Nuclear Spectra from Quantum Lanczos Algorithm with Real-Time Evolution and Multiple Reference States

TL;DR

This paper explores the quantum Lanczos algorithm with real-time evolution and multiple references, demonstrating its effectiveness in finding low-lying nuclear eigenstates and optimizing quantum circuit depth.

Contribution

It introduces a quantum Lanczos algorithm variant with real-time evolution and multiple references, showing improved convergence and circuit efficiency in nuclear eigenstate calculations.

Findings

Real-time evolution converges within tens of iterations.

Multiple references improve convergence speed and accuracy.

Spherical basis reduces quantum circuit depth.

Abstract

Models of quantum systems scale exponentially with the addition of single-particle states, which can present computationally intractable problems. Alternatively, quantum computers can store a many-body basis of $2^n$ dimensions on $n$ qubits. This motivated the quantum eigensolver algorithms developed in recent years, such as the quantum Lanczos algorithm based on the classical, iterative Lanczos algorithm. I performed numerical simulations to find the low-lying eigenstates of $^{20}$Ne, $^{22}$Na, and $^{29}$Na to compare imaginary- and real-time evolution. Though imaginary-time evolution leads to faster convergence, real-time evolution still converges within tens of iterations and satisfies the requirement for unitary operators on quantum computers. Additionally, using multiple reference states leads to faster convergences or higher accuracy for a fixed number of real-time iterations. I performed quantum circuit prototype numerical simulations on a classical computer of the QLanczos algorithm with real-time evolution and multiple reference states to find the low-lying eigenstates of $^{8}$Be. These simulations were run in both the spherical basis and Hartree-Fock basis, demonstrating that an M-scheme spherical basis leads to lower depth circuits than the Hartree-Fock basis. Finally, I present the quantum circuits for the QLanczos algorithm with real-time evolution and multiple references.