  We develop computationally affordable and encoding independent gradient
evaluation procedures for unitary coupled-cluster type operators, applicable on
quantum computers. We show that, within our framework, the gradient of an
expectation value with respect to a parameterized n-fold fermionic excitation
can be evaluated by four expectation values of similar form and size, whereas
most standard approaches based on the direct application of the
parameter-shift-rule come with an associated cost of O(2^(2n)) expectation
values. For real wavefunctions, this cost can be further reduced to two
expectation values. Our strategies are implemented within the open-source
package tequila and allow blackboard style construction of differentiable
objective functions. We illustrate initial applications for electronic ground
and excited states.
