Simulating the silicon band structure with a silicon quantum processor

One of the most promising applications of quantum computing is to simulate molecules or solids which can be classically intractable. While spin qubits are one of the leading qubit platforms, quantum chemistry simulations have been limited to the hydrogen molecule so far [1]. Here we exploit the high-fidelity operations and the all-to-all connectivity in our four-qubit (one electron and three nuclear spins) quantum processor [2] to simulate the band structure of silicon – the host material of many spin qubits. For this we map the 8x8 tight-binding Hamiltonian (two atoms with each atom includes sp³ orbitals) onto three nuclear spin qubits. Both the ground and excited states of a certain k-point in the band structure are obtained from the same variational quantum circuit, which generates an orthogonal set of states by using different input states (from |000> to |111>). Various ways to optimize the energy cost function are investigated. This work demonstrates the accuracy of our 4-qubit processor and paves the way for solving larger scale quantum computational chemistry problems.



[1] Xiao Xue et al., Nature 601, no. 7893 (2022): 343-347.

[2] Ian Thorvaldson et al., arXiv preprint arXiv:2404.08741 (2024), accepted in Nature Nanotechology (Oct, 2024).