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arXiv:2602.17612 · Physical Review Research

Trainable, self-verifying variational quantum eigensolver using adiabatic warm starts

Bojan Žunkovič, Marco Ballarin, Lewis Wright, Michael Lubasch

quant-phSubmitted Feb 19, 2026• Announced Feb 20, 2026• 0 citations• Revised Oct 29, 2026 (v2)
v1 · Feb 19, 2026v2 · Oct 29, 2026
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Abstract

We study an adiabatic variant of the variational quantum eigensolver (VQE) in which VQE is performed iteratively for a sequence of Hamiltonians along an adiabatic path. We derive the conditions under which gradient-based optimization successfully prepares the adiabatic ground states. These conditions define a trainable tracking region. Additionally, when combined with a gap lower bound, energy-standard-deviation measurements certify eigenstate accuracy at run-time and verify convergence to the global optimum.

Journal reference
Phys. Rev. Research 8, L042013 (2026)
DOI
10.1103/m538-45pk
Comments
7 pages, 2 figures + 31 pages, 5 figures

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We study an adiabatic variant of the variational quantum eigensolver (VQE) in which VQE is performed iteratively for a sequence of Hamiltonians along an adiabatic path. We derive the conditions under which gradient-based optimization successfully prepares the adiabatic ground states. These conditions define a trainable tracking region. Additionally, when combined with a gap lower bound, energy-standard-deviation measurements certify eigenstate accuracy at run-time and verify convergence to the global optimum.
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Variational Quantum Eigensolver (VQE) is widely used in near-term hardware. However, their performances remain limited by the poor trainability and are dependent on random parameter initialization. In this work, we propose a warm start method inspired by imaginary time evolution, allowing for determining initial parameters that prioritize lower energy states in a resource-efficient way. Using classical simulations, we demonstrate that this warm start method significantly improves the success rate and reduces the number of iterations required for the convergence of VQE. The numerical results also indicate that the warm start approach effectively mitigates statistical errors arising from a finite number of measurements, and to a certain extent alleviates the effect of barren plateaus.
Abstract Variational Quantum Eigensolver (VQE) is widely used in near-term hardware. However, their performances remain limited by the poor trainability and are dependent on random parameter initialization. In this work, we propose a warm start method inspired by imaginary time evolution, allowing for determining initial parameters that prioritize lower energy states in a resource-efficient way. Using classical simulations, we demonstrate that this warm start method significantly improves the success rate and reduces the number of iterations required for the convergence of VQE. The numerical results also indicate that the warm start approach effectively mitigates statistical errors arising from a finite number of measurements, and to a certain extent alleviates the effect of barren plateaus.
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 may be more efficient to find low-energy excited states than those of minimizing energy or variance alone. We further reveal that the optimization can be boosted with stochastic gradient descent by Hamiltonian sampling, which uses only a few terms of the Hamiltonian and thus significantly reduces the quantum resource for evaluating variance and its gradients.
The Variational Quantum Eigensolver (VQE) is a Variational Quantum Algorithm (VQA) to determine the ground state of quantum-mechanical systems. As a VQA, it makes use of a classical computer to optimize parameter values for its quantum circuit. However, each iteration of the VQE requires a multitude of measurements, and the optimization is subject to obstructions, such as barren plateaus, local minima, and subsequently slow convergence. We propose a warm-starting technique, that utilizes an approximation to generate beneficial initial parameter values for the VQE aiming to mitigate these effects. The warm-start is based on Approximate Complex Amplitude Encoding, a VQA using fidelity estimations from classical shadows to encode complex amplitude vectors into quantum states. Such warm-starts open the path to fruitful combinations of classical approximation algorithms and quantum algorithms. In particular, the evaluation of our approach shows that the warm-started VQE reaches higher quality solutions earlier than the original VQE.
We present a hybrid classical-quantum algorithm to solve optimization problems in current quantum computers, whose basic idea is to assist variational quantum eigensolvers (VQE) with adiabatic change of the Hamiltonian. The rational for this new algorithm is to circumvent the problem of facing very small gradients in the classical optimization piece of a VQE, while being able to run in current hardware efficient devices. A discrete concatenation of VQEs adapted to interpolating Hamiltonians provides a method to keep the quantum state always close to a path faithfully directed to find the final solution. We benchmark this Adiabatically Assisted Variational Quantum Eigensolver (AAVQE) on quantum Hamiltonians and hard classical problems, for which our approach shows fast convergence.