Simulating excited states of the Lipkin model on a quantum computer
We simulate the excited states of the Lipkin model using the recently
proposed Quantum Equation of Motion (qEOM) method. The qEOM generalizes the EOM
on classical computers and gives access to collective excitations based on
quasi-boson operators $\hat{O}^\dagger_n(\alpha)$ of increasing configuration
complexity $\alpha$. We show, in particular, that the accuracy strongly depends
on the fermion to qubit encoding. Standard encoding leads to large errors, but
the use of symmetries and the Gray code reduces the quantum resources and
improves significantly the results on current noisy quantum devices. With this
encoding scheme, we use IBM quantum machines to compute the energy spectrum for
a system of $N=2, 3$ and $4$ particles and compare the accuracy against the
exact solution. We found that the results of the approach with $\alpha = 2$, an
analog of the second random phase approximation (SRPA), are, in principle, more
accurate than with $\alpha = 1$, which corresponds to the random phase
approximation (RPA), but the SRPA is more amenable to noise for large coupling
strengths. Thus, the proposed scheme shows potential for achieving higher
spectroscopic accuracy by implementations with higher configuration complexity,
if a proper error mitigation method is applied.
Manqoba Q. Hlatshwayo Yinu Zhang Herlik Wibowo Ryan LaRose Denis Lacroix Elena Litvinova