New approaches into computational quantum chemistry can be developed through the use of quantum computing. While universal, fault-tolerant quantum computers are still not available, and we want to utilize today's noisy quantum processors. One of their flagship applications is the variational quantum eigensolver (VQE)-an algorithm for calculating the minimum energy of a physical Hamiltonian. In this study, we investigate how various types of errors affect the VQE and how to efficiently use the available resources to produce precise computational results. We utilize a simulator of a noisy quantum device, an exact statevector simulator, and physical quantum hardware to study the VQE algorithm for molecular hydrogen. We find that the optimal method of running the hybrid classical-quantum optimization is to: (i) allow some noise in intermediate energy evaluations, using fewer shots per step and fewer optimization iterations, but ensure a high final readout precision; (ii) emphasize efficient problem encoding and ansatz parametrization; and (iii) run all experiments within a short time-frame, avoiding parameter drift with time. Nevertheless, current publicly available quantum resources are still very noisy and scarce/expensive, and even when using them efficiently, it is quite difficult to perform trustworthy calculations of molecular energies.
New approaches into computational quantum chemistry can be developed through the use of quantum computing. While universal, fault-tolerant quantum computers are still not available, and we want to utilize today's noisy quantum processors. One of their flagship applications is the variational quantum eigensolver (VQE)-an algorithm for calculating the minimum energy of a physical Hamiltonian. In this study, we investigate how various types of errors affect the VQE and how to efficiently use the available resources to produce precise computational results. We utilize a simulator of a noisy quantum device, an exact statevector simulator, and physical quantum hardware to study the VQE algorithm for molecular hydrogen. We find that the optimal method of running the hybrid classical-quantum optimization is to: (i) allow some noise in intermediate energy evaluations, using fewer shots per step and fewer optimization iterations, but ensure a high final readout precision; (ii) emphasize efficient problem encoding and ansatz parametrization; and (iii) run all experiments within a short time-frame, avoiding parameter drift with time. Nevertheless, current publicly available quantum resources are still very noisy and scarce/expensive, and even when using them efficiently, it is quite difficult to perform trustworthy calculations of molecular energies.
Variational quantum eigensolvers (VQEs) are among the most promising quantum algorithms for solving electronic structure problems in quantum chemistry, particularly during the noisy intermediate-scale quantum (NISQ) era. In this study, we investigate the capabilities and limitations of VQE algorithms implemented on current quantum hardware for determining molecular ground-state energies, focusing on the adaptive derivative-assembled pseudo-Trotter ansatz VQE (ADAPT-VQE). To address the significant computational challenges posed by molecular Hamiltonians, we explore various well known strategies to simplify the Hamiltonian, optimize the ansatz, and improve classical parameter optimization through modifications of the COBYLA optimizer. These enhancements are integrated into a tailored quantum computing implementation designed to minimize the circuit depth and computational cost. Using benzene as a benchmark system, we demonstrate the application of these optimizations on an IBM quantum computer. Despite these improvements, our results highlight the limitations imposed by current quantum hardware, particularly the impact of quantum noise on state preparation and energy measurement. The noise levels in today's devices prevent meaningful evaluations of molecular Hamiltonians with sufficient accuracy to produce reliable quantum chemical insights. Finally, we extrapolate the requirements for future quantum hardware to enable practical and scalable quantum chemistry calculations using VQE algorithms. This work provides an assessment of current quantum algorithms for molecular modeling on real quantum hardware, highlighting the impact of noise and hardware limitations on the achievable accuracy.
Abstract Quantum computers are expected to be highly beneficial for chemistry simulations, promising significant improvements in accuracy and speed. The most prominent algorithm for chemistry simulations on NISQ devices is the Variational Quantum Eigensolver (VQE). It is a hybrid quantum-classical algorithm which calculates the ground state energy of a Hamiltonian based on parametrized quantum circuits, while a classical optimizer is used to find optimal parameter values. However, quantum hardware is affected by noise, and it needs to be understood to which extent it can degrade the performance of the VQE algorithm. In this paper, we study the impact of noise on the example of the hydrogen molecule. First, we compare the VQE performance for a set of various optimizers, from which we find NFT to be the most suitable one. Next, we quantify the effect of different noise sources by systematically increasing their strength. The noise intensity is varied around values common to superconducting devices of IBM Q, and curve fitting is used to model the relationship between the obtained energy values and the noise magnitude. Since the amount of noise in a circuit highly depends on its architecture, we perform our studies for different ansatzes, including both hardware-efficient and chemistry-inspired ones. Finally, we compare our results from noisy simulations with experiments on different IBM hardware devices.
The Variational Quantum Eigensolver (VQE) is a promising quantum algorithm for applications in chemistry within the Noisy Intermediate-Scale Quantum (NISQ) era. The ability for a quantum computer to simulate electronic structures with high accuracy would have a profound impact on material and biochemical science with potential applications e.g., to the development of new drugs. However, considering the variety of quantum hardware architectures, it is still uncertain which hardware concept is most suited to execute the VQE for e.g., the simulation of molecules. Aspects to consider here are the required connectivity of the quantum circuit used, the size and the depth and thus the susceptibility to noise effects. Besides theo-retical considerations, empirical studies using available quantum hardware may help to clarify the question of which hardware technology might be better suited for a certain given application and algorithm. Going one step into this direction, within this work, we present results using the VQE for the simulation of the hydrogen molecule, comparing superconducting and ion trap quantum computers. The experiments are carried out with a standardized setup of ansatz and optimizer, selected to reduce the number of required iterations. The findings are analyzed considering different quantum processor types, calibration data as well as the depth and gate counts of the circuits required for the different hardware concepts after transpilation.
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.
Quantum chemistry is one of the most promising applications of quantum computers in the near future. For noisy intermediate-scale quantum devices, the quantum-classical hybrid framework based on the variational quantum eigensolver (VQE) has become the method of choice. In the literature, there are many different variants of VQE, but it is not known which one is optimal for a given molecule. For this purpose, we perform a thorough benchmarking on more than ten different kinds of VQE ansatzes (in systems up to 30 qubits), based on their performance on the energy accuracy, runtime until convergence, and number of parameters. Our results show that the ADAPT ansatz can be used to obtain more accurate energy for small systems (below 14 qubits), but it costs much more computational resources. For larger molecules, UCCSD0 has better performance. However, all the tested ansatzes can hardly reach chemical accuracy at stretched bond lengths. Our results were obtained using MindSpore Quantum, where the codes and the benchmarking toolkit are publicly available at Gitee.
Exponential scaling presents a significant challenge in electronic structure calculations performed on classical computers. This paper explores how quantum computer algorithms can accurately represent quantum systems. Variational Quantum Eigensolver (VQE) algorithm is used to compute the ground state energy of hydrogen and helium sequences by implementing variational principle and quantum gates as trial wavefunction. This technique combines classical optimization with quantum computing calculations to simulate quantum systems on noisy and resource-limited computers. The resulting calculated energy is highly consistent to the corresponding exact values and Hartree-Fock calculations with a trend of when the number of atoms increases the calculated energy becomes more negative, leading to a decrease in the percentage error. Moreover, the convergence of the ground state energy of hydrogen and helium atoms was effectively optimized. The desired energy was reached, proven by adjusting the expectation value, and gradually achieving unity in state overlap. These findings demonstrate the VQE method's accuracy in calculating simple quantum systems and its scalability for larger atomic and molecular system, such as those in quantum chemistry and material science. However, challenges in quantum computer simulations, such as limited in qubit numbers and the presence of noise, require further advancements. Therefore, implementing a larger basis sets, advanced qubit mapping, specific chemistry ansatz, and flexible optimization techniques is one way to improve overall calculation.