Demonstration of the Rodeo Algorithm on a Quantum Computer
The rodeo algorithm is an efficient algorithm for eigenstate preparation and
eigenvalue estimation for any observable on a quantum computer. This makes it a
promising tool for studying the spectrum and structure of atomic nuclei as well
as other fields of quantum many-body physics. The only requirement is that the
initial state has sufficient overlap probability with the desired eigenstate.
While it is exponentially faster than well-known algorithms such as phase
estimation and adiabatic evolution for eigenstate preparation, it has yet to be
implemented on an actual quantum device. In this work, we apply the rodeo
algorithm to determine the energy levels of a random one-qubit Hamiltonian,
resulting in a relative error of $0.08\%$ using mid-circuit measurements on the
IBM Q device Casablanca. This surpasses the accuracy of directly-prepared
eigenvector expectation values using the same quantum device. We take advantage
of the high-accuracy energy determination and use the Hellmann-Feynman theorem
to compute eigenvector expectation values for a different random one-qubit
observable. For the Hellmann-Feynman calculations, we find a relative error of
$0.7\%$. We conclude by discussing possible future applications of the rodeo
algorithm for multi-qubit Hamiltonians.
Zhengrong Qian Jacob Watkins Gabriel Given Joey Bonitati Kenneth Choi Dean Lee