Open quantum systems, effective Hamiltonians, and device characterization
DwyerVincent
DuffusStephen N.A.
EverittMark
2017
High fidelity models, which are able to both support accurate device characterization and correctly account for
environmental effects, are crucial to the engineering of scalable quantum technologies. As it ensures positivity
of the density matrix, one preferred model of open systems describes the dynamics with a master equation in
Lindblad form. In practice, Linblad operators are rarely derived from first principles, and often a particular form of
annihilator is assumed. This results in dynamical models that miss those additional terms which must generally be
added for the master equation to assume the Lindblad form, together with the other concomitant terms that must
be assimilated into an effective Hamiltonian to produce the correct free evolution. In first principles derivations,
such additional terms are often canceled (or countered), frequently in a somewhat ad hoc manner, leading to
a number of competing models. Whilst the implications of this paper are quite general, to illustrate the point
we focus here on an example anharmonic system; specifically that of a superconducting quantum interference
device (SQUID) coupled to an Ohmic bath. The resulting master equation implies that the environment has a
significant impact on the system’s energy; we discuss the prospect of keeping or canceling this impact and note
that, for the SQUID, monitoring the magnetic susceptibility under control of the capacitive coupling strength and
the externally applied flux results in experimentally measurable differences between a number of these models.
In particular, one should be able to determine whether a squeezing term of the form ˆX ˆ P + ˆ P ˆX should be present
in the effective Hamiltonian or not. If model generation is not performed correctly, device characterization will
be prone to systemic errors.