Quantum computing is currently emerging as a new computational technology for solving complex computational problems.Current quantum computers are unfortunately too noisy to provide sufficient accuracy, and quantum-classical hybrid algorithms emerged as a solution.Variational Quantum Algorithms are currently showing promising results at overcoming noise introduced by the current level of quantum hardware.Variational Quantum Deflation (VQD) has gained significant attention when computing the full spectrum of eigenvalues in quantum chemistry and solid-state physics.The noise in the VQD calculations performed on the current noisy quantum computers, or their simulators, can be partly suppressed by methods available in the Qiskit Python package provided by IBM.In our study, several error suppression and mitigation methods have been tested, and our results offer a unique comparison in the case of calculations on the electronic structure of crystals, where performance is sensitive to the actual point in the reciprocal space.
Quantum computing is currently emerging as a new computational technology for solving complex computational problems.Current quantum computers are unfortunately too noisy to provide sufficient accuracy, and quantum-classical hybrid algorithms emerged as a solution.Variational Quantum Algorithms are currently showing promising results at overcoming noise introduced by the current level of quantum hardware.Variational Quantum Deflation (VQD) has gained significant attention when computing the full spectrum of eigenvalues in quantum chemistry and solid-state physics.The noise in the VQD calculations performed on the current noisy quantum computers, or their simulators, can be partly suppressed by methods available in the Qiskit Python package provided by IBM.In our study, several error suppression and mitigation methods have been tested, and our results offer a unique comparison in the case of calculations on the electronic structure of crystals, where performance is sensitive to the actual point in the reciprocal space.
Quantum computing is currently emerging as a useful paradigm for solving highly complex computational problems.Current quantum computers are unfortunately too noisy to provide sufficient accuracy, and quantumclassical hybrid algorithms emerged as a solution.Variational Quantum Deflation (VQD) has gained significant attention for addressing challenges in quantum chemistry, material science, etc. VQDs typically use multiple optimization methods, and the correct choice of optimization method can significantly impact performance.In our study, we focused on the comparison of multiple optimization methods used in VQD when applied to the electronic structure of crystals.The quantum part of VQD ran on a classical simulator with imported noise models from real quantum computers from the IBM Quantum Platform.
Abstract Variational Quantum Eigensolver (VQE) and its extension, Variational Quantum Deflation (VQD), have emerged as promising algorithms for computing ground and excited state energy eigenvalues of Hamiltonians, particularly in quantum physics, chemistry, and materials science. Recently, the VQE and VQD algorithms were implemented to calculate the electronic band structure described by the tight-binding Hamiltonian. Despite their success for simple models, scalability remains a challenge due to the need for a large number of circuit executions, limited qubit coherence times, and low gate fidelities. In this work, we implemented the VQE and VQD algorithms for tight-binding models of diamond and zincblende crystal structures (Sn, C, Si, Ge, AlP, AlAs, AlSb, and GaP) using a quantum computer simulator. We investigate the scalability challenges, focusing on the significant overhead caused by a large number of quantum circuit executions required to find the energy eigenvalues. Our analysis highlights the substantial amount of both measurement and optimization overheads in VQD, particularly as the number of excited states increases. Based on our findings, we critically discuss the implications of implementing VQD on current noisy intermediate-scale quantum (NISQ) devices.
Over the last decade, researchers have been working to improve a crucial aspect of quantum computing to predict Hamiltonian energy of solids. Quantum algorithms such as Variational Quantum Eigensolver (VQE) and Variational Quantum Deflation (VQD) have been used to study the molecular systems. However, there is growing interest in adapting and applying these methods to periodic solid-state materials. In this work, we have integrated first-principles density functional theory with VQE and VQD algorithms and utilizing the Wannier Tight-Binding Hamiltonian (WTBH) method to predict the electronic characteristics of solids. We demonstrate that VQE and VQD algorithms can be used to accurately predict electronic characteristics in a variety of multi-component prototype solid-state materials such as - Silicon (semiconductor), Gold (metallic), Boron Nitrile (insulator), Graphene (semi-metal). Efficient SU2 performs well among all the predefined ansatz used in the study. COBYLA is the fastest optimizer among the classical optimizers with minimum number of iterations for convergence. Results of noise models help to understand the band structure when calculated on real quantum hardware. As quantum hardware advances, our method might be a starting point for using quantum computers to study materials and could help make material discovery more automatic in the future.
Variational Quantum Algorithms (VQAs) provide a promising framework for solving electronic structure problems using the computational capabilities of quantum computers to explore high-dimensional Hilbert spaces efficiently. This research investigates the performance of VQAs in electronic structure calculations of gallium arsenide (GaAs), a semiconductor with a zinc-blende structure. Utilizing a tight-binding Hamiltonian and a Jordan-Wigner-like transformation, we map the problem to a 10-qubit Hamiltonian. We analyze the impact of quantum circuit architectures, algorithm hyperparameters, and optimization methods on two VQAs: Variational Quantum Deflation (VQD) and Subspace Search Variational Quantum Eigensolver (SSVQE). We observed that while both algorithms offer promising results, the choice of ansatz and hyperparameter tuning were especially critical in achieving reliable outcomes, particularly for higher energy states. Adjusting the hyperparameters in VQD significantly enhanced the accuracy of higher energy state calculations, reducing the error by an order of magnitude, whereas tuning the hyperparameters in SSVQE had minimal impact. Our findings provide insights into optimizing VQAs for electronic structure problems, paving the way for their application to more complex systems on near-term quantum devices.
As a hybrid quantum-classical algorithm, the variational quantum eigensolver is widely applied in quantum chemistry simulations, especially in computing the electronic structure of complex molecular systems. However, on existing noisy intermediate-scale quantum devices, some factors such as quantum decoherence, measurement errors, and gate operation imprecisions are unavoidable. To overcome these challenges, this study proposes an efficient noise-mitigating variational quantum eigensolver for accurate computation of molecular ground state energies in noisy environments. We design the quantum circuit with reference to the structure of matrix product states and utilize it to pre-train the circuit parameters, which ensures circuit stability and mitigates fluctuations caused by initialization. We also employ zero-noise extrapolation to mitigate quantum noise and combine it with neural networks to improve the accuracy of the noise-fitting function, which significantly eliminates noise interference. Furthermore, we implement an intelligent grouping strategy for measuring Hamiltonian Pauli strings, which not only reduces measurement errors but also improves sampling efficiency. We perform numerical simulations to solve the ground state energy of the H4molecule by using MindSpore Quantum framework, and the results demonstrate that our algorithm can constrain noise errors within the range of O(10−2)∼O(10−1), outperforming mainstream variational quantum eigensolvers. This work provides a new strategy for high-precision quantum chemistry calculations on near-term noisy quantum hardware.
Quantum computers, currently in the noisy intermediate-scale quantum (NISQ) era, have started to provide scientists with a novel tool to explore quantum physics and chemistry. While several electronic systems have been extensively studied, Frenkel excitons, as prototypical optical excitations, remain among the less-explored applications. Here, we first use variational quantum deflation to calculate the eigenstates of the Frenkel Hamiltonian and evaluate the observables based on the oscillator strength for each eigenstate. Furthermore, using NISQ quantum computers requires performing error mitigation techniques alongside simulations. To deal with noisy qubits, we developed a deep-learning-based framework combined with a post-selection technique to learn the noise pattern and mitigate the error. Our mitigation methods work well and outperform the conventional post-selection and remain valid on real hardware.