Recently, the Quantum Algorithm Application R&D team at the Beijing Academy of Quantum Information Sciences (BAQIS), in collaboration with Tsinghua University, has made new strides in quantum algorithms. Utilizing the linear combination of unitary operators(LCU) and the Powered-Full Quantum Eigensolver (P-FQE), they have developed a quantum algorithm capable of computing the band structure of condensed matter systems. On June 12, 2024, this work was published online in "Physical Review B" under the title "Improving the full quantum eigensolver with exponentiated operators."

In condensed matter physics, especially in solid-state physics, the band structure describes the distribution of electron energy levels as a function of wave vectors within materials. Calculating the band structure is crucial for understanding the electronic properties of materials, designing new materials, and explaining material behaviors. The complexity of band structure calculations increases rapidly with the number of electrons and ions, posing a significant challenge for large-scale computations. Quantum computing, however, has the potential to reduce computational complexity and enhance efficiency.

Building on their previous research, the team has improved the Full Quantum Eigensolver (FQE) through exponentiation, achieving exponential increases in the success probability of measuring target states in certain scenarios (where the number of generators in the operator's exponent shows a logarithmic polynomial dependence on the number of orbitals). Additionally, the team conducted numerical calculations of the energy spectrum for the Fermi-Hubbard model and the band structure of twisted bilayer graphene. The feasibility and robustness of the P-FQE algorithm were experimentally verified on superconducting quantum computers on quantum cloud platforms such as Quafu, for graphene and Weyl semimetals. A significant advantage of this algorithm is its reduced requirement for high-performance hardware, making it more suitable for energy spectrum calculations on Noisy Intermediate-Scale Quantum (NISQ) devices.

Figure 1: (a) Logic diagram of the quantum algorithm; (b) Quantum simulation of the moiré band structure of bilayer graphene; (c) Experimental demonstration of the band structure quantum simulation for Weyl semimetals; (d) Experimental demonstration of the band structure quantum simulation for monolayer graphene.

The first author of the paper is Bozhi Wang, a Ph.D. student at Tsinghua University. The corresponding authors are Shijie Wei, Assistant Researcher at BAQIS, and Guilu Long, Professor at Tsinghua University and Concurrent Researcher at BAQIS. Collaborators include Jiawei Wu, a postdoctoral researcher at the National University of Singapore, among others. This work was supported by the National Natural Science Foundation of China and the Beijing Nova Program.

Original link: https://journals.aps.org/prb/abstract/10.1103/PhysRevB.109.245117