On the CNOT-cost of TOFFOLI gates

Details On the CNOT-cost of TOFFOLI gates On the CNOT-cost of TOFFOLI gates

2008-03-15

arxiv.org/abs/0803.2316v1

Quant.Inf.Comp. 9(5-6):461-486 (2009)

Physics

Quantum Physics

28 pages

Scientific paper

The three-input TOFFOLI gate is the workhorse of circuit synthesis for classical logic operations on quantum data, e.g., reversible arithmetic circuits. In physical implementations, however, TOFFOLI gates are decomposed into six CNOT gates and several one-qubit gates. Though this decomposition has been known for at least 10 years, we provide here the first demonstration of its CNOT-optimality. We study three-qubit circuits which contain less than six CNOT gates and implement a block-diagonal operator, then show that they implicitly describe the cosine-sine decomposition of a related operator. Leveraging the canonicity of such decompositions to limit one-qubit gates appearing in respective circuits, we prove that the n-qubit analogue of the TOFFOLI requires at least 2n CNOT gates. Additionally, our results offer a complete classification of three-qubit diagonal operators by their CNOT-cost, which holds even if ancilla qubits are available.

Affiliated with

Also associated with

No associations

Rating

On the CNOT-cost of TOFFOLI gates does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On the CNOT-cost of TOFFOLI gates, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the CNOT-cost of TOFFOLI gates will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-438820