![]() ![]() These experiments compress the model based on its symmetries methods of this form, while having running time scaling polynomially with system size, are complex enough that solving a post-classical Fermi-Hubbard instance would not be viable on a near-term quantum computer. Small-scale experiments have used quantum algorithms to find ground states of the interacting Fermi-Hubbard model for instances on up to 4 sites 17, 18, 19 using up to 4 qubits. As well as its direct application to understanding technologically-relevant correlated materials, the regularity and relative simplicity of the Fermi-Hubbard Hamiltonian suggest that it may be easier to solve using a quantum computer than, for example, a large unstructured molecule on the other hand, the challenge that it presents for classical methods makes it an excellent benchmark for quantum algorithms. The Fermi-Hubbard model has been widely proposed as an early target for quantum simulation algorithms 9, 10, 11, 12, 13, 14, 15, 16. Quantum computers can represent quantum systems natively, and may enable the solution of physical problems that classical computers cannot handle. Approximate methods can address much larger systems, but suffer from significant uncertainties in computing physically relevant quantities in certain regimes 1. Although a highly simplified model of interacting electrons in a lattice, to date the largest Fermi-Hubbard system which has been solved exactly consisted of just 17 electrons on 22 sites 8. This problem is thrown into sharp relief by the iconic Fermi-Hubbard model 6, 7, the simplest system that includes non-trivial correlations not captured by classical methods (e.g. Yet classical methods are unable to represent the quantum correlations occurring in such systems efficiently, and accurately solving the many-electron problem for arbitrary large systems is beyond the capacity of the world’s most powerful supercomputers. This challenge is motivated both by practical considerations, such as the design and characterisation of novel materials 2, and by fundamental science 3, 4, 5. Understanding systems of many interacting electrons is a grand challenge of condensed-matter physics 1. We also introduce a new variational optimisation algorithm based on iterative Bayesian updates of a local surrogate model. We use a variety of error-mitigation techniques, including symmetries of the Fermi-Hubbard model and a recently developed technique tailored to simulating fermionic systems. Consistent with predictions for the ground state, we observe the onset of the metal-insulator transition and Friedel oscillations in 1D, and antiferromagnetic order in both 1D and 2D. We address 1 × 8 and 2 × 4 instances on 16 qubits on a superconducting quantum processor, substantially larger than previous work based on less scalable compression techniques, and going beyond the family of 1D Fermi-Hubbard instances, which are solvable classically. Here we show experimentally that an efficient, low-depth variational quantum algorithm with few parameters can reproduce important qualitative features of medium-size instances of the Fermi-Hubbard model. However, accurately representing the Fermi-Hubbard ground state for large instances may be beyond the reach of near-term quantum hardware. Other categories: Fashion | Beauty | Glamour | Fine Art | Transportation | Electronics | Still life | Fitness | Lifestyle | Erotica | Landscape | Toronto | Pregnancy | More.The famous, yet unsolved, Fermi-Hubbard model for strongly-correlated electronic systems is a prominent target for quantum computers. Any unauthorized use, distribution, copying or creation of derivative works is NOT allowed. ![]()
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