Naoum C. Bacalis
Functionals that have local minima at the excited states of a non degenerate Hamiltonian are presented. Then, improved mutually orthogonal approximants of the ground and the first excited state are reported.
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The ground and excited state calculations at key geometries, such as the Frank-Condon (FC) and the conical intersection (CI) geometries, are essential for understanding photophysical properties. To compute these geometries on noisy intermediate-scale quantum devices, we proposed a strategy that combined a chemistry-inspired spin-restricted ansatz and a new excited state calculation method called the variational quantum eigensolver under automatically-adjusted constraints (VQE/AC). Unlike the conventional excited state calculation method, called the variational quantum deflation, the VQE/AC doe…
The variational quantum eigensolver (VQE), a variational algorithm to obtain an approximated ground state of a given Hamiltonian, is an appealing application of near-term quantum computers. The original work [A. Peruzzo et al.; \textit{Nat. Commun.}; \textbf{5}, 4213 (2014)] focused only on finding a ground state, whereas the excited states can also induce interesting phenomena in molecules and materials. Calculating excited states is, in general, a more difficult task than finding ground states for classical computers. To extend the framework to excited states, we here propose an algorithm, t…
The calculation of excited state energies of electronic structure Hamiltonians has many important applications, such as the calculation of optical spectra and reaction rates. While low-depth quantum algorithms, such as the variational quantum eigenvalue solver (VQE), have been used to determine ground state energies, methods for calculating excited states currently involve the implementation of high-depth controlled-unitaries or a large number of additional samples. Here we show how overlap estimation can be used to deflate eigenstates once they are found, enabling the calculation of excited s…
Excited-CAFQA: A classical simulation bootstrap for the variational estimation of molecular excited states
针对变分量子算法在量子化学中噪声管理不足的问题，提出Excited-CAFQA初始化方法，通过经典模拟离散搜索为VQD算法提供准确初始参数，在H2和HeH+分子系统上实现了90至99+%的激发态估计准确率。
Solving for molecular excited states remains one of the key challenges of modern quantum chemistry. Traditional methods are constrained by existing computational capabilities, limiting the complexity of the molecules that can be studied or the accuracy of the results that can be obtained. Several quantum computing methods have been suggested to address this limitation. However, these typically have hardware requirements which may not be achieved in the near term. We propose a variational quantum machine learning based method to determine molecular excited states aiming at being as resilient as…
Ground and excited state energy calculations of the H2 molecule using a variational quantum eigensolver algorithm on an NMR quantum simulator
本文在NMR量子处理器上实验实现了变分量子本征求解器与变分量子紧缩算法，分别计算H2分子的基态和激发态能量，并首次证明单个NMR量子比特即可达到所需精度。
We propose an excited-state molecular dynamics simulation method based on variational quantum algorithms at a computational cost comparable to that of ground-state simulations. We utilize the feature that excited states can be obtained as metastable states in the restricted variational quantum eigensolver calculation with a hardware-efficient ansatz. To demonstrate the effectiveness of the method, molecular dynamics simulations are performed for the S1 excited states of H2 and CH2NH molecules. The results are consistent with those of the exact adiabatic simulations in the S1 states, except for…
Subspace-Search Quantum Imaginary Time Evolution for Excited State Computations
针对激发态量子计算缺乏高效算法的问题，提出整合SSVQE和VarQITE关键元素的SSQITE方法，经基准系统验证其有效性及避免局部极小值的鲁棒性，有望推动激发态量子计算发展。
Crossing The Gap Using Variational Quantum Eigensolver: A Comparative Study
本文比较 VQD 与 SSVQE 计算 LiH 低激发态的表现，并提出结合 FS-VQE 的 FS-VQD 与 FS-SSVQE 以探索 H₄ 高激发态。
Excitation Gaps of Ground and Excited State Energy of the Fermi-Hubbard Model Using Variational Quantum Eigensolver
本文提出融合 HVA 与 NPA 的新型 ansatz 电路，并用 COBYLA 与 L-BFGS 混合优化，计算 4×1 和 2×2 Hubbard 晶格的基态及前两个激发态能量与激发隙。
Demonstration of subspace-search variational quantum eigensolver using photonic orbital angular momentum qudits
研究针对NISQ硬件VQE多局限于基态的问题，利用光子轨道角动量qudits实现SSVQE，估算HeH⁺分子和海森堡链的激发态能量，确立光子qudits是高效的激发态量子模拟途径。
Unified adiabatic and diabatic excited-state description via the ensemble-variational quantum eigensolver
本文提出了一种基于集合变分量子特征求解器的方法，用于统一处理绝热和非绝热激发态问题，并展示了如何扩展该方法以处理三个或更多耦合电子态的模型。
Calculating the energy spectrum of a quantum system is an important task, for example to analyse reaction rates in drug discovery and catalysis. There has been significant progress in developing algorithms to calculate the ground state energy of molecules on near-term quantum computers. However, calculating excited state energies has attracted comparatively less attention, and it is currently unclear what the optimal method is. We introduce a low depth, variational quantum algorithm to sequentially calculate the excited states of general Hamiltonians. Incorporating a recently proposed techniqu…
How an Equi-ensemble Description Systematically Outperforms the Weighted-ensemble Variational Quantum Eigensolver
本文提出等权集合方法在计算激发态时优于加权集合方法，通过变分原理推广实现更优性能。
Variational low-energy subspaces for chemically accurate excited states
提出将变分激发态优化重新表述为电子哈密顿量低能子空间的迭代类基态问题，开发了EXIDOS方法，无需显式正交约束或对称性，在多个分子体系中实现化学精度。
We present a time-dependent localized Hartree-Fock density-functional linear response approach for the treatment of photoionization of atomic systems. This approach employs a spin-dependent localized Hartree-Fock (SLHF) exchange potential to calculate electron orbitals and kernel functions, and thus can be used to study the photoionization from atomic excited states. We have applied the approach to the calculation of photoionization cross sections of Ne ground state. The results are in agreement with available experimental data and have comparable accuracies with other ab initio theoretical re…
The maturation of analytical derivative theory over the past few decades has enabled classical electronic structure theory to provide accurate and efficient predictions of a wide variety of observable properties. However, classical implementations of analytical derivative theory take advantage of explicit computational access to the approximate electronic wavefunctions in question, which is not possible for the emerging case of hybrid quantum/classical methods. Here, we develop an efficient Lagrangian-based approach for analytical first derivatives of hybrid quantum/classical methods using onl…
A Unified Variational Framework for Quantum Excited States
提出一种基于最小化逆重叠矩阵与哈密顿矩阵乘积迹的新变分原理，无需正交约束即可同时确定多个低能激发态，在多种物理系统与计算平台上验证了其准确性与通用性。
It is proven that the exact excited-state wave function and energy may be obtained by minimizing the energy expectation value of trial wave functions that are constrained only to have the correct nodes of the state of interest. This excited-state nodal minimum principle has the advantage that it requires neither minimization with the constraint of wave-function orthogonality to all lower eigenstates nor the antisymmetry of the trial wave functions. It is also found that the minimization over the entire space can be partitioned into several interconnected minimizations within the individual nod…
Hybrid QPE-Ansatz Strategy for Reliable Excited-State Variational Quantum Deflation
本文提出一种结合守恒对称性保护的ansatz和浅层量子相位估计的方案，用于NISQ时代激发态计算，通过辅助寄存器编码自旋信息以抑制自旋污染。
Qumode-Based Variational Quantum Eigensolver for Molecular Excited States
QSS-VQE利用量子模计算分子激发态，通过映射哈密顿量到福克空间并减少量子资源需求，展示出在复杂分子模拟中的潜力。
Ground or Excited State: a State-Specific Variational Quantum Eigensolver for Them All
针对传统VQE难获取特定对称性适配激发态、需深度电路及基态先验信息的问题，提出统一态特定VQE框架，通过多行列式参考态与全对称自旋标量幺正实现态选择，避免变分坍缩与累积误差，适用于近期量子器件。
Most literature in the Variational Quantum Eigensolver (VQE) algorithm focuses on finding the ground state of a physical system, by minimizing a quantum-computed cost-function. When excited states are required, the cost-function is usually modified to include additional terms ensuring orthogonality with the ground state. This generally requires additional quantum circuit executions and measurements, increasing algorithmic complexity. Here we present a design strategy for the variational ansatz which enforces orthogonality in candidate excited states while still fully exploring the remaining su…
Grassmann Variational Monte Carlo with neural wave functions
本研究基于 Hilbert 空间的 Grassmann 几何严格形式化神经量子态框架，推广 Stochastic Reconfiguration 方法以同时优化多个变分波函数，并在方格 Heisenberg 模型上实现了大量激发态的高精度能量与物理可观测量计算。
The possibility of performing quantum chemical calculations using quantum computers has attracted much interest. In this regard, variational quantum deflation (VQD) is a quantum-classical hybrid algorithm for the calculation of excited states with noisy intermediate-scale quantum (NISQ) devices. Although the validity of this method has been demonstrated, there have been few practical applications, primarily because of the uncertain effect of calculation conditions on the results. In the present study, calculations of the core-excited and core-ionized states for common molecules based on the VQ…
Variational quantum eigensolver(VQE) typically minimizes energy with hybrid quantum-classical optimization, which aims to find the ground state. Here, we propose a VQE by minimizing energy variance, which is called as variance-VQE(VVQE). The VVQE can be viewed as an self-verifying eigensolver for arbitrary eigenstate by designing, since an eigenstate for a Hamiltonian should have zero energy variance. We demonstrate properties and advantages of VVQE for solving a set of excited states with quantum chemistry problems. Remarkably, we show that optimization of a combination of energy and variance…
Efficient charge-preserving excited state preparation with variational quantum algorithms
本文提出保电荷VQD（CPVQD）算法，将对称性与守恒电荷纳入VQD框架实现维度缩减，显著提升激发态计算效率，并在最高24量子比特系统上通过GPU加速模拟验证其在高能物理、核物理和量子化学中的性能。
Highly excited states of quantum many-body systems are central objects in the study of quantum dynamics and thermalization that challenge classical computational methods due to their volume-law entanglement content. In this work, we explore the potential of variational quantum algorithms to approximate such states. We propose an adaptive variational algorithm, adaptive VQE-X, that self-generates a variational ansatz for arbitrary eigenstates of a many-body Hamiltonian $H$ by attempting to minimize the energy variance with respect to $H$. We benchmark the method by applying it to an Ising spin …
A programmable quantum device that has a large number of qubits without fault-tolerance has emerged recently. Variational Quantum Eigensolver (VQE) is one of the most promising ways to utilize the computational power of such devices to solve problems in condensed matter physics and quantum chemistry. As the size of the current quantum devices is still not large for rivaling classical computers at solving practical problems, Fujii et al. proposed a method called "Deep VQE" which can provide the ground state of a given quantum system with the smaller number of qubits by combining the VQE and the…
Using quantum devices supported by classical computational resources is a promising approach to quantum-enabled computation. One example of such a hybrid quantum-classical approach is the variational quantum eigensolver (VQE) built to utilize quantum resources for the solution of eigenvalue problems and optimizations with minimal coherence time requirements by leveraging classical computational resources. These algorithms have been placed among the candidates for first to achieve supremacy over classical computation. Here, we provide evidence for the conjecture that variational approaches can …
Excited-State Quantum Chemistry on Qumode-Based Processors via Variational Quantum Deflation
提出QumVQD框架，在玻色子量子处理器上计算电子和振动激发态能量，通过汉明权重过滤减少qumode需求，在H₂和H₄中达到化学精度，并在CO₂和H₂S中实现光谱精度，门数量比基于量子比特的方法低一个数量级。
Equivariant Variational Quantum Eigensolver to detect Phase Transitions through Energy Level Crossings
本研究提出等变量子电路保持自旋和平移对称性，精确描述链上J1-J2海森堡模型的单重态和三重态激发态，通过能级交叉检测相变点，并验证零噪声外推可恢复噪声下的物理性质。
The variational quantum eigensolver (VQE) algorithm, designed to calculate the energy of molecular ground states on near-term quantum computers, requires specification of symmetries that describe the system, e.g. spin state and number of electrons. This opens the possibility of using VQE to obtain excited states as the lowest energy solutions of a given set of symmetries. In this paper, the performances of various unitary coupled cluster (UCC) ansätze applied to VQE calculations on excited states are investigated, using quantum circuits designed to represent single reference and multireference…
Reflecting the increasing interest in quantum computing, the variational quantum eigensolver (VQE) has attracted much attentions as a possible application of near-term quantum computers. Although the VQE has often been applied to quantum chemistry, high computational cost is required for reliable results because infinitely many measurements are needed to obtain an accurate expectation value and the expectation value is calculated many times to minimize a cost function in the variational optimization procedure. Therefore, it is necessary to reduce the computational cost of the VQE for a practic…
We present a variational formulation of Time-Dependent Density Functional Theory similar to the constrained-search variational formulation of ground-state density-function theory. The formulation is applied to justify the time-dependent Kohn-Sham method. Other promising applications to advance TDDFT are suggested.
We present a general approach to converge excited state solutions to any quantum chemistry orbital optimization process, without the risk of variational collapse. The resulting Square Gradient Minimization (SGM) approach only requires analytic energy/Lagrangian orbital gradients and merely costs 3 times as much as ground state orbital optimization (per iteration), when implemented via a finite difference approach. SGM is applied to both single determinant $Δ$SCF and spin-purified Restricted Open-Shell Kohn-Sham (ROKS) approaches to study the accuracy of orbital optimized DFT excited states. It…
Artificial neural networks have been recently introduced as a general ansatz to compactly represent many- body wave functions. In conjunction with Variational Monte Carlo, this ansatz has been applied to find Hamil- tonian ground states and their energies. Here we provide extensions of this method to study properties of ex- cited states, a central task in several many-body quantum calculations. First, we give a prescription that allows to target eigenstates of a (nonlocal) symmetry of the Hamiltonian. Second, we give an algorithm that allows to compute low-lying excited states without symmetri…
Ground and Excited States from Ensemble Variational Principles
本文证明了系综变分原理中系综能量收敛则本征态和本征能同样收敛的关键假设，推导出误差的线性界限并证明其紧致性，为辅助权重的最优选择提供了依据。
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