Real-Time Evolution for Ultracompact Hamiltonian Eigenstates on Quantum Hardware

In this work we present a detailed analysis of variational quantum phase estimation (VQPE), method based on real-time evolution for ground- and excited-state near-term hardware. We derive the theoretical ground which approach stands, demonstrate that it provides one most compact expansions to date solving strongly correlated Hamiltonians, when starting from an appropriate reference state. At center VQPE lies set equations, with simple geometrical interpretation, conditions time grid in order decouple eigenstates out time-evolved expansion states, connects classical filter-diagonalization algorithm. Furthermore, introduce what call unitary formulation VQPE, number matrix elements need be measured scales linearly provide effects noise substantially improves previous considerations. The allows direct comparison iterative estimation. Our results mark as both natural highly efficient algorithm calculations general many-body systems. hardware implementation transverse field Ising model. illustrate its power paradigmatic example strong correlation (Cr2 def2-SVP basis set), show is possible reach chemical accuracy few approximately 50 steps.4 MoreReceived 5 April 2021Revised 17 February 2022Accepted 1 March 2022DOI:https://doi.org/10.1103/PRXQuantum.3.020323Published by American Physical Society under terms Creative Commons Attribution 4.0 International license. Further distribution must maintain attribution author(s) published article's title, journal citation, DOI.Published SocietyPhysics Subject Headings (PhySH)Research AreasQuantum algorithmsQuantum computationQuantum simulationCondensed Matter, Materials & Applied PhysicsQuantum Information