Fermionic quantum computing for condensed-matter physics

Experiments with fermionic atoms in optical lattices have led to progress in understanding fundamental condensed-matter phenomena in regimes difficult to access for classical numerics. However, elevating such experiments from a tool of scientific exploration to a computational tool capable of quantitatively predicting molecule and material properties requires overcoming decoherence with error correction techniques. Existing approaches encode qubits into atoms, losing one of the fundamental advantages of cold atoms: their fermionic nature. In this talk, we introduce a fault-tolerant qubit-fermion quantum computing framework by encoding logical fermionic degrees of freedom into fermionic atoms. Our scheme yields an exponential improvement in circuit depth from O(N) to O(log(N)) with respect to lattice site number N compared to state-of-the-art qubit-only approaches for simulating crystalline materials. Our work opens the door to fermion-qubit fault-tolerant quantum computation in neutral atoms, with applications in quantum chemistry, material science and high-energy physics