Quantum simulators have been actively developed that faithfully simulate the quantum computer operations on a classical computer. Since the amount of memory and operations required by quantum simulators increases exponentially with the number of qubits, MPI (Message Passing Interface) and distributed processing, which are methods to effectively use a large number of computing resources, can be used to achieve higher computation speed. In this paper, we profile the performance of the variational quantum eigensolver (VQE) algorithm by applying it to a multi-node quantum simulator to calculate the energy values of carbon dioxide (CO2) molecule. We also discuss how the size of CI (configuration interaction) ansatz and the convergence threshold of the classical optimization change the energy values. Experimental results demonstrate that the computational time is reduced as the number of computation nodes increases. The speed-up ratio is increased as the number of qubits increases. When the qubit size is 30, a maximum of 12.2 times speed-up is achieved if the computing node size is increased from 1 to 128.
Quantum simulators have been actively developed that faithfully simulate the quantum computer operations on a classical computer. Since the amount of memory and operations required by quantum simulators increases exponentially with the number of qubits, MPI (Message Passing Interface) and distributed processing, which are methods to effectively use a large number of computing resources, can be used to achieve higher computation speed. In this paper, we profile the performance of the variational quantum eigensolver (VQE) algorithm by applying it to a multi-node quantum simulator to calculate the energy values of carbon dioxide (CO2) molecule. We also discuss how the size of CI (configuration interaction) ansatz and the convergence threshold of the classical optimization change the energy values. Experimental results demonstrate that the computational time is reduced as the number of computation nodes increases. The speed-up ratio is increased as the number of qubits increases. When the qubit size is 30, a maximum of 12.2 times speed-up is achieved if the computing node size is increased from 1 to 128.
Advances in quantum simulator technology are increasingly required because research on quantum algorithms is becoming more sophisticated and complex. State vector simulation utilizes CPU and memory resources in computing nodes exponentially with respect to the number of qubits; furthermore, in a variational quantum algorithm, the large number of repeated runs by classical optimization is also a heavy load. This problem has been addressed by preparing numerous computing nodes or simulation frameworks that operate effectively. This study aimed to accelerate quantum simulation using two newly proposed methods: to efficiently utilize limited computational resources by adjusting the ratio of the MPI and distributed processing parallelism corresponding to the target problem settings and to slim down the Hamiltonian by considering the effect of accuracy on the calculation result. Ground-state energy calculations of a fermionic model were performed using a variational quantum eigensolver (VQE) on an HPC cluster with up to 1024 FUJITSU Processor A64FX connected to each other by InfiniBand; the processor is also used on supercomputer Fugaku. We achieved 200 times higher speed over VQE simulations and demonstrated 32 qubits ground-state energy calculations in acceptable time. This result indicates that > 30 qubit state vector simulations can be realistically utilized for further research on variational quantum algorithms.
Variational quantum eigensolver (VQE) is demonstrated to be the promising methodology for quantum chemistry based on near-term quantum devices. However, many problems are yet to be investigated for this methodology, such as the influences of optimization algorithm and basis size on the accuracy and efficiency for quantum computing. To address these issues, five molecules (H2, LiH, HF, N2 and F2) are studied in this work based on the VQE method using unitary coupled cluster (UCC) ansatz. The performance of the gradient optimization L-BFGS-B is compared with that of the direct search method COBYLA. The former converges more quickly, but the accuracy of energy surface is a little lower. The basis set shows a vital influence on the accuracy and efficiency. A large basis set generally provides an accurate energy surface, but induces a significant increase in computing time. The 631g basis is generally required from the energy surface of the simplest H2 molecule. For practical applications of VQE, complete active space (CAS) is suggested based on limited quantum resources. With the same number of qubits, more occupied orbitals included in CAS gives a better accuracy for the energy surface and a smaller evaluation number in the VQE optimization. Additionally, the electronic structure, such as filling fraction of orbitals, the bond strength of a molecule and the maximum nuclear charge also influences the performance of optimization, where half occupation of orbitals generally requires a large computation cost.
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.
Variational quantum eigensolver (VQE) is demonstrated to be the promising methodology for quantum chemistry based on near-term quantum devices. However, many problems are yet to be investigated for this methodology, such as the influences of optimization algorithm and basis size on the accuracy and efficiency for quantum computing. To address these issues, five molecules (H2, LiH, HF, N2 and F2) are studied in this work based on the VQE method using unitary coupled cluster (UCC) ansatz. The performance of the gradient optimization L-BFGS-B is compared with that of the direct search method COBYLA. The former converges more quickly, but the accuracy of energy surface is a little lower. The basis set shows a vital influence on the accuracy and efficiency. A large basis set generally provides an accurate energy surface, but induces a significant increase in computing time. The 631g basis is generally required from the energy surface of the simplest H2 molecule. For practical applications of VQE, complete active space (CAS) is suggested based on limited quantum resources. With the same number of qubits, more occupied orbitals included in CAS gives a better accuracy for the energy surface and a smaller evaluation number in the VQE optimization. Additionally, the electronic structure, such as filling fraction of orbitals, the bond strength of a molecule and the maximum nuclear charge also influences the performance of optimization, where half occupation of orbitals generally requires a large computation cost.
Accurately capturing electron correlation in large-scale molecular systems remains one of the foremost challenges in quantum chemistry and a primary driver for the development of quantum algorithms. Classical configuration-interaction methods, while rigorous, suffer from exponential scaling, rendering them impractical for large or strongly correlated systems. Overcoming this limitation is central to realizing the promise of quantum computing in chemistry. Here, we investigate the pyridine-Li ion complex using three quantum algorithms: the variational quantum eigensolver (VQE), the subspace quantum diagonalization (SQD) method, and the recently introduced handover iterative VQE (HI-VQE). Our results demonstrate how new generations of hybrid quantum-classical frameworks overcome the scalability and noise sensitivity that constrain conventional VQE approaches. SQD and HI-VQE achieve ground-state energy calculations for problem sizes inaccessible to classical computation, marking a clear advance toward quantum advantage. In particular, HI-VQE enables calculations within active spaces as large as (24e,22o), requiring 44 qubits-well beyond the reach of classical CASCI and VQE. This capability provides a systematic pathway for incorporating increasing numbers of electrons into quantum treatment, thereby approaching exact molecular energies. Importantly, both SQD and HI-VQE exhibit robustness against hardware noise, a critical improvement over earlier approaches. By enabling quantum simulations of molecular systems previously deemed intractable, SQD and HI-VQE offer a realistic route toward practical quantum advantage in computational chemistry. The comparison between HI-VQE and SQD shows that optimizing circuit parameters is crucial for accurate simulation.
Abstract Variational Quantum Eigensolver (VQE) methods aim to maximize the resources of existing noisy devices. However, they encounter difficulties in simulating molecules of industrially-relevant sizes, such as constructing the efficient ansatz. Adaptive variational algorithms (ADAPT-VQE) can solve this problem but with a significant increase in the number of measurements. Here, we reduce the measurement overhead of ADAPT-VQE via adding operator batches to the ansatz while keeping it compact. We reformulate the previously proposed qubit pool completeness criteria for the tapered qubit space and propose an automated pool construction procedure. Our numerical results indicate that reducing the qubit pool size from polynomial to linear conversely increases the number of measurements. We simulate a set of molecules, participating in the carbon monoxide oxidation processes using the statevector simulator and compare the results with VQE-UCCSD and classical methods. Our results pave the way towards usage of variational approaches for solving practically relevant chemical problems.