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arXiv:2509.05804 · Physical Review A

Genetic optimization of ansatz expressibility for enhanced variational-quantum-algorithm performance

Manish Mallapur, Ronit Raj, Ankur Raina

Published Feb 18, 2026• 0 citations
arXivHTMLPDF

Abstract

Variational quantum algorithms have emerged as a leading paradigm that extracts practical computation from near-term intermediate-scale quantum devices, enabling advances in quantum chemistry simulations, combinatorial optimization, and quantum machine learning. However, the performance of variational quantum algorithms is highly sensitive to the design of the ansatze. To be effective, ansatze must be expressive enough to capture target states but shallow enough to be trainable. We propose a genetic algorithm-inspired framework for designing ansatze that achieve high expressibility while maintaining shallow depth and low parameter count. Our approach evolves ansatze through mutation and selection based on an expressibility metric. The circuit generated by our framework consistently demonstrates high expressibility at any target depth and performs comparably to traditional ansatz design approaches. This work presents a problem-agnostic, scalable solution for ansatz design, producing expressive, low-depth circuits that need to be designed only once and can serve a wide range of applications.

DOI
10.1103/812w-ytnb

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Variational quantum algorithms have emerged as a leading paradigm that extracts practical computation from near-term intermediate-scale quantum devices, enabling advances in quantum chemistry simulations, combinatorial optimization, and quantum machine learning. However, the performance of variational quantum algorithms is highly sensitive to the design of the ansatze. To be effective, ansatze must be expressive enough to capture target states but shallow enough to be trainable. We propose a genetic algorithm-inspired framework for designing ansatze that achieve high expressibility while maintaining shallow depth and low parameter count. Our approach evolves ansatze through mutation and selection based on an expressibility metric. The circuit generated by our framework consistently demonstrates high expressibility at any target depth and performs comparably to traditional ansatz design approaches. This work presents a problem-agnostic, scalable solution for ansatz design, producing expressive, low-depth circuits that need to be designed only once and can serve a wide range of applications.
Post-Variational Quantum Neural Networks (PVQNNs) eliminate the need for quantum parameter optimization by employing fixed, non-parametric circuits and shifting all learning to the classical domain, thereby avoiding barren plateaus entirely. However, the performance of PV-QNNs critically depends on the choice of ansatz architecture. In this work, we propose an automatic ansatz optimization framework based on Genetic Algorithms (GAs) that searches for optimal circuit ensembles under discrete constraints of topology, depth, and gate types. Quantum features are extracted efficiently via classical shadows and processed by a shallow classical classifier, preserving the post-variational property. Experimental results on the Fashion-MNIST (0 vs 4) classification task demonstrate that GA-selected ensembles outperform all baselines, achieving 89.0 % accuracy with 8 qubits, exceeding random and manually designed templates by3−5%\mathbf{3}-\mathbf{5} {\%}3−5%. Moreover, GA ensembles achieve up to1.9×1.9 \times1.9×higher accuracy per circuit and2×2 \times2×higher accuracy per twoqubit gate, while maintaining shallower circuits (6.0 depth vs. 8.6). These results indicate that evolutionary search effectively identifies compact, information-rich quantum circuits, enabling scalable and resource-efficient post-variational learning.
Post-variational quantum neural networks (PV-QNNs) shift learning from parameterized quantum circuits to a classical head, but their performance hinges on selecting effective fixed ansätze. Manual templates or random circuit picks are brittle and scale poorly. We propose an automated, genetic-algorithm (GA) framework for PV-QNN ansatz ensemble selection. The GA searches a discrete circuit grammar (single-/two-qubit gates under topology and depth constraints) to assemble small ensembles whose quantum features are extracted via classical shadows and consumed by a shallow classical classifier. On Fashion-MNIST and MNIST (2 vs 6), GA-selected ensembles consistently outperform random and heuristic baselines while using about 40% fewer circuits; our efficiency metric, accuracy per circuit, improves by 74%. We also observe stable cross-dataset transfer, indicating that the discovered circuits capture task-relevant structure beyond a single training distribution. These results demonstrate that evolutionary search is a practical route to high-utility, low-footprint PV-QNNs, improving accuracy and sample efficiency without any quantum parameter training, and strengthening PV-QNN viability on near-term hardware.
Combinatorial optimization is a promising application for near-term quantum computers, however, identifying performant algorithms suited to noisy quantum hardware remains as an important goal to potentially realizing quantum computational advantages. To address this we present a variational quantum algorithm for solving combinatorial optimization problems with linear-depth circuits. Our algorithm uses an ansatz composed of Hamiltonian generators designed to control each term in the target combinatorial function, along with parameter updates following a modified version of quantum imaginary time evolution. We evaluate this ansatz in numerical simulations that target solutions to the MAXCUT problem. The state evolution is shown to closely mimic imaginary time evolution, and its optimal-solution convergence is further improved using adaptive transformations of the classical Hamiltonian spectrum. With these innovations, the algorithm consistently converges to optimal solutions, with interesting highly-entangled dynamics along the way. We further demonstrate the success of this approach by performing optimization of a truncated version of our ansatz with up to 32 qubits in a trapped-ion quantum computer, using measurements from the quantum computer to train the ansatz and prepare optimal solutions with high fidelity in the majority of cases we consider. The success of these large-scale quantum circuit optimizations, in the presence of realistic hardware constraints and without error mitigation, mark significant progress on the path towards solving combinatorial problems using quantum computers. We conclude our performant and resource-minimal approach is a promising candidate for potential quantum computational advantages.
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 (H2_22​, H4_44​, H6_66​, BeH2_22​, 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.
Abstract In the context of Variational Quantum Algorithms (VQAs), selecting an appropriate ansatz is crucial for efficient problem-solving. Hamiltonian expressibility has been introduced as a metric to quantify a circuit’s ability to uniformly explore the energy landscape associated with a Hamiltonian ground state search problem. However, its influence on solution quality remains largely unexplored. In this work, we estimate the Hamiltonian expressibility of a well-defined set of circuits applied to various Hamiltonians using a Monte Carlo-based approach. We analyse how ansatz depth influences expressibility and identify the most and least expressive circuits across different problem types. We then train each ansatz using the Variational Quantum Eigensolver (VQE) and analyse the correlation between solution quality and expressibility. Our results indicate that, under ideal or low-noise conditions and particularly for small-scale problems, ansätze with high Hamiltonian expressibility yield better solution quality for problems with non-diagonal Hamiltonians and superposition state solutions. Conversely, circuits with low expressibility are more effective for problems whose solutions are basis states, including those defined by diagonal Hamiltonians. Under noisy conditions, low-expressibility circuits remain preferable for problems with solutions in a computational basis state, while intermediate expressibility yields better results for some problems involving superposition state solutions.
Variational quantum algorithms (VQAs) are constrained by a trade-off: deeper circuits can cover a larger reachable quantum states but suffer from barren plateaus, while shallow circuits remain trainable yet can have insufficient reachability to the target state. Here, we propose a general framework to address this challenge by enhancing the VQA performance with a designed input state constructed using a linear combination technique. This approach modifies the set of states reachable by the original circuit, enhancing accuracy while preserving efficiency. We provide a rigorous proof that such framework increases the performance of any given VQA ansatz, and demonstrate its broad applicability across different ansatz families. In ground state preparation for representative quantum many-body models, it achieves consistently higher accuracy than standard methods at the same gate budget. These results highlight input-state design as a powerful complement to circuit design for improving reachability of the target state within a fixed ansatz. Variational quantum algorithms face a practical trade-off between circuit depth and trainability, which limits the reachability of target quantum states. Here, the authors show that input-state design based on linear combinations systematically modifies the reachable-state set of a fixed ansatz, thereby enhancing target-state reachability and improving ground-state preparation accuracy across representative quantum many-body models without increasing gate cost.