Exploiting Maximally Mixed States for Spectral Estimation by Time Evolution

TL;DR

This paper presents a new quantum spectral estimation method using time evolution of maximally mixed states, demonstrating advantages over classical sampling and experimental validation on IBM Quantum hardware.

Contribution

It introduces a novel quantum spectral estimation technique based on evolving maximally mixed states, with hardware-efficient implementation and experimental validation.

Findings

Outperforms classical statistical sampling methods

Successfully estimates spectra of 2-qubit Hamiltonians on real quantum hardware

Reduces errors through optimized native gate decompositions

Abstract

We introduce a novel approach for estimating the spectrum of quantum many-body Hamiltonians, and more generally, of Hermitian operators, using quantum time evolution. In our approach we are evolving a maximally mixed state under the Hamiltonian of interest and collecting specific time-series measurements to estimate its spectrum. We demonstrate the advantage of our technique over currently used classical statistical sampling methods. We showcase our approach by experimentally estimating the spectral decomposition of a 2-qubit Heisenberg Hamiltonian on an IBM Quantum backend. For this purpose, we develop a hardware-efficient decomposition that controls $n$-qubit Pauli rotations against the physically closest qubit alongside expressing two-qubit rotations in terms of the native entangling interaction. This substantially reduced the accumulation of errors from noisy two-qubit operations in time evolution simulation protocols. We conclude by discussing the potential impact of our work and the future directions of research it opens.