  Adaptive quantum variational algorithms are particularly promising for
simulating strongly correlated systems on near-term quantum hardware, but they
are not yet viable due, in large part, to the severe coherence time limitations
on current devices. In this work, we introduce an algorithm called
TETRIS-ADAPT-VQE, which iteratively builds up variational ans\"atze a few
operators at a time in a way dictated by the problem being simulated. This
algorithm is a modified version of the ADAPT-VQE algorithm in which the
one-operator-at-a-time rule is lifted to allow for the addition of multiple
operators with disjoint supports in each iteration. TETRIS-ADAPT-VQE results in
denser but significantly shallower circuits, without increasing the number of
CNOT gates or variational parameters. Its advantage over the original algorithm
in terms of circuit depths increases with the system size. Moreover, the
expensive step of measuring the energy gradient with respect to each candidate
unitary at each iteration is performed only a fraction of the time compared to
ADAPT-VQE. These improvements bring us closer to the goal of demonstrating a
practical quantum advantage on quantum hardware.
