Tangent Space Excitation Ansatz for Quantum Circuits

TL;DR

This paper introduces a tangent space excitation ansatz for quantum circuits that efficiently captures low-energy states, improving excited-state calculations on noisy quantum devices.

Contribution

It presents a novel tangent space excitation ansatz inspired by many-body physics, surpassing existing methods in accuracy and scalability for quantum excited-state computations.

Findings

Captures massive low-energy single-particle states with increased circuit depth.

Outperforms existing quantum excited-state algorithms in accuracy and number of excited states.

Demonstrated scalability and implementation feasibility on current quantum processors.

Abstract

Computing excitation spectra of quantum many-body systems is a promising avenue to demonstrate the practical utility of current noisy quantum devices, especially as we move toward the ``megaquop'' regime. For this task, here we introduce a \textit{tangent space excitation ansatz} for quantum circuits, motivated by the quasi-particle picture of many-body systems and the structural similarity between quantum circuits and tensor networks. Increasing circuit depth by one layer to construct tangent space around the variational optimum of a parametrized quantum circuit, we show that massive low-energy single-particle states can be captured. Our ansatz relies on a distinct mechanism from that of excitation ansatz in matrix product state and projected entangled-pair state, and avoids intrinsic limitations of the latter. Comparing our approach with existing quantum excited-state algorithms, we find that with similar computational cost, both the number of excited states and accuracy are significantly improved. We demonstrate our ansatz in both one and two dimensions, and further show that this approach, implementable using Hadamard test, is scalable and suitable for current quantum processors.