Determining the spectrum and wave functions of excited states of a system is crucial in quantum physics and chemistry. Low-depth quantum algorithms, such as the Variational Quantum Eigensolver (VQE) and its variants, can be used to determine the ground-state energy. However, current approaches to computing excited states require numerous controlled unitaries, making the application of the original Variational Quantum Deflation (VQD) algorithm to problems in chemistry or physics suboptimal. In this study, we introduce a charge-preserving VQD (CPVQD) algorithm, designed to incorporate symmetry and the corresponding conserved charge into the VQD framework. This results in dimension reduction, significantly enhancing the efficiency of excited-state computations. We present benchmark results with GPU-accelerated simulations using systems up to 24 qubits, showcasing applications in high-energy physics, nuclear physics, and quantum chemistry. This work is performed on NERSC's Perlmutter system using NVIDIA's open-source platform for accelerated quantum supercomputing - CUDA-Q.

翻译：确定系统的激发态谱与波函数在量子物理与化学中至关重要。低深度量子算法，如变分量子本征求解器（VQE）及其变体，可用于确定基态能量。然而，当前计算激发态的方法需要大量受控酉操作，使得原始的变分量子紧缩（VQD）算法在化学或物理问题中的应用效果欠佳。在本研究中，我们引入了一种电荷守恒VQD（CPVQD）算法，旨在将对称性及相应的守恒荷纳入VQD框架。这实现了维度缩减，显著提升了激发态计算的效率。我们展示了使用多达24量子比特系统的GPU加速模拟基准测试结果，并呈现了该算法在高能物理、核物理及量子化学中的应用。本工作于NERSC的Perlmutter系统上完成，使用了NVIDIA的开源加速量子超算平台——CUDA-Q。