing error suppression techniques from Q-CTRL (Fire Opal) resulted in a 12x to 22x improvement in accuracy when simulating the free induction decay (FID) signal. This allowed for the reproduction of salient features in the 1D NMR spectra, even for the 34-spin system beyond the traditional Liouville limit.

Quantum Hamiltonian Evolution for NMR Quantum Hamiltonian evolution is utilized to simulate NMR spectra, offering a potential pathway toward quantum utility in fields like material science and drug discovery. Researchers successfully simulated liquid-state 1D NMR spectra for systems up to 34 spins—exceeding the classical “Liouville limit” of 32 spins—by employing Trotterization of the NMR Hamiltonian and calculating expectation values of magnetization. This approach simulates the free induction decay (FID) signal, which is then Fourier transformed into the 1D NMR spectrum. The research team performed simulations on both IBM’s superconducting-qubit computer and IonQ’s trapped-ion computer, focusing on classically “hard” spin systems like anti-3,4-difluoroheptane (16 spins), a symmetric P-H molecule (22 spins), and a phosphorous cluster (34 spins). An advanced error suppression pipeline, using Q-CTRL’s Fire Opal, significantly reduced circuit depth and improved accuracy—showing between 12x and 22x improvement in FID simulation—demonstrating a substantial reduction of quantum noise. These simulations, when compared to classical calculations using SPINACH, successfully reproduce key features of the 1D NMR spectra. The ability to simulate systems beyond the classical limit highlights the potential for quantum computers to tackle complex molecular simulations previously intractable. The use of both superconducting and trapped-ion hardware allows for investigation of different modalities and the impact of connectivity on simulation results. The quantum device is divided into smaller groups of qubits which are mitigated, these groups being automatically chosen to minimize intergroup correlations. Trotterization and FID Signal Calculation The simulation of NMR spectra using quantum computers commonly relies on calculating the free induction decay (FID) signal via quantum Hamiltonian evolution. This is achieved through Trotterization of the time evolution of the initial quantum state, broken down into K time steps. For each step, the expectation value of the magnetization operator is calculated, with the resulting collection of K values forming the FID signal, ultimately transformed into the 1D NMR spectrum. Researchers utilized Trotterization with one repetition (one time step) to simulate NMR spectra, employing both IBM‘s 156-qubit superconducting computer and IonQ’s trapped-ion computer. An advanced error suppression pipeline from Q-CTRL (Fire Opal) was key, reducing circuit depth and improving the accuracy of FID simulation by a factor of 12 to 22. These simulations successfully reproduced key features observed in restricted classical simulations using the SPINACH package. The work focused on simulating molecules beyond the classical “Liouville limit” of 32 spins, including anti-3,4-difluoroheptane (16 spins), a symmetric P-H molecule (22 spins), and a phosphorous cluster with 34 spins. By leveraging error mitigation and the latest quantum hardware, the team demonstrated a quantum Hamiltonian simulation for these systems, pushing beyond the capabilities of traditional classical methods for simulating liquid-state, high-field NMR spectra. Impact of Quantum Noise on Simulations Quantum noise significantly impacts the quality of NMR spectra simulations performed on near-term quantum computers, particularly within the NISQ era. The depth of the quantum circuits used for Hamiltonian evolution is directly correlated with the complexity of the molecule being simulated and the level of quantum noise experienced. Researchers addressed this by utilizing advanced error mitigation and suppression techniques – specifically Q-CTRL’s Fire Opal – achieving a 12x to 22x improvement in simulation accuracy compared to raw outputs from quantum devices. The research team successfully simulated NMR spectra for systems up to 34 spins – exceeding the classical Liouville limit of 32 spins. This was accomplished using Trotterization of the NMR Hamiltonian on both IBM’s superconducting qubit computer (156 qubits) and IonQ’s trapped-ion computer. Utilizing error suppression techniques, they reduced the depth of quantum circuits and improved the fidelity of simulations for molecules like anti-3,4-difluoroheptane (16 spins) and a phosphorous cluster (34 spins). These simulations demonstrate a significant advancement in overcoming the challenges posed by quantum noise in NMR spectroscopy. The researchers observed a substantial improvement in accuracy, with mean square error reduced by a factor of 22. Their work reproduces salient features of 1D NMR spectra for systems previously intractable for full classical simulations, representing a step toward near-term quantum utility in the field. We have used a tuned version of Fire Opal [17], the automatic error suppression and mitigation tool developed by Q-CTRL [18]. Hardware Used: IBM and IonQ Computers Researchers utilized both IBM’s 156-qubit superconducting-qubit computer, ibm aachen, and IonQ’s Forte Enterprise trapped-ion quantum computer for simulating nuclear magnetic resonance (NMR) spectra. These computations focused on molecules identified as classically difficult to simulate – specifically, systems with 16, 22, and 34 spins. Employing both platforms allowed for investigation into how different quantum hardware modalities, particularly all-to-all connectivity in the IonQ system, impact simulation results.

The team implemented an advanced error suppression pipeline utilizing Q-CTRL’s Fire Opal, which significantly reduced circuit depth and improved simulation accuracy – achieving between 12x and 22x improvement compared to raw quantum device output. This error suppression was crucial given the challenges of quantum noise in the noisy intermediate-scale quantum (NISQ) computing era, and its impact grows with the complexity of the simulated molecules and depth of the quantum circuits. Simulations were performed on molecules including anti-3,4-difluoroheptane (16 spins), a symmetric P-H molecule (22 spins), and a phosphorous cluster (34 spins, exceeding the classical Liouville limit of 32 spins). By comparing the quantum simulations with restricted classical simulations from the SPINACH package, researchers were able to reproduce the key features of the 1D NMR spectra, demonstrating a step toward near-term quantum utility in NMR spectroscopy. Error Suppression and Mitigation Techniques Researchers employed advanced error mitigation and error suppression techniques, specifically utilizing the Q-CTRL Fire Opal pipeline, to improve the accuracy of quantum Hamiltonian simulations of NMR spectra. This pipeline resulted in a substantial reduction of quantum circuit depth with low overhead, achieving between 12x and 22x improvement in accuracy when simulating the free induction decay (FID) signal. These techniques were crucial for tackling simulations beyond the classical Liouville limit of approximately 32 spins. The work focused on simulating liquid-state 1D NMR spectra for systems up to 34 spins—exceeding the approximately 20-spin limit for full classical simulations and pushing beyond the 32-spin Liouville limit. Simulations were performed on both a 156-qubit IBM superconducting computer and a trapped-ion computer from IonQ.

The team identified classically hard spin systems – DFH (16 spins), a symmetric P-H molecule (22 spins), and a phosphorous cluster (34 spins) – for these simulations. These simulations represent a step towards near-term quantum utility in NMR spectroscopy. By reducing quantum noise and improving the mean square error, the researchers were able to obtain salient features of 1D NMR spectra for systems beyond the reach of traditional classical methods. The use of both superconducting and trapped-ion hardware, along with advanced error suppression, demonstrates a pathway for tackling complex molecular simulations with quantum computers. Simulated Molecules and NMR Spectra Researchers successfully performed quantum Hamiltonian simulations of liquid-state 1D NMR spectra for molecules containing up to 34 spins. This surpasses the classical “Liouville limit” of around 32 spins, where full simulations become impractical. Utilizing quantum computers from both IBM (superconducting qubits) and IonQ (trapped ions), they focused on classically challenging spin systems like anti-3,4-difluoroheptane (16 spins), a symmetric P-H molecule (22 spins), and a phosphorous cluster (34 spins). The simulations relied on Trotterization of the NMR Hamiltonian, with computations performed with one Trotter step per repetition. An advanced error suppression pipeline utilizing Q-CTRL’s Fire Opal significantly reduced circuit depth and improved accuracy, achieving between 12x and 22x improvement in simulating the free induction decay (FID) signal. This reduction in error is critical given the impact of quantum noise on the quality of spectra obtained in the current NISQ computing era. Comparisons to restricted classical simulations, using the SPINACH package, demonstrated that the quantum simulations reproduce key features of the 1D NMR spectra. The research highlights a step toward near-term quantum utility in NMR spectroscopy, offering a potential path to tackle problems intractable for conventional methods. Molecules were chosen for their complexity and the difficulties they present for classical computation, further demonstrating the potential of this approach. Source: https://arxiv.org/pdf/2512.14513 Tags: