Quantum error mitigation (QEM) is essential for extracting chemically accurate results from near-term quantum hardware. Many widely used QEM methods rely on uncontrolled heuristics whose bias depends on the specific circuit and noise realization. In this work, we employ QESEM---a characterization-based, unbiased quasi-probabilistic mitigation method---on IBM's Aachen quantum processor to compute the ground-state potential energy surface (PES) of the symmetrically-stretched water molecule. We consider a classically-optimized, single-layer perfect-pairing tiled unitary product state ansatz. We map this ansatz to an 8-qubit register corresponding to a (4,4) active space and the STO-3G basis set. Compared to the statevector reference, we find that raw QPU results typically overestimate the ground-state energy by around 500~mHa across the scanned geometries. On the other hand, QESEM-mitigated results fall approximately within 100~mHa, 30~mHa, or ``chemical accuracy'' ($\sim$1.5~mHa), depending on the target precision. We benchmark QESEM at both loose (0.1~Ha) and tight (0.01~Ha) precision targets, evaluating both individual and merged batches of runs. As the precision target is tightened, the accuracy improves systematically, matching or exceeding results reported in the literature. We further quantify the sampling cost of these results, reporting the number of shots required at each precision level. Our results show how, with the current levels of hardware error, reaching the highest accuracies demands substantial QPU time. The results demonstrate that the characterization-based, unbiased error mitigation provided by QESEM allows to measure quantitatively meaningful potential energy surfaces on current quantum hardware. Concurrently, they highlight the sampling overhead associated with QEM, which remains a central bottleneck en route to larger chemical problems and higher precision.
Quantum error mitigation (QEM) is essential for extracting chemically accurate results from near-term quantum hardware. Many widely used QEM methods rely on uncontrolled heuristics whose bias depends on the specific circuit and noise realization. In this work, we employ QESEM---a characterization-based, unbiased quasi-probabilistic mitigation method---on IBM's Aachen quantum processor to compute the ground-state potential energy surface (PES) of the symmetrically-stretched water molecule. We consider a classically-optimized, single-layer perfect-pairing tiled unitary product state ansatz. We map this ansatz to an 8-qubit register corresponding to a (4,4) active space and the STO-3G basis set. Compared to the statevector reference, we find that raw QPU results typically overestimate the ground-state energy by around 500mHa across the scanned geometries. On the other hand, QESEM-mitigated results fall approximately within 100mHa, 30mHa, or ``chemical accuracy'' (∼1.5mHa), depending on the target precision. We benchmark QESEM at both loose (0.1Ha) and tight (0.01Ha) precision targets, evaluating both individual and merged batches of runs. As the precision target is tightened, the accuracy improves systematically, matching or exceeding results reported in the literature. We further quantify the sampling cost of these results, reporting the number of shots required at each precision level. Our results show how, with the current levels of hardware error, reaching the highest accuracies demands substantial QPU time. The results demonstrate that the characterization-based, unbiased error mitigation provided by QESEM allows to measure quantitatively meaningful potential energy surfaces on current quantum hardware. Concurrently, they highlight the sampling overhead associated with QEM, which remains a central bottleneck en route to larger chemical problems and higher precision.
Error mitigation is essential for unlocking the full potential of quantum algorithms and accelerating the timeline toward quantum advantage. As quantum hardware progresses to push the boundaries of classical simulation, efficient and robust error mitigation methods are becoming increasingly important for producing accurate and reliable outputs. However, existing error-mitigation approaches face a fundamental tradeoff between practical performance and reliability: heuristic methods such as zero-noise extrapolation (ZNE) enjoy faster runtime but lack accuracy guarantees, while rigorous techniques such as probabilistic error cancellation (PEC) provide unbiased estimates at prohibitive computational cost. We introduce a characterization-based, rigorously-grounded quantum error mitigation and error suppression framework (QESEM) that resolves this tradeoff by leveraging the accuracy guarantees of quasi-probabilistic mitigation with dramatically reduced overhead. We explain the innovative methods underlying QESEM and demonstrate its capabilities in the largest utility-scale error mitigation experiment based on an unbiased method. This experiment simulates the kicked transverse field Ising model with far-from-Clifford parameters on an IBM Heron device. We further validate QESEM's versatility across arbitrary quantum circuits and devices through high-accuracy error-mitigated molecular VQE circuits executed on IBM Heron and IonQ trapped-ion devices. Compared with multiple variants of the widely used zero-noise extrapolation method, QESEM consistently achieves higher accuracy while avoiding the prohibitive runtime overhead associated with PEC. These results mark a significant step forward in accuracy and reliability for running quantum circuits on current devices across diverse applications. Finally, we provide projections of QESEM's performance on near-term devices toward quantum advantage.
We present a large-scale experimental study of quantum-computing-based molecular simulation carried out on IQM's Sirius 24-qubit superconducting processor, utilizing up to 16 operational qubits. The work employs Sample-based Quantum Diagonalization (SQD) together with the Local Unitary Cluster Jastrow (LUCJ) ansatz to estimate ground-state energies for a set of benchmark molecules, including H2, LiH, BeH2, H2O, and NH3. In addition, we introduce a Linear-CNOT variant of the Unitary Coupled-Cluster Singles and Doubles (LCNot-UCCSD) ansatz within the SQD workflow, trading higher circuit depth for reduced classical preprocessing. A comparison between these ansätze is provided, clarifying their respective strengths, limitations, and suitability for near-term quantum hardware. We further explore potential energy landscapes through 1D scans for H2 and HeH+ using both STO-3G and 6-31G basis sets, and for LiH and BeH2 in STO-3G. Extending beyond this, we demonstrate the experimental construction of a full 2D potential energy surface for the water molecule on quantum hardware, mapped over a 32 × 32 grid in bond length and bond angle. To move beyond small benchmark systems, we combine SQD(LUCJ) with Density Matrix Embedding Theory (DMET) to compute active-space energies for a set of ligand-like molecules, as well as the pharmacologically relevant amantadine system. Across all studies, the majority of quantum-computed energies agree with reference FCI results, as well as with DMET-CASCI energies for embedded systems, to within chemical accuracy for the chosen basis sets. These results demonstrate the reliability of sample-based diagonalization approaches and underscore the potential of hybrid embedding strategies for extending quantum simulations to increasingly complex molecular systems, while also highlighting their practicality on current IQM quantum hardware.
Quantum processors have crossed the one-hundred-qubit mark, but noise continues to limit circuit performance, while full quantum error correction remains too costly for routine use. Error suppression and mitigation therefore play an important role in extracting value from current hardware, yet independent comparisons of commercial solutions on identical workloads and devices remain scarce. We benchmark IBM Qiskit Runtime, Q-CTRL Performance Management, and Qedma QESEM on IBM Pittsburgh, a 156-qubit IBM Quantum Heron r3 processor. For Sampler workloads, we run Bernstein-Vazirani, quantum phase estimation, GHZ-state preparation, and randomized mirror circuits with up to 100 measured qubits, comparing raw execution, IBM measurement twirling, and Q-CTRL. For Estimator workloads, we measure chain-averaged magnetization and correlation observables of an eight-layer transverse-field Ising circuit at 25, 50, and 75 qubits against an exact matrix-product-state reference, comparing IBM raw execution, IBM TREX plus twirling, Q-CTRL, and QESEM. Q-CTRL produced the best results on the three structured Sampler workloads while keeping reported QPU times within the same order as the IBM configurations. Across six Ising observable and system-size cases, aggregate mean absolute error was 0.0883 for IBM raw execution, 0.0807 for IBM TREX plus twirling, 0.0285 for Q-CTRL, and 0.0188 for QESEM. Relative to raw execution, Q-CTRL and QESEM reduced aggregate error by factors of 3.10 and 4.70, respectively, while QESEM used 7.5 to 11.1 times the reported QPU time of Q-CTRL. These results show that managed error suppression and mitigation can substantially improve current hardware performance, but with distinct accuracy and execution-time tradeoffs.
We introduce a cost-effective quantum error mitigation technique that builds upon the recent Ansatz-based gate and readout error mitigation method (M0). The technique, tiled M0, leverages the unique structure of tiled Ansätze (e.g., tUPS, QNP, hardware-efficient circuits) to apply a locality approximation to M0 that results in an exponential reduction in the QPU cost of the noise characterization. We validate the technique for molecular ground state energy calculations with the tUPS Ansatz on LiH, molecular hydrogen, water, butadiene, and benzene (4-12 qubits), demonstrating little to no loss in accuracy compared to M0 in noisy simulations. We also show the performance of the technique in quantum experiments, highlighting its potential use in near-term applications.
Nuclear gradients and Hessians are fundamental quantities in computational chemistry, essential for a wide range of applications including geometry optimization, vibrational spectroscopy, and molecular property calculations. In this work, we present their analytical implementation on quantum hardware. The methodology is formulated within an active-space framework combining orbital optimization and linear-response theory.
On the quantum-computing side, the approach employs the tiled unitary product state (tUPS) ansatz to directly evaluate the tensor elements required for solving the response equations. Moreover, the expectation values are corrected using an adapted confusion-matrix error-mitigation scheme in combination with post-selection criteria. The resulting workflow is assessed on molecular hydrogen and on water through the calculation of potential energy surfaces, nuclear gradients, Hessians, and vibrational frequencies, enabling the evaluation of both its capabilities and current limitations.
The results demonstrate good performance for the hydrogen molecule, whereas the water molecule provides a more demanding test of quantum-hardware resources and highlights the trade-offs associated with error-mitigation strategies. The quantified analysis of the results identify the main sources of errors, suggesting improvement directions for more accurate quantum computer applications.
The accurate computation of properties of large molecular systems is classically infeasible and is one of the applications in which it is hoped that quantum computers will demonstrate an advantage over classical devices. However, due to the limitations of present-day quantum hardware, variational-hybrid algorithms introduced to tackle these problems struggle to meet the accuracy and precision requirements of chemical applications. Here, we apply the quantum computed moments (QCM) approach combined with a variety of noise-mitigation techniques to an eight qubit and spin-orbital representation of the water molecule (H2O). A noise-stable improvement on the variational result for a four-excitation trial state (circuit depth 25, 22 cz gates) was obtained, with the ground-state energy computed to be within $1.0\ifmmode\pm\else\textpm\fi{}0.8$ mHa of exact diagonalization in the 14 spin-orbital basis. Thus, the QCM approach, despite an increased number of measurements and noisy quantum hardware (cz error rates c.0.3% corresponding to expected error rates on the trial-state circuit of order 7%), is able to determine the ground-state energy of a nontrivial molecular system at the required accuracy (c.0.05%). To the best of our knowledge, these results are the largest calculations performed on a physical quantum computer to date to achieve millihartree agreement with exact diagonalization, and a promising indicator of how such hybrid approaches might scale to problems of interest in the low-error and fault-tolerant regimes as quantum computers develop.