Feynmans ideas to employ quantum systems for simulating other quantum systems gave rise to quantum simulation. While current quantum computers are still prone to decoherence and rely on error correction, the development of hybrid algorithms that employ both quantumand classical computation allow to perform quantum simulation. Among these algorithms, the Variational Quantum Eigensolver algorithm has permitted to explore the electronic structure of simple atoms and molecules by exploiting the Rayleigh Ritz variational principle. In this work we provide the implementation of the VQE algorithm for finding the ground state energy of the hydrogen molecule on Qiskit library for python.
In order to answer the problem of Quantum Phase Estimation Algorithm been not suitable for NISQ devices, and allows one to outperform classical computers, Variational Quantum Algorithms (VQAs) were designed. Our subject of interest is the so-called Variational Quantum Eigensolver (VQE) algorithm and was originally designed to simulate electronic structures and to compute the ground state of a given molecule. VQE is made of two main components : an ansatz and a classical optimizer. The ansatz runs on the quantum device and aims to simulate the wavefunction, the parameters of the ansatz will be …
The variational quantum eigensolver (VQE) is one of the most appealing quantum algorithms to simulate electronic structure properties of molecules on near-term noisy intermediate-scale quantum devices. In this work, we generalize the VQE algorithm for simulating extended systems. However, the numerical study of an one-dimensional (1D) infinite hydrogen chain using existing VQE algorithms shows a remarkable deviation of the ground state energy with respect to the exact full configuration interaction (FCI) result. Here, we present two schemes to improve the accuracy of quantum simulations for ex…
With the increasing rise of publicly available high level quantum computing languages, the field of Quantum Computing has reached an important milestone of separation of software from hardware. Consequently, the study of Quantum Algorithms is beginning to emerge as university courses and disciplines around the world, spanning physics, math, and computer science departments alike. As a continuation to its predecessor: "Introduction to Coding Quantum Algorithms: A Tutorial Series Using Qiskit", this tutorial series aims to help understand several of the most promising quantum algorithms to date,…
A family of Variational Quantum Eigensolver (VQE) methods is designed to maximize the resource of existing noisy intermediate-scale quantum (NISQ) devices. However, VQE approaches encounter various difficulties in simulating molecules of industrially relevant sizes, among which the choice of the ansatz for the molecular wavefunction plays a crucial role. In this work, we push forward the capabilities of adaptive variational algorithms (ADAPT-VQE) by demonstrating that the measurement overhead can be significantly reduced via adding multiple operators at each step while keeping the ansatz compa…
Variational quantum eigensolver (VQE) is promising to show quantum advantage on near-term noisy-intermediate-scale quantum (NISQ) computers. One central problem of VQE is the effect of noise, especially the physical noise on realistic quantum computers. We study systematically the effect of noise for the VQE algorithm, by performing numerical simulations with various local noise models, including the amplitude damping, dephasing, and depolarizing noise. We show that the ground state energy will deviate from the exact value as the noise probability increase and normally noise will accumulate as…
Quantum computers have the potential to transform the ways in which we tackle some important problems. The efforts by companies like Google, IBM and Microsoft to construct quantum computers have been making headlines for years. Equally important is the challenge of translating problems into a state that can be fed to these machines. Because quantum computers are in essence controllable quantum systems, the problems that most naturally map to them are those of quantum mechanics. Quantum chemistry has seen particular success in the form of the variational quantum eigensolver (VQE) algorithm, whi…
Quantum computational chemistry (QCC) is the use of quantum computers to solve problems in computational quantum chemistry. We develop a high performance variational quantum eigensolver (VQE) simulator for simulating quantum computational chemistry problems on a new Sunway supercomputer. The major innovations include: (1) a Matrix Product State (MPS) based VQE simulator to reduce the amount of memory needed and increase the simulation efficiency; (2) a combination of the Density Matrix Embedding Theory with the MPS-based VQE simulator to further extend the simulation range; (3) A three-level p…
The practical benefits of hybrid quantum information processing hardware that contains continuous-variable objects (bosonic modes such as mechanical or electromagnetic oscillators) in addition to traditional (discrete-variable) qubits have recently been demonstrated by experiments with bosonic codes that reach the break-even point for quantum error correction and by efficient Gaussian boson sampling simulation of the Franck-Condon spectra of triatomic molecules that is well beyond the capabilities of current qubit-only hardware. The goal of this Co-design Center for Quantum Advantage (C2QA) pr…
Variational quantum eigensolver (VQE) is an efficient computational method promising chemical accuracy in electronic structure calculations on a universal-gate quantum computer. However, such a simple task as computing the electronic energy of a hydrogen molecular cation, H$_2^+$, is not possible for a general VQE protocol because the calculation will invariably collapse to a lower energy of the corresponding neutral form, H$_2$. The origin of the problem is that VQE effectively performs an unconstrained energy optimization in the Fock space of the original electronic problem. We show how this…
Integration of Variational Quantum Algorithms into Atomistic Simulation Workflows
Institute for Physical and Theoretical Chemistry, Bremen Center for Computational Materials Science University of Bremen and MAPEX Center for Materials and Processes（不莱梅大学物理与理论化学研究所、不莱梅计算材料科学中心以及材料与过程MAPEX中心）
Combinatorial optimization on near-term quantum devices is a promising path to demonstrating quantum advantage. However, the capabilities of these devices are constrained by high noise or error rates. In this paper, we propose an iterative Layer VQE (L-VQE) approach, inspired by the Variational Quantum Eigensolver (VQE). We present a large-scale numerical study, simulating circuits with up to 40 qubits and 352 parameters, that demonstrates the potential of the proposed approach. We evaluate quantum optimization heuristics on the problem of detecting multiple communities in networks, for which …
We demonstrate the simulation of a noncollinear molecule, e.g. H2O molecule using Variational Quantum Eigensolver (VQE) with high chemical accuracy. The 2D and 3D potential energy surface (PES) were reported. Taking advantage of the potential speedup in Qiskit runtime program, the optimal initial parameters for the variational quantum circuits were obtained after several consecutive iterations, thus resulting in accurate prediction of water's PES matching result obtained from exact diagonalization of the full Hamiltonian.
We study the effective matrix model for for gauge fields and fermions on a quantum computer. We use the Variational Quantum Eigensolver (VQE) using IBM QISKit for the effective matrix model for SU(2) and SU(3) including fermions in the fundamental representation. For SU(2) we study the effects of finite temperature and nonzero chemical potential. In all cases we find excellent agreement with the classical computation.
We study the Z3 gauge theory with fermions on the quantum computer using the Variational Quantum Eigensolver (VQE) algorithm with IBM QISKit software. Using up to 9 qubits we are able to obtain accurate results for the ground state energy. Introducing nonzero chemical potential we are able to determine the Equation of State (EOS) for finite density on the quantum computer. We discuss possible realizations of quantum advantage for this system over classical computers with regards to finite density simulations and the fermion sign problem.
Solving combinatorial optimization problems on current noisy quantum devices is currently being advocated for (and restricted to) binary polynomial optimization with equality constraints via quantum heuristic approaches. This is achieved using, e.g., the variational quantum eigensolver (VQE) and the quantum approximate optimization algorithm (QAOA). We present a decomposition-based approach to extend the applicability of current approaches to "quadratic plus convex" mixed binary optimization (MBO) problems, so as to solve a broad class of real-world optimization problems. In the MBO framework,…
Quantum computers promise to efficiently solve important problems that are intractable on a conventional computer. Quantum computational algorithms have the potential to be an exciting new way of studying quantum cosmology. In quantum cosmology, we learn about the dynamics of the universe without constructing a complete theory of quantum gravity. Since the universal wavefunction exists in an infinite-dimensional superspace over all possible 3D metrics and modes of matter configurations, we take minisuperspaces for our work by constraining the degrees of freedom to particular 3D metrics and uni…
QSeqSim: A Symbolic Simulator for Qiskit While Loops Using Sequential Quantum Circuits
Key Laboratory of System Software (Chinese Academy of Sciences), Institute of Software, Chinese Academy of Sciences（中国科学院软件研究所系统软件重点实验室）；University of Chinese Academy of Sciences（中国科学院大学）；Centre for Quantum Software and Information, University of Technology Sydney（悉尼科技大学量子软件与信息研究中心）
We simulate the dynamics of braiding Majorana zero modes on an IBM Quantum computer. We find the native quantum gates introduce too much noise to observe braiding. Instead, we use Qiskit Pulse to develop scaled two-qubit quantum gates that better match the unitary time evolution operator and enable us to observe braiding. This work demonstrates that quantum computers can be used for simulation, and highlights the use of pulse-level control for programming quantum computers and constitutes the first experimental evidence of braiding via dynamical Hamiltonian evolution.
The emerging field of quantum simulation of many-body systems is widely recognized as a very important application of quantum computing. A crucial step towards its realization in the context of many-electron systems requires a rigorous quantum mechanical treatment of the different interactions. In this pilot study, we investigate the physical effects beyond the mean-field approximation, known as electron correlation, in the ground state energies of atomic systems using the classical-quantum hybrid variational quantum eigensolver (VQE) algorithm. To this end, we consider three isoelectronic spe…
Quantum algorithms can be used to perform unsupervised machine learning tasks like data clustering by mapping the distance between data points to a graph optimization problem (i.e. MAXCUT) and finding optimal solution through energy minimization using hybrid quantum classical methods. Taking advantage of the IBM runtime environment, we benchmark the performance of the "Warm-Start" (ws) variant of Quantum Approximate Optimization Algorithm (QAOA) versus the standard implementation of QAOA and the variational quantum eigensolver (VQE) for unstructured clustering problems using real world dataset…
The variational quantum eigensolver (VQE) is one of the most representative quantum algorithms in the noisy intermediate-size quantum (NISQ) era, and is generally speculated to deliver one of the first quantum advantages for the ground-state simulations of some non-trivial Hamiltonians. However, short quantum coherence time and limited availability of quantum hardware resources in the NISQ hardware strongly restrain the capacity and expressiveness of VQEs. In this Letter, we introduce the variational quantum-neural hybrid eigensolver (VQNHE) in which the shallow-circuit quantum ansatz can be f…
We propose a divide-and-conquer method for the quantum-classical hybrid algorithm to solve larger problems with small-scale quantum computers. Specifically, we concatenate a variational quantum eigensolver (VQE) with a reduction in the system dimension, where the interactions between divided subsystems are taken as an effective Hamiltonian expanded by the reduced basis. Then the effective Hamiltonian is further solved by VQE, which we call deep VQE. Deep VQE allows us to apply quantum-classical hybrid algorithms on small-scale quantum computers to large systems with strong intra-subsystem inte…
We use the Variational Quantum Eigensolver (VQE) as implemented in the Qiskit software package to compute the ground state energy of small molecules derived from water, H$_2$O, and hydrogen cyanide, HCN. The work aims to benchmark algorithms for calculating the electronic structure and energy surfaces of molecules of relevance to prebiotic chemistry, beginning with water and hydrogen cyanide, and to run them on the available simulated and physical quantum hardware. The numerical calculations of the algorithms for small quantum processors allow us to design more efficient protocols to be run in…
Scaling of Quantum Resources for Simulating a Long-Range System
Indian Institute of Technology Roorkee（印度理工学院罗尔基分校）；Institute of Science, Banaras Hindu University（贝拿勒斯印度教大学理学院）；Indian Institute of Engineering Science and Technology, Shibpur（印度工程科学和技术学院西布浦分校）
The one-dimensional Ising model with its connections to several physical concepts plays a vital role in comprehension of several principles, phenomena and numerical methods. The Hamiltonian of a coupled one-dimensional dissipative spin system in the presence of magnetic field can be obtained from the Ising model. We simulate the above Hamiltonian by designing a quantum circuit with precise gate measurement and execute with the IBMQ experience platform through different $N$ states with controlled energy separation where we can check quantum synchronization in a dissipative lattice system. Our r…
