Lipkin model on a quantum computer
Atomic nuclei are important laboratories for exploring and testing new
insights into the universe, such as experiments to directly detect dark matter
or explore properties of neutrinos. The targets of interest are often heavy,
complex nuclei that challenge our ability to reliably model them (as well as
quantify the uncertainty of those models) with classical computers. Hence there
is great interest in applying quantum computation to nuclear structure for
these applications. As an early step in this direction, especially with regards
to the uncertainties in the relevant quantum calculations, we develop circuits
to implement variational quantum eigensolver (VQE) algorithms for the
Lipkin-Meshkov-Glick model, which is often used in the nuclear physics
community as a testbed for many-body methods. We present quantum circuits for
VQE for two and three particles and discuss the construction of circuits for
more particles. Implementing the VQE for a two-particle system on the IBM
Quantum Experience, we identify initialization and two-qubit gates as the
largest sources of error. We find that error mitigation procedures reduce the
errors in the results significantly, but additional quantum hardware
improvements are needed for quantum calculations to be sufficiently accurate to
be competitive with the best current classical methods.
Michael J. Cervia A. B. Balantekin S. N. Coppersmith Calvin W. Johnson Peter J. Love C. Poole K. Robbins M. Saffman