Abstract As quantum computing progresses, variational quantum eigensolvers (VQEs) for ground-state preparation have become an attractive option in leveraging current quantum hardware. However, a major challenge in implementing VQE is understanding whether a given quantum system can even reach the target ground state. In this work, we study reachability conditions for VQE by analyzing their inherent symmetries. We consider a Rydberg-atom quantum simulator with global controls and evaluate its ability to reach ground states for Ising and Heisenberg target Hamiltonians. Symmetry-based conclusions for a smaller number of qubits are corroborated by VQE simulations, demonstrating the reliability of our approach in predicting whether a given quantum architecture could successfully reach the ground state. Our framework also suggests approaches to overcome symmetry restrictions by adding additional quantum resources or choosing different initial states, offering practical guidance for implementing VQE in quantum simulation architectures. Finally, we illustrate connections to adiabatic state preparation.
Abstract As quantum computing progresses, variational quantum eigensolvers (VQEs) for ground-state preparation have become an attractive option in leveraging current quantum hardware. However, a major challenge in implementing VQE is understanding whether a given quantum system can even reach the target ground state. In this work, we study reachability conditions for VQE by analyzing their inherent symmetries. We consider a Rydberg-atom quantum simulator with global controls and evaluate its ability to reach ground states for Ising and Heisenberg target Hamiltonians. Symmetry-based conclusions for a smaller number of qubits are corroborated by VQE simulations, demonstrating the reliability of our approach in predicting whether a given quantum architecture could successfully reach the ground state. Our framework also suggests approaches to overcome symmetry restrictions by adding additional quantum resources or choosing different initial states, offering practical guidance for implementing VQE in quantum simulation architectures. Finally, we illustrate connections to adiabatic state preparation.
Abstract The variational quantum eigensolver (VQE) is one of the most promising and widely used algorithms for exploiting the capabilities of current Noisy Intermediate-Scale Quantum (NISQ) devices. However, VQE algorithms suffer from a plethora of issues, such as barren plateaus, local minima, quantum hardware noise, and limited qubit connectivity, thus posing challenges for their successful deployment on hardware and simulators. In this work, we propose a VQE optimization strategy that builds upon recent advances in the literature, and exhibits very shallow circuit depths when applied to the specific system of interest, namely a model Hamiltonian representing a cuprate superconductor. These features make our approach a favorable candidate for generating good ground state approximations on current NISQ devices. Our findings illustrate the potential of VQE algorithmic development for leveraging the full capabilities of NISQ devices.
In conventional variational quantum eigensolvers (VQEs), trial states are prepared by applying series of parametrized gates to a reference state, with the gate parameters being varied to minimize the energy of the target system. Recognizing that the gates are intermediates, which are ultimately compiled into a set of control pulses to be applied to each qubit in the lab, the recently proposed ctrl-VQE algorithm takes the amplitudes, frequencies, and phases of the pulse as the variational parameters used to minimize the molecular energy. In this work, we explore how all 3 degrees of freedom interrelate with one another. To this end, we consider several distinct strategies to parametrize the control pulses, assessing each one through numerical simulations of a transmonlike device. For each parametrization, we contrast the pulse duration required to prepare a good ansatz, and the difficulty to optimize that ansatz from a well-defined initial state. We deduce several guiding heuristics to implement practical ctrl-VQE in hardware, which we anticipate will generalize for generic device architectures.
Current quantum computers are limited in the number of qubits and coherence time, constraining the algorithms executable with sufficient fidelity. The variational quantum eigensolver (VQE) is an algorithm to find an approximate ground state of a quantum system and is expected to work on even such a device. The deep VQE [K. Fujii, et al., arXiv:2007.10917] is an extension of the original VQE algorithm, which takes a divide-and-conquer approach to relax the hardware requirement. While the deep VQE is successfully applied for spin models and periodic material, its validity on a molecule, where the Hamiltonian is highly nonlocal in the qubit basis, is still unexplored. Here, we discuss the performance of the deep VQE algorithm applied to quantum chemistry problems. Specifically, we examine different subspace-forming methods and compare their accuracy and complexity on a 10 H-atom treelike molecule as well as a 13 H-atom version. Additionally, we examine the performance on the natural occurring molecule retinal. This work also proposes multiple methods to lower the number of qubits required to calculate the ground state of a molecule. We find that the deep VQE can simulate the electron-correlation energy of the ground state to an error of below 1%, thus helping us to reach chemical accuracy in some cases. The accuracy differences and qubits' reduction highlights the basis creation method's impact on the deep VQE.
The variational quantum eigensolver (VQE) is a hybrid quantum classical algorithm designed for current and near-term quantum devices. Despite its initial success, there is a lack of understanding involving several of its key aspects. There are problems with VQE that forbid a favorable scaling towards quantum advantage. In order to alleviate the problems, we propose and extensively test a quantum annealing inspired heuristic that supplements VQE. The improved VQE enables an efficient initial state-preparation mechanism, in a recursive manner, for a quasidynamical unitary evolution. We conduct an in-depth scaling analysis of finding the ground-state energies with increasing lattice sizes of the Heisenberg model, employing simulations of up to 40 qubits that manipulate the complete state vector. In addition to systematically finding the ground-state energy, we observe that it avoids barren plateaus, escapes local minima, and works with low-depth circuits. For the current devices, we further propose a benchmarking toolkit using a mean-field model and test it on IBM Q devices. Realistic gate execution times estimate a longer computational time to complete the same computation on a fully functional error-free quantum computer than on a quantum computer emulator implemented on a classical computer. However, our proposal can be expected to help accurate estimations of the ground-state energies beyond 50 qubits when the complete state vector can no longer be stored on a classical computer, thus enabling quantum advantage.
Abstract Variational quantum algorithms aim at harnessing the power of noisy intermediate-scale quantum (NISQ) computers, by using a classical optimizer to train a parameterized quantum circuit to solve tractable quantum problems. The variational quantum eigensolver (VQE) is one of the aforementioned algorithms designed to determine the ground-state of many-body Hamiltonians. Here, we apply the VQE to study the ground-state properties of N -component fermions. With such knowledge, we study the persistent current of interacting SU( N ) fermions, which is employed to reliably map out the different quantum phases of the system. Our approach lays out the basis for a current-based quantum simulator of many-body systems that can be implemented on NISQ computers.
The ground state search problem is central to quantum computing, with applications spanning quantum chemistry, condensed matter physics, and optimization. The Variational Quantum Eigensolver (VQE) has shown promise for small systems but faces significant limitations. These include barren plateaus, restricted ansatz expressivity, and reliance on domain-specific structure. We present SpinGQE, an extension of the Generative Quantum Eigensolver (GQE) framework to spin Hamiltonians. Our approach reframes circuit design as a generative modeling task. We employ a transformer-based decoder to learn distributions over quantum circuits that produce low-energy states. Training is guided by a weighted mean-squared error loss between model logits and circuit energies evaluated at each gate subsequence. We validate our method on the four-qubit Heisenberg model, demonstrating successfulconvergencetonear-groundstates. Throughsystematichyperparameterexploration, we identify optimal configurations: smaller model architectures (12 layers, 8 attention heads), longer sequence lengths (12 gates), and carefully chosen operator pools yield the most reliable convergence. Our results show that generative approaches can effectively navigate complex energy landscapes without relying on problem-specific symmetries or structure. This provides a scalable alternative to traditional variational methods for general quantum systems. An open-source implementation is available at https://github.com/Mindbeam-AI/SpinGQE.