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arXiv:2503.18279 · The Journal of Chemical Physics

Blockwise optimization for projective variational quantum dynamics (BLOP-VQD): Algorithm and implementation for lattice systems

Harshdeep Singh, Sonjoy Majumder, Sabyashachi Mishra

Published Sep 22, 2025• 1 citation
arXivHTMLPDF

Abstract

We present an efficient approach to simulate real-time quantum dynamics using projected variational quantum dynamics, where the computational cost is reduced by strategically optimizing only a subset of the variational parameters at each time step. Typically, the variational Ansatz consists of repeated blocks of parameterized quantum circuits, where all parameters are updated in a standard optimization procedure. In contrast, our method selectively optimizes one block at a time while keeping the others fixed, allowing for significant reductions in computational overhead. This semi-global optimization strategy ensures that all qubits are still involved in the evolution, but the optimization is localized to specific blocks, thus avoiding the need to update all parameters simultaneously. We propose different approaches for choosing the next block for optimization, including sequential, random, and fidelity-based updation. We demonstrate the performance of the proposed methods in a series of spin-lattice models with varying sizes and complexity. Our method preserves the accuracy of the time evolution with a much lower computational cost. This new optimization strategy provides a promising path toward high-fidelity simulation of the time evolution of complex quantum systems with reduced computational resources.

DOI
10.1063/5.0289105

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We present an efficient approach to simulate real-time quantum dynamics using projected variational quantum dynamics, where the computational cost is reduced by strategically optimizing only a subset of the variational parameters at each time step. Typically, the variational Ansatz consists of repeated blocks of parameterized quantum circuits, where all parameters are updated in a standard optimization procedure. In contrast, our method selectively optimizes one block at a time while keeping the others fixed, allowing for significant reductions in computational overhead. This semi-global optimization strategy ensures that all qubits are still involved in the evolution, but the optimization is localized to specific blocks, thus avoiding the need to update all parameters simultaneously. We propose different approaches for choosing the next block for optimization, including sequential, random, and fidelity-based updation. We demonstrate the performance of the proposed methods in a series of spin-lattice models with varying sizes and complexity. Our method preserves the accuracy of the time evolution with a much lower computational cost. This new optimization strategy provides a promising path toward high-fidelity simulation of the time evolution of complex quantum systems with reduced computational resources.
We introduce a novel hybrid algorithm to simulate the real-time evolution of quantum systems using parameterized quantum circuits. The method, named "projected – Variational Quantum Dynamics" (p-VQD) realizes an iterative, global projection of the exact time evolution onto the parameterized manifold. In the small time-step limit, this is equivalent to the McLachlan's variational principle. Our approach is efficient in the sense that it exhibits an optimal linear scaling with the total number of variational parameters. Furthermore, it is global in the sense that it uses the variational principle to optimize all parameters at once. The global nature of our approach then significantly extends the scope of existing efficient variational methods, that instead typically rely on the iterative optimization of a restricted subset of variational parameters. Through numerical experiments, we also show that our approach is particularly advantageous over existing global optimization algorithms based on the time-dependent variational principle that, due to a demanding quadratic scaling with parameter numbers, are unsuitable for large parameterized quantum circuits.
Accurate real-time simulation of correlated quantum systems remains challenging for both classical methods and near-term quantum hardware. We introduce operator-projected variational quantum real-time evolution (OVQRTE), which updates a parameterized circuit by enforcing the Ehrenfest equations for a selected set of observables. OVQRTE requires only expectation-value measurements, while the choice of operator set enables a systematic trade-off between accuracy and measurement cost, substantially reducing quantum-resource requirements relative to existing variational real-time-evolution algorithms. After implementing OVQRTE dynamics of Heisenberg model on a simulator, we benchmark the algorithm for the Anderson impurity models on the IQM Emerald superconducting processor using up to 24 qubits. We further use OVQRTE to sample computational-basis states for quantum-selected configuration interaction (QSCI), enabling the calculation of the ground-state energy and density of states within a self-consistent ghost-Gutzwiller Ansatz (gGut) embedding loop. Our results establish OVQRTE as a promising approach for investigating correlated condensed-matter systems on near-term quantum hardware.
We propose an adaptive quantum algorithm to prepare accurate variational time evolved wave functions. The method is based on the projected variational quantum dynamics (pVQD) algorithm, that performs a global optimization with linear scaling in the number of variational parameters. Instead of fixing a variational ansatz at the beginning of the simulation, the circuit is grown systematically during the time evolution. Moreover, the adaptive step does not require auxiliary qubits and the gate search can be performed in parallel on different quantum devices. We apply the algorithm, named adaptive pVQD, to the simulation of driven spin models and fermionic systems, where it shows an advantage when compared to both Trotterized circuits and nonadaptive variational methods. Finally, we use the shallower circuits prepared using the adaptive pVQD algorithm to obtain more accurate measurements of physical properties of quantum systems on hardware. Published by the American Physical Society 2024
Variational compression can significantly lower implementation overheads for encoding the time evolution of Hamiltonians into quantum circuits. However, they usually lack global convergence guarantees and well-established scaling behavior. In this work, we provide a recipe for choosing the initial point of such variational optimizations that guarantees convergence to a quantum circuit with near-optimal gate complexity O(N t polylog(N t/ε))\mathcal{O}\left( N \, t \, \text{polylog}(N \, t/ε) \right)O(Ntpolylog(Nt/ε)) for all local and translationally invariant Hamiltonians. We demonstrate our method by encoding the globally controlled time evolution of a Heisenberg antiferromagnet on a Kagome lattice. For N=48N = 48N=48 sites, evolution time t=0.1t=0.1t=0.1 and infidelity ε≈1%ε\approx1\%ε≈1%, the controlled time-evolution circuit requires 960 two-qubit B gates, for which we propose a straightforward implementation scheme for ion-trap setups. Thereby, our recipe extends digital quantum simulators toward system sizes and geometries that are challenging for classical computation.
The exponential runtime of quantum simulators on classical machines, along with long queue times and high costs associated with real quantum devices, presents significant challenges for the efficient optimization of Variational Quantum Algorithms (VQAs) such as the Variational Quantum Eigensolver (VQE), Quantum Approximate Optimization Algorithm (QAOA), and Quantum Neural Networks (QNNs). To address these limitations, we propose a novel approach, DyPP (Dynamic Parameter Prediction), which accelerates the convergence of VQAs by leveraging regular trends in the parameter weights to update parameters efficiently. We introduce two techniques for optimal prediction performance: Naive Prediction (NaP) and Adaptive Prediction (AdaP). Through extensive experimentation and training of multiple QNN models on various datasets, we demonstrate that DyPP achieves a speedup of approximately 2.25×compared to standard training methods, while also providing improved accuracy (up to 2.3% higher) and lower loss (up to 6.1% reduction) with minimal storage and computational overhead. We further evaluate DyPP’s effectiveness in VQE for molecular ground-state energy estimation and in QAOA for graph MaxCut. Our results show that, on average, DyPP leads to a speedup of up to 3.1× for VQE and 2.91× for QAOA compared to traditional optimization, while requiring up to 3.3× fewer shots (i.e., repeated circuit executions). Even in the presence of hardware noise, DyPP outperforms existing optimization techniques, delivering up to 3.33× speedup and requiring 2.5× fewer shots, thereby enhancing the efficiency of VQAs.
Abstract We propose an optimization method for the Variational Quantum Eigensolver (VQE) that combines adaptive and physics-inspired ansatz design. Instead of optimizing multiple layers simultaneously, the ansatz is built incrementally from its operator subsets, enabling subspace optimization that provides better initialization for subsequent steps. This quasi-dynamical approach preserves expressivity and hardware efficiency while avoiding the overhead of operator selection associated with adaptive methods. Benchmarks on one- and two-dimensional Heisenberg and Hubbard models with up to 20 qubits show improved fidelities, reduced function evaluations, or both, compared to fixed-layer VQE. The method is simple, cost-effective, and particularly well-suited for current noisy intermediate-scale quantum (NISQ) devices.