ApplyAnd operation
Inverts a given target qubit if and only if both control qubits are in the 1 state, using measurement to perform the adjoint operation.
Inverts target
if and only if both controls are 1, but assumes that
target
is in state 0. The operation has Tcount 4, Tdepth 2 and
requires no helper qubit, and may therefore be preferable to a CCNOT
operation, if target
is known to be 0. The adjoint of this operation
is measurement based and requires no T gates.
The controlled application of this operation requires no helper qubit,
2^c
Rz
gates and is not optimized for depth, where c
is the number
of overall control qubits including the two controls from the ApplyAnd
operation. The adjoint controlled application requires 2^c  1
Rz
gates (with an angle twice the size of the nonadjoint operation), no
helper qubit and is not optimized for depth.
operation ApplyAnd (control1 : Qubit, control2 : Qubit, target : Qubit) : Unit
 Functors

Adjoint Controlled
Input
 control1
 Qubit
First control qubit
 control2
 Qubit
Second control qubit
 target
 Qubit
Target auxiliary qubit; must be in state 0
Output
Unit
References
 Cody Jones: "Novel constructions for the faulttolerant Toffoli gate", Phys. Rev. A 87, 022328, 2013 arXiv:1212.5069 doi:10.1103/PhysRevA.87.022328
 Craig Gidney: "Halving the cost of quantum addition", Quantum 2, page 74, 2018 arXiv:1709.06648 doi:10.1103/PhysRevA.85.044302
 Mathias Soeken: "Quantum Oracle Circuits and the Christmas Tree Pattern", Blog article from December 19, 2019 (note: explains the multiple controlled construction)