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Efficient charge-preserving excited state preparation with variational quantum algorithms

Zohim Chandani, Kazuki Ikeda, Zhong-Bo Kang, Dmitri E. Kharzeev, Alexander McCaskey, Andrea Palermo, C. R. Ramakrishnan, Pooja Rao, Ranjani G. Sundaram, Kwangmin Yu

Abstract

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.

Efficient charge-preserving excited state preparation with variational quantum algorithms

Abstract

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.

Paper Structure

This paper contains 12 sections, 30 equations, 6 figures, 1 table.

Table of Contents

  1. Introduction
  2. Charge-Preserving VQD
  3. Experimental Setup
  4. Application to Quantum Chemistry
  5. Dimensional reduction method to compute the full spectra of a fixed charge sector
  6. Efficient Quantum Simulation of Ions
  7. Application to Quantum Physics
  8. Preliminaries
  9. A massive Dirac model
  10. Quantum Electrodynamics (QED)
  11. Mass gap in the (1+1)d-QED
  12. Conclusion and Discussion

Figures (6)

  • Figure 1: A single layer of the four-qubit ansatz.
  • Figure 2: Number of reduced qubits with respect to system size $N$ for various charges $q$.
  • Figure 3: The bond-length dependence of the spectrum (in Hartree) of $H_2$ in the charge 0 sector, where all energy spectra carry charge 0 in the STO-3G basis. The red curves and the blue dots are obtained by exact diagonalization and VQD, respectively.
  • Figure 4: The reduced number of qubits as a function of the system size evaluated according to eq.\ref{['eq:reduced']}.
  • Figure 5: The bond-length dependence of the spectra (in Hartree) of $\text{HeH}^+$ in the charge 1 sector. All charge +1 spectra in the STO-3G basis are shown here. The red curves and the blue dots are obtained by exact diagonalization and CPVQD, respectively.
  • ...and 1 more figures