Quantum Simulation of 2D Fermi-Hubbard Dynamics Achieved Using Programmable 72-Qubit Digital Quantum Computer

Understanding the behaviour of interacting electrons remains a fundamental challenge in physics, with implications for materials science and our understanding of complex systems. Faisal Alam, Jan Lukas Bosse, Ieva Čepaitė, and colleagues now demonstrate a significant step forward in this field, achieving programmable digital simulation of the 2D Fermi-Hubbard model using superconducting qubits. This research overcomes limitations of classical computation by implementing simulations on a 72-qubit processor, allowing the team to explore phenomena such as magnetic polaron formation and dynamical symmetry breaking at a scale previously inaccessible. By validating their results against established methods where possible, the scientists demonstrate that quantum simulation offers a competitive approach to modelling interacting electron systems, opening new avenues for materials discovery and fundamental research.

Computers allow for the programming of all model parameters and the output of any desired physical quantity, however, performing such simulations on today’s quantum computers at a scale beyond the reach of classical methods requires advances in the efficiency of simulation algorithms and error mitigation techniques. This work demonstrates programmable digital quantum simulation of the dynamics of the 2D Fermi-Hubbard model, one of the best-known simplified models of electrons in crystalline solids, at a scale beyond exact classical simulation.

Tensor Networks and Time-Dependent Quantum Simulation

Scientists continually develop methods for simulating quantum systems using both quantum and classical computers. Central to many classical approaches are tensor networks, which efficiently represent the wavefunctions of complex quantum systems. These networks, including Matrix Product States and Projected Entangled Pair States, allow researchers to model quantum behaviour, but their effectiveness is limited by the amount of entanglement they can handle. Alongside tensor networks, techniques like the Time-Dependent Variational Principle and the Density Matrix Renormalization Group provide powerful tools for understanding quantum dynamics and finding the ground state of many-body systems.

Fermi-Hubbard Model Simulated on Quantum Processor

Scientists have achieved a breakthrough in simulating complex quantum systems, demonstrating programmable digital simulation of the 2D Fermi-Hubbard model on Google’s Willow processor. The team successfully implemented simulations on lattice sizes up to 6×6 sites, requiring a total of 72 qubits, and explored a range of physical parameters including on-site electron-electron interaction strength and magnetic flux. Experiments focused on studying several aspects of Fermi-Hubbard dynamics, including the formation of magnetic polarons, charge carriers surrounded by local magnetic polarization, starting from various initial states. Researchers observed the emergence of these polarons from a single holon on a chequerboard pattern, providing insights into the behavior of interacting electrons in crystalline solids.

The simulations also investigated dynamical symmetry breaking in stripe-ordered states and the attraction of charge carriers on an entangled state known as a valence bond solid, revealing complex quantum phenomena. Measurements confirm the ability to simulate the time evolution of quantum systems, a computationally demanding task for classical computers. This achievement opens new avenues for exploring materials and chemicals, potentially accelerating the discovery of novel compounds for technologies such as batteries and photovoltaics.

Fermi-Hubbard Simulation Achieves Quantum Advantage

This work presents the first successful digital quantum simulation of the two-dimensional Fermi-Hubbard model on lattice sizes up to 6×6, a significant achievement in the field of quantum simulation. Researchers demonstrated this capability through highly efficient algorithmic implementation, optimised for the specific hardware and target problem, and novel fermionic training-based noise mitigation methods. These techniques leverage the properties of interacting electron models to reduce computational complexity and improve accuracy. The team validated their results against exact calculations where feasible and benchmarked the quantum simulation against established classical methods, including tensor network and operator propagation techniques. In some instances, the classical methods failed to match the results obtained from the quantum hardware, suggesting a potential advantage for quantum simulation in this domain. Future research directions include exploiting continuously tunable gate parameters and further refining the fermionic training-based noise mitigation methods to enhance performance and expand the scope of accessible electronic structure models.