We report a pre-registered benchmark of an entanglement-forged H4 ground-state calculation on IonQ Forte Enterprise 1, a live trapped-ion processor. The analysis was frozen and publicly committed before any hardware data existed. The experiment comprised one submission of 81 new circuits at 1,100 shots per circuit, with device debiasing disabled. A three-parameter analytic noise model, fixed in advance, predicted the uncorrected energy error to within approximately 1%: 23.84 kcal/mol measured versus 24.06 kcal/mol predicted. However, the frame-free corrected estimator returned an error of 3.46 kcal/mol, compared with 0.83 kcal/mol predicted. This missed the conventional chemical-accuracy threshold of 1 kcal/mol. The shot-noise-weighted chi-square per degree of freedom increased from approximately 2 in simulator rehearsals to 5.93 on hardware. Analysis of 732 residuals identified elevated discrepancies in strongly corrected, high-weight XY-type observables and a systematic offset in one measurement group. A subsequent correction-magnitude refit showed that improving the goodness-of-fit statistic did not necessarily improve energy accuracy. These results demonstrate that a noise model that predicts uncorrected hardware behaviour accurately may still fail to predict the performance of the correction built from it. The paper reports the pre-registered experimental design, hardware results, residual diagnostics, follow-up tests, and methodological limitations. This work is not a blind variational ground-state search. The exact-state dependencies of the shared-frame estimator are disclosed, and the results do not establish reliable chemical accuracy for the frame-free estimator. Code and data repository: https://github.com/Venkatallu11/quantum-chemistry-vqe
We report a pre-registered benchmark of an entanglement-forged H4 ground-state calculation on IonQ Forte Enterprise 1, a live trapped-ion processor. The analysis was frozen and publicly committed before any hardware data existed. The experiment comprised one submission of 81 new circuits at 1,100 shots per circuit, with device debiasing disabled. A three-parameter analytic noise model, fixed in advance, predicted the uncorrected energy error to within approximately 1%: 23.84 kcal/mol measured versus 24.06 kcal/mol predicted. However, the frame-free corrected estimator returned an error of 3.46 kcal/mol, compared with 0.83 kcal/mol predicted. This missed the conventional chemical-accuracy threshold of 1 kcal/mol. The shot-noise-weighted chi-square per degree of freedom increased from approximately 2 in simulator rehearsals to 5.93 on hardware. Analysis of 732 residuals identified elevated discrepancies in strongly corrected, high-weight XY-type observables and a systematic offset in one measurement group. A subsequent correction-magnitude refit showed that improving the goodness-of-fit statistic did not necessarily improve energy accuracy. These results demonstrate that a noise model that predicts uncorrected hardware behaviour accurately may still fail to predict the performance of the correction built from it. The paper reports the pre-registered experimental design, hardware results, residual diagnostics, follow-up tests, and methodological limitations. This work is not a blind variational ground-state search. The exact-state dependencies of the shared-frame estimator are disclosed, and the results do not establish reliable chemical accuracy for the frame-free estimator. Code and data repository: https://github.com/Venkatallu11/quantum-chemistry-vqe
molecule, emphasizing practical implementation and performance on current quantum hardware. Our research presents a comparative study of HEA and UCCSD ansätze on noiseless and noisy simulations and implements VQE on recent IBM quantum computer noise models and a real quantum computer, IBM Fez, providing a fully functional code employing Qiskit 1.2. Our experiments confirm UCCSD's reliability in ideal conditions, while the HEA demonstrates greater robustness to hardware noise, achieving chemical accuracy on state-vector simulation (SVS). The results reveal that achieving ground-state energy within chemical accuracy is feasible without error mitigation during VQE convergence. We demonstrate that current quantum devices effectively optimize circuit parameters despite misestimating simulated energies. The SVS-evaluated energies provide a more accurate representation of the solution quality compared to QPU-estimated energy values, indicating that VQE converges to the correct ground state despite quantum noise. Our study also applies noise mitigation as a postprocessing technique, using zero-noise extrapolation (ZNE) on a real quantum computer. The detailed methodologies presented in this study, including Hamiltonian construction and Fermionic-to-qubit transformations, facilitate flexible adaptation of the VQE approach for various algorithm variants and across different levels of algorithmic implementation.
Current noisy intermediate-scale quantum (NISQ) trapped-ion devices are subject to errors which can significantly impact the accuracy of calculations if left unchecked. A form of error mitigation called zero noise extrapolation (ZNE) can decrease an algorithm's sensitivity to these errors without increasing the number of required qubits. Here we explore different methods for integrating this error mitigation technique into the Variational Quantum Eigensolver (VQE) algorithm for calculating the ground state of the HeH+ molecule at 0.8A˚ in the presence of experimental noise. Using the Quantum Scientific Computing Open User Testbed (QSCOUT) trapped-ion device, we test three methods of scaling noise for extrapolation: time stretching the two-qubit gates, scaling the sideband detuning parameter, and inserting two-qubit gate identity operations into the ansatz circuit. We find that time stretching and sideband detuning scaling fail to scale the noise on our particular hardware in a way that can be extrapolated to zero noise. Scaling our noise with global gate identity insertions and extrapolating after variational optimization, we achieve error suppression of 96.8, resulting in an energy estimate within $\ensuremath{-}0.004\ifmmode\pm\else\textpm\fi{}0.04$ hartree of the ground state energy. This is an improvement, but still outside the chemical accuracy threshold of 0.0016 hartree. Our results show that the efficacy of this error mitigation technique depends on choosing the correct implementation for a given device architecture.
Estimating molecular ground-state energies is a central application of quantum computing, requiring both the preparation of accurate quantum states and efficient energy readout. Understanding the effect of hardware noise on these experiments is crucial to distinguish errors that have low impact, errors that can be mitigated, and errors that must be reduced at the hardware level. We ran a state preparation and energy measurement protocol on an ion-trap quantum computer, without any non-scalable off-loading of computational tasks to classical computers, and show that leakage errors are the main obstacle to chemical accuracy. More specifically, we apply adiabatic state preparation to prepare the ground state of a six-qubit encoding of the H3+ molecule and extract its energy using a noise-resilient variant of iterative quantum phase estimation. Our results improve upon the classical Hartree-Fock energy. Analyzing the effect of hardware noise on the result, we find that while coherent and incoherent noise have little influence, the hardware results are mainly impacted by leakage errors. Absent leakage errors, noisy numerical simulations show that with our experimental settings we would have achieved close to chemical accuracy, even shot noise included. These insights highlight the importance of targeting leakage suppression in future algorithm and hardware development.
High Resolution Image Download MS PowerPoint Slide The variational quantum eigensolver (VQE) algorithm has positioned quantum chemistry calculation methods as promising applications for noisy intermediate-scale quantum (NISQ) devices. In NISQ devices, where the quantum noise is considerable, it is desirable to have an ansatz for the quantum circuit that is practical to implement and capable of achieving high chemical accuracy. Hardware-efficient Ansätze (HEA), such as the RyRz linear ansatz (RLA) and its modified form that preserves physical quantities─the symmetry preserving ansatz (SPA)─are constructed using quantum gates that can be implemented easily on a quantum computer. However, the extent to which HEA can accurately yield the electronic state energies of actual molecules and the number of quantum gates required to achieve chemical accuracy─which, in practical cases, should be within 1 kcal/mol of the exact energy value─are not well understood. In this study, we aimed to gain a detailed understanding of these aspects by performing noiseless simulations to obtain the ground and low-lying excited state using high-depth HEA quantum circuits for several molecules, including LiH, H 2 O, BeH 2, CH 4, and N 2 . From the results, we demonstrated that symmetry preserving HEA, such as SPA, can achieve accurate computational results that maintain CCSD-level chemical accuracy by increasing the number of layers. We quantitatively analyze how the expressibility and entangling capability of RLA and SPA quantum circuits evolve with circuit depth. Our results reveal that while increased layers generally expand accessible Hilbert space and entanglement, differences in their limitations highlight the importance of considering physically allowed entanglement for performance of a parametric quantum circuit in VQE. We also studied the potential energy surface of the dissociation of these molecules and found that quantum circuits using SPA can capture static electron correlation, which is challenging to address with classical single-reference quantum chemistry methods such as CCSD. These results from SPA demonstrate its potential to represent electronic states, as it achieves highly accurate results with fewer gate operations compared to physically inspired quantum circuits such as the Unitary Coupled Cluster (UCC) method. This study establishes a possible path for the application of quantum devices in solving quantum chemistry problems.
Quantum computing offers a potential for algorithmic speedups for applications, such as large-scale simulations in chemistry and physics. However, these speedups must yield results that are sufficiently accurate to predict realistic outcomes of experiments precisely. Delivering on the promise of high accuracy and precision requires methods to evaluate the computational accuracy of the quantum computing devices. We develop a framework to estimate the computational accuracy of near-term noisy, intermediate scale quantum (NISQ) computing devices using a quantum chemistry application. Application benchmarks that run on NISQ devices require techniques for mitigating errors to improve accuracy and precision. We use device agnostic error-mitigation schemes, quantum error detection and readout error detection, with post-selection to mitigate the dominant sources of noise. We evaluate the framework by simulating the ground state of molecular hydrogen with the variational quantum eigensolver (VQE) algorithm, estimating the energy and calculating the precision of the estimate using numerical simulations with realistic noise models. We first quantify the improvement in the logical error rate and state fidelity of the VQE application when encoded with the [[4,2,2]] quantum error detection code. When additionally encoded with readout error detection, we show that compared to the unencoded simulation, the encoded simulation yields a more accurate estimate by more than 1 mHa (0.027 eV) with comparable precision and higher state fidelity. Additionally, unlike the best estimate from the unencoded simulations, the results from the encoded simulation fall within the chemical accuracy threshold of 1.6 mHa of the exact energy. The estimated accuracy and precision indicate that current quantum computers can achieve error rates that yield useful outcomes for chemical applications.
Emergent quantum computing technologies are widely expected to provide novel approaches in the simulation of quantum chemistry. Despite rapid improvements in the scale and fidelity of quantum computers, high resource requirements make the execution of quantum chemistry experiments challenging. Typical experiments are limited in the number of qubits used, incur a substantial shot cost, or require complex architecture-specific optimization and error mitigation techniques. In this paper, we propose a conceptually simple benchmarking approach involving the use of multi-ancilla quantum phase estimation. Our approach is restricted to very small chemical systems, and does not scale favorably beyond molecular systems that can be described with 2 qubits; however, this restriction allows us to generate circuits that scale quadratically in gate count with the number of qubits in the readout register. This enables the execution of quantum chemistry circuits that act on many qubits, while producing meaningful results with limited shot counts. We use this technique (with 200 shots per experiment) to calculate the ground state energy of molecular hydrogen to 50 bits of precision (8.9×10−16 hartree) on a 56-qubit trapped-ion quantum computer, negating Trotter error. Including Trotter error, we obtain between 32 and 36 bits of precision (1.5∗10−10 and 6.0∗10−11 hartree respectively), vastly exceeding chemical accuracy (1.6∗10−3 hartree) against Full Configuration Interaction. We consider application of the approach to deeper circuits, and discuss potential as a benchmark task for near-term quantum devices.