Resource-Efficient Quantum Circuits for Molecular Simulations: A Case Study of Umbrella Inversion in Ammonia

We conducted a thorough evaluation of various state-of-the-art strategies to prepare the ground state wavefunction of a system on a quantum computer, specifically within the framework of variational quantum eigensolver (VQE). Despite the advantages of VQE and its variants, the current quantum computational chemistry calculations often provide inaccurate results for larger molecules, mainly due to the polynomial growth in the depth of quantum circuits and the number of two-qubit gates, such as CNOT gates. To alleviate this problem, we aim to design efficient quantum circuits that would outperform the existing ones on the current noisy quantum devices. In this study, we designed a novel quantum circuit that reduces the required circuit depth and number of two-qubit entangling gates by about 60%, while retaining the accuracy of the ground state energies close to the chemical accuracy. Moreover, even in the presence of device noise, these novel shallower circuits yielded substantially low error rates than the existing approaches for predicting the ground state energies of molecules. By considering the umbrella inversion process in ammonia molecule as an example, we demonstrated the advantages of this new approach and estimated the energy barrier for the inversion process.Comment: 7 pages, 8 figure

Deep Neural Network Assisted Quantum Chemistry Calculations on Quantum Computers

The variational quantum eigensolver (VQE) is a widely employed method to solve electronic structure problems on the current noisy intermediate-scale quantum (NISQ) devices. However, due to inherent noise in the NISQ devices, VQE results on NISQ devices often deviate significantly from the results obtained on noiseless statevector simulators or traditional classical computers. The iterative nature of the VQE further amplifies the errors in each loop. Recent works have explored ways to integrate deep neural networks (DNN) with VQE to mitigate the iterative errors, albeit, primarily limited to the noiseless statevector simulators. In this work, we trained DNN models across various quantum circuits and examined the potential of two DNN-VQE approaches, DNN1 and DNNF, for predicting the ground state energies of small molecules in the presence of device noise. We carefully examined the accuracy of the DNN1, DNNF, and VQE methods on both noisy simulators and real quantum devices by considering different ansatzes of varying qubit counts and circuit depths. Our results illustrate the advantages and limitations of both VQE and DNN-VQE approaches. Notably, both DNN1 and DNNF methods consistently outperform the standard VQE method in providing more accurate ground-state energies in noisy environments. However, despite being more accurate than VQE, the energies predicted using these methods on real quantum hardware remain meaningful only at reasonable circuit depths (depth = 15, gates = 21). At higher depths (depth = 83, gates = 112), they deviate significantly from the exact results. Additionally, we find that DNNF does not offer any notable advantage over VQE in terms of speed. Consequently, our study recommends DNN1 as the preferred method for obtaining quick and accurate ground state energies of molecules on the current quantum hardware, particularly for quantum circuits with lower depth and fewer qubits

Cobalt anti-MXenes as Promising Anode Materials for Sodium-ion Batteries

The current electric vehicle market is entirely dominated by lithium-ion batteries (LIBs). However, due to the limited and unequal distribution of LIB raw materials on earth, there is a continuous effort to design alternate storage devices. Among the alternatives to LIBs, sodium-ion batteries (NIBs) are at the forefront because sodium resources are ubiquitous worldwide and virtually inexhaustible. However, one of the major drawbacks of the NIBs is their low specific charge capacity. Since the specific charge capacity of a cell can be improved by increasing the specific charge capacity of the anode material, there is a constant effort to find suitable anode materials. Recent studies suggested that cobalt-boride (CoB) anti-MXene material (a newly discovered two-dimensional material) can yield superior specific charge capacities for LIBs than traditional graphite-based anodes. Inspired by these findings, in this work, we considered six cobalt-based anti-MXene materials (Co-anti-MXenes), namely, CoAs, CoB, CoP, CoS, CoSe, and CoSi, and examined their competency as anode materials for NIBs. Our findings suggest that Co-anti-MXenes possess superior specific charge capacities (~ 390–590 mAh/g) than many well-studied anode materials like MoS2 (146 mAh/g), Cr2C (276 mAh/g), expanded graphite (284 mAh/g), etc. Moreover, their greater affinity (-0.55 to -1.16 eV) to Na atoms, along with reasonably small diffusion energy barriers (0.32 to 0.59 eV) and low average sodiation voltages (0.2 to 0.64 V), suggest that these Co-anti-MXenes can serve as excellent anode materials for NIBs