Quantum Computation for Simulating Periodic Solid-state Systems Using Plane-wave Basis

Schrödinger equation is a notorious high dimensional partial differential equation. The “curse of dimensionality” makes Schrödinger equation very difficult to be solved accurately. As quantum computer has inherent advantage on solving quantum many-body system without wavefunction sign problem, quantum strategies are considered as the future promising ways to solve high dimensional Schrödinger equation. Here, we firstly adopt the Kohn-Sham wavefunction with the plane-wave basis sets and sophisticated pseudopotentials, which permit us to efficiently and accurately construct the Hamiltonian for solid-state materials. Secondly, we develop an enhanced qubit-efficient encoding scheme for reducing the qubit number to satisfy N reference states of specific conditions and symmetries. Then, we utilize an imaginary-time control for less resource requirements and error mitigation. Finally, we numerically demonstrate that this method for ground-state preparation and energy estimation requires Ο(log₂N) qubits in total, and successfully predicts electronic band structure properties of several systems such as hydrogen chain and multi-component solid-state materials. Our quantum algorithm and results show the feasibility of quantum simulations for large-scale quantum systems in the current noisy intermediate-scale quantum (NISQ) device.