Fast gradient-free optimization of excitations in variational quantum eigensolvers

• URL: http://arxiv.org/abs/2409.05939v3
• Date: Wed, 05 Nov 2025 04:07:07 GMT
• Title: Fast gradient-free optimization of excitations in variational quantum eigensolvers
• Authors: Jonas Jäger, Thierry Nicolas Kaldenbach, Max Haas, Erik Schultheis,
• Abstract summary: We introduce Excitation, a fast quantum-aware that is globally-informed and gradient-free.<n>By uniting physical insight with efficient optimization, Excitation paves the way for scalable quantum chemistry calculations.
• Score: 4.8631532419368835
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Finding molecular ground states and energies with variational quantum eigensolvers is central to chemistry applications on quantum computers. Physically motivated ans\"atze based on excitation operators respect physical symmetries, but existing quantum-aware optimizers, such as Rotosolve, have been limited to simpler operator types. To fill this gap, we introduce ExcitationSolve, a fast quantum-aware optimizer that is globally-informed, gradient-free, and hyperparameter-free. ExcitationSolve extends these optimizers to parameterized unitaries with generators $G$ of the form $G^3=G$ exhibited by excitation operators in approaches such as unitary coupled cluster. ExcitationSolve determines the global optimum along each variational parameter using the same quantum resources that gradient-based optimizers require for one update step. We provide optimization strategies for both fixed and adaptive variational ans\"atze, along with generalizations for simultaneously selecting and optimizing multiple excitations. On molecular ground state energy benchmarks, ExcitationSolve outperforms state-of-the-art optimizers by converging faster, achieving chemical accuracy for equilibrium geometries in a single parameter sweep, yielding shallower adaptive ans\"atze and remaining robust to real hardware noise. By uniting physical insight with efficient optimization, ExcitationSolve paves the way for scalable quantum chemistry calculations.

Related papers

• HOPSO: A Robust Classical Optimizer for VQE [0.0]
  Variational Quantum Eigensolver (VQE) is one of few approaches where the hope for near-term quantum advantage concentrates.<n>We show that a properly tailored classical part of VQE algorithms can tackle with current problems and gives hope for its scalability for larger systems.
  arXiv  Detail & Related papers  (2025-08-19T09:01:30Z)
• Blockwise Optimization for Projective Variational Quantum Dynamics (BLOP-VQD): Algorithm and Implementation for Lattice Systems [0.0]
  We present an efficient approach to simulate real-time quantum dynamics using Projected Variational Quantum Dynamics. Our method selectively optimize one block at a time while keeping the others fixed, allowing for significant reductions in computational overhead. We demonstrate the performance of the proposed methods in a series of spin-lattice models with varying sizes and complexity.
  arXiv  Detail & Related papers  (2025-03-24T01:48:37Z)
• Optimizing a parameterized controlled gate with Free Quaternion Selection [0.4353365283165517]
  In this study, we propose an algorithm to estimate the optimal parameters for locally minimizing the cost value of a single-qubit gate. To benchmark the performance, we apply the proposed method to various optimization problems, including the Variational Eigensolver (VQE) for Ising and molecular Hamiltonians.
  arXiv  Detail & Related papers  (2024-09-20T14:46:00Z)
• Quantum algorithms for the variational optimization of correlated electronic states with stochastic reconfiguration and the linear method [0.0]
  We present quantum algorithms for the variational optimization of wavefunctions correlated by products of unitary operators. While an implementation on classical computing hardware would require exponentially growing compute cost, the cost (number of circuits and shots) of our quantum algorithms is in system size.
  arXiv  Detail & Related papers  (2024-08-03T17:53:35Z)
• Pulse-based variational quantum optimization and metalearning in superconducting circuits [3.770494165043573]
  We introduce pulse-based variational quantum optimization (PBVQO) as a hardware-level framework. We illustrate the framework by optimizing external superconducting on quantum interference devices. The synergy between PBVQO and meta-learning provides an advantage over conventional gate-based variational algorithms.
  arXiv  Detail & Related papers  (2024-07-17T15:05:36Z)
• Analyzing and Enhancing the Backward-Pass Convergence of Unrolled Optimization [50.38518771642365]
  The integration of constrained optimization models as components in deep networks has led to promising advances on many specialized learning tasks. A central challenge in this setting is backpropagation through the solution of an optimization problem, which often lacks a closed form. This paper provides theoretical insights into the backward pass of unrolled optimization, showing that it is equivalent to the solution of a linear system by a particular iterative method. A system called Folded Optimization is proposed to construct more efficient backpropagation rules from unrolled solver implementations.
  arXiv  Detail & Related papers  (2023-12-28T23:15:18Z)
• Randomized Benchmarking of Local Zeroth-Order Optimizers for Variational Quantum Systems [65.268245109828]
  We compare the performance of classicals across a series of partially-randomized tasks. We focus on local zeroth-orders due to their generally favorable performance and query-efficiency on quantum systems.
  arXiv  Detail & Related papers  (2023-10-14T02:13:26Z)
• GRAPE optimization for open quantum systems with time-dependent decoherence rates driven by coherent and incoherent controls [77.34726150561087]
  The GRadient Ascent Pulse Engineering (GRAPE) method is widely used for optimization in quantum control. We adopt GRAPE method for optimizing objective functionals for open quantum systems driven by both coherent and incoherent controls. The efficiency of the algorithm is demonstrated through numerical simulations for the state-to-state transition problem.
  arXiv  Detail & Related papers  (2023-07-17T13:37:18Z)
• A self-consistent field approach for the variational quantum eigensolver: orbital optimization goes adaptive [52.77024349608834]
  We present a self consistent field approach (SCF) within the Adaptive Derivative-Assembled Problem-Assembled Ansatz Variational Eigensolver (ADAPTVQE) This framework is used for efficient quantum simulations of chemical systems on nearterm quantum computers.
  arXiv  Detail & Related papers  (2022-12-21T23:15:17Z)
• Benchmarking of Different Optimizers in the Variational Quantum Algorithms for Applications in Quantum Chemistry [0.0]
  Classical yardsticks play a crucial role in determining the accuracy and convergence of variational quantum algorithms. We consider a few popular yardsticks and assess their performance in variational quantum algorithms for applications in quantum chemistry.
  arXiv  Detail & Related papers  (2022-08-22T13:02:00Z)
• Monte Carlo Tree Search based Hybrid Optimization of Variational Quantum Circuits [7.08228773002332]
  We propose a new variational quantum algorithm called MCTS-QAOA. It combines a Monte Carlo tree search method with an improved natural policy gradient solver to optimize the discrete and continuous variables in the quantum circuit. We find that MCTS-QAOA has excellent noise-resilience properties and outperforms prior algorithms in challenging instances of the generalized QAOA.
  arXiv  Detail & Related papers  (2022-03-30T23:15:21Z)
• Progress towards analytically optimal angles in quantum approximate optimisation [0.0]
  The Quantum Approximate optimisation algorithm is a $p$ layer, time-variable split operator method executed on a quantum processor. We prove that optimal parameters for $p=1$ layer reduce to one free variable and in the thermodynamic limit, we recover optimal angles. We moreover demonstrate that conditions for vanishing gradients of the overlap function share a similar form which leads to a linear relation between circuit parameters, independent on the number of qubits.
  arXiv  Detail & Related papers  (2021-09-23T18:00:13Z)
• Variational Quantum Optimization with Multi-Basis Encodings [62.72309460291971]
  We introduce a new variational quantum algorithm that benefits from two innovations: multi-basis graph complexity and nonlinear activation functions. Our results in increased optimization performance, two increase in effective landscapes and a reduction in measurement progress.
  arXiv  Detail & Related papers  (2021-06-24T20:16:02Z)
• Adaptive variational quantum eigensolvers for highly excited states [4.038971004196936]
  Highly excited states of quantum many-body systems are central objects in the study of quantum dynamics and thermalization. We propose an adaptive variational algorithm, adaptive VQE-X, that self-generates a variational ansatz for arbitrary eigenstates of a many-body Hamiltonian $H$.
  arXiv  Detail & Related papers  (2021-04-26T15:03:51Z)
• Unitary Block Optimization for Variational Quantum Algorithms [0.0]
  We describe the unitary block optimization scheme (UBOS) and apply it to two variational quantum algorithms. The goal of VQE is to optimize a classically intractable parameterized quantum wave function to target a physical state of a Hamiltonian. We additionally describe how UBOS applies to real and imaginary time-evolution.
  arXiv  Detail & Related papers  (2021-02-16T19:00:05Z)
• Benchmarking adaptive variational quantum eigensolvers [63.277656713454284]
  We benchmark the accuracy of VQE and ADAPT-VQE to calculate the electronic ground states and potential energy curves. We find both methods provide good estimates of the energy and ground state. gradient-based optimization is more economical and delivers superior performance than analogous simulations carried out with gradient-frees.
  arXiv  Detail & Related papers  (2020-11-02T19:52:04Z)
• Direct Optimal Control Approach to Laser-Driven Quantum Particle Dynamics [77.34726150561087]
  We propose direct optimal control as a robust and flexible alternative to indirect control theory. The method is illustrated for the case of laser-driven wavepacket dynamics in a bistable potential.
  arXiv  Detail & Related papers  (2020-10-08T07:59:29Z)
• Adaptive pruning-based optimization of parameterized quantum circuits [62.997667081978825]
  Variisy hybrid quantum-classical algorithms are powerful tools to maximize the use of Noisy Intermediate Scale Quantum devices. We propose a strategy for such ansatze used in variational quantum algorithms, which we call "Efficient Circuit Training" (PECT) Instead of optimizing all of the ansatz parameters at once, PECT launches a sequence of variational algorithms.
  arXiv  Detail & Related papers  (2020-10-01T18:14:11Z)
• Hessian-based optimization of constrained quantum control [0.0]
  gradient-based textscgrape algorithm is successfully applied in a wide range of different branches of quantum physics. We derive and implement exact $2mathrmnd$ order analytical derivatives of the coherent dynamics. We demonstrate performance improvements for both the best and average errors of constrained unitary gate synthesis on a circuit-textscqed system.
  arXiv  Detail & Related papers  (2020-06-01T13:31:06Z)
• Cross Entropy Hyperparameter Optimization for Constrained Problem Hamiltonians Applied to QAOA [68.11912614360878]
  Hybrid quantum-classical algorithms such as Quantum Approximate Optimization Algorithm (QAOA) are considered as one of the most encouraging approaches for taking advantage of near-term quantum computers in practical applications. Such algorithms are usually implemented in a variational form, combining a classical optimization method with a quantum machine to find good solutions to an optimization problem. In this study we apply a Cross-Entropy method to shape this landscape, which allows the classical parameter to find better parameters more easily and hence results in an improved performance.
  arXiv  Detail & Related papers  (2020-03-11T13:52:41Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.