A Domain-agnostic, Noise-resistant Evolutionary Variational Quantum Eigensolver for Hardware-efficient Optimization in the Hilbert Space.

fewer CX gates than those obtained by VQE with a unitary coupled cluster ansatz. EVQE demonstrates significant noise-resistance properties, obtaining results in noisy simulation with at least

3.6\times

less error than VQE using any tested ansatz configuration. We successfully evaluated EVQE on a real 5-qubit IBMQ quantum computer. The experimental results, which we obtained both via simulation and on real quantum hardware, demonstrate the effectiveness of EVQE for general-purpose optimization on the quantum computers of the present and near future.

Related papers

A Domain-agnostic, Noise-resistant, Hardware-efficient Evolutionary Variational Quantum Eigensolver

Arthur G. Rattew, Shaohan Hu, Marco Pistoia +2 more

Variational quantum algorithms have shown promise in numerous fields due to their versatility in solving problems of scientific and commercial interest. However, leading algorithms for Hamiltonian simulation, such as the Variational Quantum Eigensolver (VQE), use fixed preconstructed ansatzes, limiting their general applicability and accuracy. Thus, variational forms---the quantum circuits that implement ansatzes ---are either crafted heuristically or by encoding domain-specific knowledge. In this paper, we present an Evolutionary Variational Quantum Eigensolver (EVQE), a novel variational algorithm that uses evolutionary programming techniques to minimize the expectation value of a given Hamiltonian by dynamically generating and optimizing an ansatz. The algorithm is equally applicable to optimization problems in all domains, obtaining accurate energy evaluations with hardware-efficient ansatzes. In molecular simulations, the variational forms generated by EVQE are up to $18.6\times$ shallower and use up to $12\times$ fewer CX gates than those obtained by VQE with a unitary coupled cluster ansatz. EVQE demonstrates significant noise-resistance properties, obtaining results in noisy simulation with at least $3.6\times$ less error than VQE using any tested ansatz configuration. We successfully evaluated EVQE on a real 5-qubit IBMQ quantum computer. The experimental results, which we obtained both via simulation and on real quantum hardware, demonstrate the effectiveness of EVQE for general-purpose optimization on the quantum computers of the present and near future.Variational quantum algorithms have shown promise in numerous fields due to their versatility in solving problems of scientific and commercial interest. However, leading algorithms for Hamiltonian simulation, such as the Variational Quantum Eigensolver (VQE), use fixed preconstructed ansatzes, limiting their general applicability and accuracy. Thus, variational forms---the quantum circuits that implement ansatzes ---are either crafted heuristically or by encoding domain-specific knowledge. In this paper, we present an Evolutionary Variational Quantum Eigensolver (EVQE), a novel variational algorithm that uses evolutionary programming techniques to minimize the expectation value of a given Hamiltonian by dynamically generating and optimizing an ansatz. The algorithm is equally applicable to optimization problems in all domains, obtaining accurate energy evaluations with hardware-efficient ansatzes. In molecular simulations, the variational forms generated by EVQE are up to $18.6\times$ shallower and use up to $12\times$ fewer CX gates than those obtained by VQE with a unitary coupled cluster ansatz. EVQE demonstrates significant noise-resistance properties, obtaining results in noisy simulation with at least $3.6\times$ less error than VQE using any tested ansatz configuration. We successfully evaluated EVQE on a real 5-qubit IBMQ quantum computer. The experimental results, which we obtained both via simulation and on real quantum hardware, demonstrate the effectiveness of EVQE for general-purpose optimization on the quantum computers of the present and near future.

arXiv:1910.09694Oct 21, 201944 citations

Benchmarking Adaptative Variational Quantum Algorithms on QUBO Instances

Gloria Turati, Maurizio Ferrari Dacrema, Paolo Cremonesi

In recent years, Variational Quantum Algorithms (VQAs) have emerged as a promising approach for solving optimization problems on quantum computers in the NISQ era. However, one limitation of VQAs is their reliance on fixed-structure circuits, which may not be taylored for specific problems or hardware configurations. A leading strategy to address this issue are Adaptative VQAs, which dynamically modify the circuit structure by adding and removing gates, and optimize their parameters during the training. Several Adaptative VQAs, based on heuristics such as circuit shallowness, entanglement capability and hardware compatibility, have already been proposed in the literature, but there is still lack of a systematic comparison between the different methods. In this paper, we aim to fill this gap by analyzing three Adaptative VQAs: Evolutionary Variational Quantum Eigensolver (EVQE), Variable Ansatz (VAns), already proposed in the literature, and Random Adapt-VQE (RA-VQE), a random approach we introduce as a baseline. In order to compare these algorithms to traditional VQAs, we also include the Quantum Approximate Optimization Algorithm (QAOA) in our analysis. We apply these algorithms to QUBO problems and study their performance by examining the quality of the solutions found and the computational times required. Additionally, we investigate how the choice of the hyperparameters can impact the overall performance of the algorithms, highlighting the importance of selecting an appropriate methodology for hyperparameter tuning. Our analysis sets benchmarks for Adaptative VQAs designed for near-term quantum devices and provides valuable insights to guide future research in this area.In recent years, Variational Quantum Algorithms (VQAs) have emerged as a promising approach for solving optimization problems on quantum computers in the NISQ era. However, one limitation of VQAs is their reliance on fixed-structure circuits, which may not be taylored for specific problems or hardware configurations. A leading strategy to address this issue are Adaptative VQAs, which dynamically modify the circuit structure by adding and removing gates, and optimize their parameters during the training. Several Adaptative VQAs, based on heuristics such as circuit shallowness, entanglement capability and hardware compatibility, have already been proposed in the literature, but there is still lack of a systematic comparison between the different methods. In this paper, we aim to fill this gap by analyzing three Adaptative VQAs: Evolutionary Variational Quantum Eigensolver (EVQE), Variable Ansatz (VAns), already proposed in the literature, and Random Adapt-VQE (RA-VQE), a random approach we introduce as a baseline. In order to compare these algorithms to traditional VQAs, we also include the Quantum Approximate Optimization Algorithm (QAOA) in our analysis. We apply these algorithms to QUBO problems and study their performance by examining the quality of the solutions found and the computational times required. Additionally, we investigate how the choice of the hyperparameters can impact the overall performance of the algorithms, highlighting the importance of selecting an appropriate methodology for hyperparameter tuning. Our analysis sets benchmarks for Adaptative VQAs designed for near-term quantum devices and provides valuable insights to guide future research in this area.

arXiv:2308.01789IEEE International Conference on Quantum Computing and Engineering (QCE)Sep 17, 20235 citations

Qubit-excitation-based adaptive variational quantum eigensolver

Yordan S. Yordanov, V. Armaos, Crispin H. W. Barnes +1 more

Abstract Molecular simulations with the variational quantum eigensolver (VQE) are a promising application for emerging noisy intermediate-scale quantum computers. Constructing accurate molecular ansatze that are easy to optimize and implemented by shallow quantum circuits is crucial for the successful implementation of such simulations. Ansatze are, generally, constructed as series of fermionic-excitation evolutions. Instead, we demonstrate the usefulness of constructing ansatze with ``qubit-excitation evolutions', which, contrary to fermionic excitation evolutions, obey ``qubit commutation relations'. We show that qubit excitation evolutions, despite the lack of some of the physical features of fermionic excitation evolutions, accurately construct ansatze, while requiring asymptotically fewer gates. Utilizing qubit excitation evolutions, we introduce the iterative qubit excitation based VQE (IQEB-VQE) algorithm. The IQEB-VQE performs molecular simulations using a problem-tailored ansatz, grown iteratively by appending evolutions of single and double qubit excitation operators. By performing numerical simulations for small molecules, we benchmark the IQEB-VQE, and compare it against other competitive VQE algorithms. In terms of circuit efficiency and time complexity, we find that the IQEB-VQE systematically outperforms the previously most circuit-efficient, practically scalable VQE algorithms.Abstract Molecular simulations with the variational quantum eigensolver (VQE) are a promising application for emerging noisy intermediate-scale quantum computers. Constructing accurate molecular ansatze that are easy to optimize and implemented by shallow quantum circuits is crucial for the successful implementation of such simulations. Ansatze are, generally, constructed as series of fermionic-excitation evolutions. Instead, we demonstrate the usefulness of constructing ansatze with ``qubit-excitation evolutions', which, contrary to fermionic excitation evolutions, obey ``qubit commutation relations'. We show that qubit excitation evolutions, despite the lack of some of the physical features of fermionic excitation evolutions, accurately construct ansatze, while requiring asymptotically fewer gates. Utilizing qubit excitation evolutions, we introduce the iterative qubit excitation based VQE (IQEB-VQE) algorithm. The IQEB-VQE performs molecular simulations using a problem-tailored ansatz, grown iteratively by appending evolutions of single and double qubit excitation operators. By performing numerical simulations for small molecules, we benchmark the IQEB-VQE, and compare it against other competitive VQE algorithms. In terms of circuit efficiency and time complexity, we find that the IQEB-VQE systematically outperforms the previously most circuit-efficient, practically scalable VQE algorithms.

arXiv:2011.10540Communications PhysicsOct 14, 2021145 citations

MoG-VQE: Multiobjective genetic variational quantum eigensolver

Чивилихин Даниил Сергеевич, Samarin, A., Ульянцев Владимир Игоревич +3 more

Variational quantum eigensolver (VQE) emerged as a first practical algorithm for near-term quantum computers. Its success largely relies on the chosen variational ansatz, corresponding to a quantum circuit that prepares an approximate ground state of a Hamiltonian. Typically, it either aims to achieve high representation accuracy (at the expense of circuit depth), or uses a shallow circuit sacrificing the convergence to the exact ground state energy. Here, we propose the approach which can combine both low depth and improved precision, capitalizing on a genetically-improved ansatz for hardware-efficient VQE. Our solution, the multiobjective genetic variational quantum eigensolver (MoG-VQE), relies on multiobjective Pareto optimization, where topology of the variational ansatz is optimized using the non-dominated sorting genetic algorithm (NSGA-II). For each circuit topology, we optimize angles of single-qubit rotations using covariance matrix adaptation evolution strategy (CMA-ES) -- a derivative-free approach known to perform well for noisy black-box optimization. Our protocol allows preparing circuits that simultaneously offer high performance in terms of obtained energy precision and the number of two-qubit gates, thus trying to reach Pareto-optimal solutions. Tested for various molecules (H $_2$ , H $_4$ , H $_6$ , BeH $_2$ , LiH), we observe nearly ten-fold reduction in the two-qubit gate counts as compared to the standard hardware-efficient ansatz. For 12-qubit LiH Hamiltonian this allows reaching chemical precision already at 12 CNOTs. Consequently, the algorithm shall lead to significant growth of the ground state fidelity for near-term devices.Variational quantum eigensolver (VQE) emerged as a first practical algorithm for near-term quantum computers. Its success largely relies on the chosen variational ansatz, corresponding to a quantum circuit that prepares an approximate ground state of a Hamiltonian. Typically, it either aims to achieve high representation accuracy (at the expense of circuit depth), or uses a shallow circuit sacrificing the convergence to the exact ground state energy. Here, we propose the approach which can combine both low depth and improved precision, capitalizing on a genetically-improved ansatz for hardware-efficient VQE. Our solution, the multiobjective genetic variational quantum eigensolver (MoG-VQE), relies on multiobjective Pareto optimization, where topology of the variational ansatz is optimized using the non-dominated sorting genetic algorithm (NSGA-II). For each circuit topology, we optimize angles of single-qubit rotations using covariance matrix adaptation evolution strategy (CMA-ES) -- a derivative-free approach known to perform well for noisy black-box optimization. Our protocol allows preparing circuits that simultaneously offer high performance in terms of obtained energy precision and the number of two-qubit gates, thus trying to reach Pareto-optimal solutions. Tested for various molecules (H$_2$, H$_4$, H$_6$, BeH$_2$, LiH), we observe nearly ten-fold reduction in the two-qubit gate counts as compared to the standard hardware-efficient ansatz. For 12-qubit LiH Hamiltonian this allows reaching chemical precision already at 12 CNOTs. Consequently, the algorithm shall lead to significant growth of the ground state fidelity for near-term devices.

arXiv:2007.04424Jul 8, 202045 citations

Limitations of quantum hardware for molecular energy estimation using VQE

Abel Carreras, Román Orús, David Casanova

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.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.

arXiv:2506.03995Physical Chemistry Chemical PhysicsJan 1, 20265 citations

Robust resource-efficient quantum variational ansatz through an evolutionary algorithm

Yuhan Huang, Qingyu Li, Xiaokai Hou +4 more

Variational quantum algorithms (VQAs) are promising methods to demonstrate quantum advantage on near-term devices as the required resources are divided between a quantum simulator and a classical optimizer. As such, designing a VQA which is resource-efficient and robust against noise is a key factor to achieve a potential advantage with the existing noisy quantum simulators. It turns out that a fixed VQA circuit design, such as the widely used hardware-efficient ansatz, is not necessarily robust against imperfections. In this work, we propose a genome-length-adjustable evolutionary algorithm to design a robust VQA circuit that is optimized over variations of both circuit ansatz and gate parameters, without any prior assumptions on circuit structure or depth. Remarkably, our method not only generates a noise-effect-minimized circuit with shallow depth, but also accelerates the classical optimization by substantially reducing the number of parameters. In this regard, the optimized circuit is far more resource-efficient with respect to both quantum and classical resources. As applications, based on two typical error models in VQA, we apply our method to calculate the ground energy of the hydrogen and the water molecules as well as the Heisenberg model. Simulations suggest that, compared with conventional hardware-efficient ansatz, our circuit-structure-tunable method can generate circuits apparently more robust against both coherent and incoherent noise and hence is more likely to be implemented on near-term devices.Variational quantum algorithms (VQAs) are promising methods to demonstrate quantum advantage on near-term devices as the required resources are divided between a quantum simulator and a classical optimizer. As such, designing a VQA which is resource-efficient and robust against noise is a key factor to achieve a potential advantage with the existing noisy quantum simulators. It turns out that a fixed VQA circuit design, such as the widely used hardware-efficient ansatz, is not necessarily robust against imperfections. In this work, we propose a genome-length-adjustable evolutionary algorithm to design a robust VQA circuit that is optimized over variations of both circuit ansatz and gate parameters, without any prior assumptions on circuit structure or depth. Remarkably, our method not only generates a noise-effect-minimized circuit with shallow depth, but also accelerates the classical optimization by substantially reducing the number of parameters. In this regard, the optimized circuit is far more resource-efficient with respect to both quantum and classical resources. As applications, based on two typical error models in VQA, we apply our method to calculate the ground energy of the hydrogen and the water molecules as well as the Heisenberg model. Simulations suggest that, compared with conventional hardware-efficient ansatz, our circuit-structure-tunable method can generate circuits apparently more robust against both coherent and incoherent noise and hence is more likely to be implemented on near-term devices.

arXiv:2202.13714Physical Review AMay 10, 202248 citations

18.6\times

shallower and use up to

12\times

fewer CX gates than those obtained by VQE with a unitary coupled cluster ansatz. EVQE demonstrates significant noise-resistance properties, obtaining results in noisy simulation with at least

3.6\times

18.6\times

shallower and use up to

12\times

fewer CX gates than those obtained by VQE with a unitary coupled cluster ansatz. EVQE demonstrates significant noise-resistance properties, obtaining results in noisy simulation with at least

3.6\times

_2

, H

_4

, H

_6

, BeH

_2

, LiH), we observe nearly ten-fold reduction in the two-qubit gate counts as compared to the standard hardware-efficient ansatz. For 12-qubit LiH Hamiltonian this allows reaching chemical precision already at 12 CNOTs. Consequently, the algorithm shall lead to significant growth of the ground state fidelity for near-term devices.