Quantum Computer Simulates 56-Qubit Fermionic Dynamics, Exceeding Classical Capabilities

Simulating the behaviour of fermions, fundamental particles that underpin much of chemistry and materials science, presents a significant challenge for classical computers, hindering progress in fields ranging from biochemistry to clean energy. Faisal Alam, Jan Lukas Bosse, Ieva Čepaitė, and colleagues now demonstrate a quantum simulation of fermionic dynamics on Quantinuum’s Model H2 trapped-ion computer, achieving a complexity beyond the reach of exact classical methods. The team successfully models the behaviour of a 56-qubit system, revealing evidence of spin-charge separation, a phenomenon where an electron’s charge and spin decouple, and observing behaviour that diverges from predictions made by classical tensor network methods. This achievement marks a crucial step towards utilising quantum computers to simulate strongly correlated electronic systems, opening new avenues for understanding and designing advanced materials.

However, the performance of all previous digital quantum simulations has been matched by classical methods, and it has thus far remained unclear whether near-term, intermediate-scale quantum hardware could offer any computational advantage in this area. The research focuses on the periodic spinful 2D Fermi-Hubbard model and presents evidence of spin-charge separation, where the elementary electron’s charge and spin decouple.

Tensor Networks and Quantum System Simulation

Early work established the theoretical foundations for simulating quantum many-body systems using classical methods like Density Matrix Renormalization Group and Tensor Networks. These techniques approximate the behaviour of complex quantum systems, providing a crucial starting point for comparison with quantum computers. Software libraries such as ITensor and Quimb provide the tools necessary to implement these computationally intensive algorithms. A significant portion of the research addresses the concept of quantum advantage, demonstrating that quantum computers can perform tasks intractable for classical computers.

Studies explore random circuit sampling, a benchmark involving running random quantum circuits and measuring the output distribution. Researchers also develop and refine benchmarking techniques, including Cross-Entropy Benchmarking and Linear Cross-Entropy Benchmarking, to accurately assess quantum computer performance. The need for error mitigation and correction is also implicit in these efforts. Several software packages are specifically designed for quantum simulation, including ITensor, Quimb, TeNPy, and Yao. jl. Overall, this compilation provides a comprehensive overview of the state-of-the-art in quantum simulation and benchmarking, covering both theoretical foundations and practical tools, reflecting the rapid growth and complexity of the field.

Fermi-Hubbard Model Simulated on Quantum Computer

Scientists have achieved a significant breakthrough in simulating complex quantum systems using a 56-qubit trapped-ion computer, exceeding the capabilities of classical simulation. This simulation, performed on a 7×4 lattice with periodic boundary conditions, explores a vast computational space, making exact classical computation impractical. Experiments revealed evidence of spin-charge separation, where the fundamental properties of an electron, its charge and spin, decouple.

The team initialized the system with a dimerised state containing a holon and a doublon, then time-evolved it for durations ranging from 0. 1 to 2 units of inverse hopping integral J−1, measuring the real-space occupation basis to determine spin-resolved densities. Results demonstrate behaviour differing from predictions made by classical tensor network methods, particularly in the effective gauge field between spinons and the effective potential between charge carriers. The study explored both non-interacting and interacting regimes, leveraging the trapped-ion computer’s connectivity to implement periodic boundary conditions, minimizing spurious boundary effects. This approach allows for approximately capturing translational invariance without requiring excessively large model sizes. The team’s achievement heralds a new era in quantum computing, enabling the simulation of strongly correlated electronic systems previously inaccessible to classical computation and opening avenues for advancements in materials science and chemistry.

Simulating Fermions Reveals Novel Quantum Behaviour

This research demonstrates the successful simulation of the time dynamics of a 56-qubit Fermi-Hubbard model on a trapped-ion computer, a complexity exceeding the capabilities of exact classical simulation. The team observed evidence of spin-charge separation, where the fundamental properties of electrons, charge and spin, behave independently, and found results consistent with classical simulations where comparison was possible. Importantly, the observed behaviour differed from predictions generated by classical tensor network methods, suggesting the potential for new insights into strongly correlated electronic systems. The study further establishes a computational advantage over existing classical approaches, specifically demonstrating superior performance compared to a high-bond-dimension matrix product state method when generating samples. The researchers developed a novel method for estimating circuit fidelity, based on minimizing a LogXEB score, which provides a robust measure of performance and reinforces the benefits of the quantum hardware. While acknowledging limitations inherent in near-term quantum devices, the team suggests future work could focus on exploring larger systems and refining simulation techniques to further validate these findings and expand our understanding of complex quantum phenomena.