Optimizing VQE Ansatz Studies Tight-Binding Models with sd-Interaction and On-Site Coulomb Repulsion

Understanding the behaviour of electrons in materials requires increasingly sophisticated computational methods, and researchers continually seek ways to improve these techniques. Oleg Udalov, working independently, investigates how to optimise a specific quantum computing algorithm, the Variational Quantum Eigensolver (VQE), for modelling complex materials. This work focuses on tight-binding models, which describe electron behaviour, incorporating both interactions between electrons and their repulsion due to charge. By refining the structure of the VQE algorithm, and testing it on simulations of materials, this research significantly reduces the computational demands of modelling these systems, paving the way for more accurate and efficient materials design.

Modifications to the standard methods for building quantum circuits are proposed, significantly reducing the number of two-qubit gates needed for computation. Currently, quantum computer simulations of physical systems attract increasing attention due to the growing availability of quantum hardware, with multiple companies now providing access to their devices. The authors explore different quantum circuit designs, known as ansatze, and optimisation strategies to efficiently represent the ground state of the model on near-term quantum computers. Key findings demonstrate the potential of these techniques for understanding complex materials. The study compares various quantum circuit ansatze, including hardware-efficient designs and more complex ones, to assess their ability to accurately represent the ground state of the Fermi-Hubbard model.

Researchers highlight the challenges associated with optimising the parameters of the quantum circuit, including the presence of barren plateaus. They explore different classical optimisers to overcome these challenges, evaluating performance in terms of energy accuracy and scalability. The research compares the results obtained from the VQE algorithm with those from classical methods to assess the potential advantages and limitations of the quantum approach, acknowledging the impact of noise and discussing potential mitigation strategies. Overall, the research contributes to the development of efficient and accurate quantum algorithms for simulating complex quantum systems, paving the way for the use of quantum computers in materials science and condensed matter physics.

Simplified Quantum Circuits Model Electron Interactions

Researchers have achieved significant reductions in the complexity of quantum circuits used to model complex physical systems, specifically focusing on finding the ground state of a lattice model with interacting electrons. The team systematically investigated various quantum circuit designs, known as ansatze, and developed a simplified approach that dramatically lowers the number of quantum gates required for computation. Initial experiments revealed that a standard “cluster” ansatz required a rapidly increasing number of two-qubit gates. Implementing the YAB ansatz reduced the gate count, but the most substantial gains were achieved with a novel, simplified YAB ansatz, which further reduced the gate count.

Remarkably, restricting the ansatz to utilise only single-electron transitions led to an even more drastic reduction, decreasing the number of gates by roughly an order of magnitude. For a system with four sites, the simplified YAB ansatz with single-electron transitions required only 114 two-qubit gates, compared to 3572 gates for the standard approach. Repeating this single-transition ansatz three times, while expanding the accessible state space, maintained a significantly lower gate count. The team also explored the impact of initial conditions on the optimisation process, designing circuits to prepare specific initial states, accelerating convergence and avoiding trapping the optimisation in incorrect solutions. The team systematically compared the performance of several quantum circuit designs, known as ansatze, including both cluster and more generic forms, and proposed modifications to the cluster ansatz that significantly reduce the number of two-qubit gates required for computation. Multiple classical optimisation algorithms were integrated within the VQE framework and their effectiveness was rigorously evaluated. The study reveals that, under ideal conditions, the SLSQP and BFGS optimisers yielded the most accurate results.

Importantly, the researchers achieved a substantial reduction in circuit complexity, from approximately 15,000 two-qubit gates to around 300, by strategically modifying the cluster ansatz and repeating single transition operators. This simplification proved particularly beneficial in noisy simulations, where shorter circuits exhibit improved energy accuracy. Interestingly, the fidelity of the calculated wave function remained largely unaffected by the introduction of noise, even as energy prediction precision decreased. The authors acknowledge that the performance of optimisation algorithms is generally slower in the presence of noise, requiring more computational iterations. Future work could focus on developing noise-mitigation strategies tailored to VQE algorithms and exploring the potential of these techniques on larger, more complex quantum systems.