Quantum addition using ApplyAnd

[msoeken]

Describe the solution you'd like
A ripple-carry adder using the ApplyAnd or ApplyLowDepthAnd operations as described in Fig. 1 in Halving the cost of quantum addition.

Describe alternatives you've considered
Updating RippleCarryAdderD to use ApplyAnd.

Implementation plan

Development in branch feature/adder

• Rewriting of RippleCarryAdderD RippleCarryAdderD update #358 Refactoring improved adder implementation #359
• Validate requirements for control lines
• Investigate implications for Numerics API review

[TviNet]

Hey, is this issue about replacing the CCNOT gates with ApplyAnd in RippleCarryAdderD or implementing the circuit given in Fig. 1 which does not compute the Carry out bit?

[msoeken]

I suppose that RippleCarryAdderD could be updated. However, it's not just replacing existing CCNOT since the current implementation used two CCNOT for each Carry, where only one is necessary. It also should support a Carry bit, unlike the figure in the paper.

Also one can make use of newer Q# features such as within / apply.