Demonstrating Quantum Computation for Quasiparticle Band Structures

TL;DR

The authors demonstrate ab initio calculation of a quasiparticle band structure for a periodic solid on actual quantum devices. They combine quantum subspace expansion with a VQE-based ground state to form a low-dimensional subspace and extract band energies, while reducing qubit requirements through active space selection and symmetry-based qubit tapering. Readout-error mitigation and zero-noise extrapolation are employed to combat hardware noise, enabling results that reproduce noise-free CASCI references. This work marks a significant step toward practical quantum simulations of solid-state materials on near-term devices and outlines paths for scaling with advanced error mitigation and hybrid algorithms.

Abstract

Understanding and predicting the properties of solid-state materials from first-principles has been a great challenge for decades. Owing to the recent advances in quantum technologies, quantum computations offer a promising way to achieve this goal. Here, we demonstrate the first-principles calculation of a quasiparticle band structure on actual quantum computers. This is achieved by hybrid quantum-classical algorithms in conjunction with qubit-reduction and error-mitigation techniques. Our demonstration will pave the way to practical applications of quantum computers.

Figures (8)

• Figure 1: Quantum circuit used in the present study. The input state $\ket{\psi_0}$ and the unitary operator ${\hat{U}} ({\bm \theta})$ correspond to $\ket{00}$ and the whole of the operators, respectively. The HF state is $\ket{11}$ which we obtain after the operation of X-gates. Four variational parameters $\theta_i$ for the $R_y$ rotation gates are optimized during VQE calculations.
• Figure 2: Quasiparticle band structure of the Si crystal obtained by QSE. Results with different ground states obtained by VQE, CASCI, and FCI are presented. The ground states were prepared on a classical computer. For the VQE ground states, the QSE calculations were performed on actual quantum devices. The valence band energy at the $\Gamma$ point obtained by CASCI is set to 0 eV.
• Figure 3: Error mitigation schemes. (a) Diagonal elements of the calibration matrix measured at various times (measurement cycle). (b) Histograms of 40 independent calculation results for the valence and conduction band energies at the $\Gamma$ point. In these results, REM was applied. The vertical dashed lines represent the ideal noise-free values obtained by a statevector simulator. On the other hand, the vertical solid lines show the mean values of the calculation results obtained on quantum devices.
• Figure 4: Energies in the VQE optimization processes obtained by a noiseless sampling simulator or actual quantum devices. In the latter, we applied REM or both REM and ZNE. The error bars represent statistical errors. The exact value by CASCI is set to 0 eV. The dashed horizontal lines denote the $\pm$ 1 kcal/mol precision compared with CASCI.
• Figure S1: Energies of the VQE optimized state at the $\Gamma$ point. We used the variational parameters fully optimized on a statevector simulator. Blue circles represent 40 independent results obtained on the quantum device over the course of 2 days. In these results, REM was applied. The error bars represent statistical errors. The dashed line denotes the ideal noise-free result obtained by the statevector simulator. The exact value by CASCI is set to 0 eV.