Design a reversible full adder on four wires ,

PHYSICS · Multi-part · Fermi University Physics · Quantum Information & Technology · The quantum circuit model and quantum algorithms · The quantum circuit model and quantum algorithms

Quantum Information and Technology, Ch The quantum circuit model

Problem

Design a reversible full adder on four wires

a

b

c_{\rm in}

and

c_{\rm out}

, using only CNOT and Toffoli gates, with

c_{\rm out}

initialised to

|0\rangle

, such that at the end

a

and

c_{\rm in}

are unchanged,

b

holds the sum bit

s=a\oplus b\oplus c_{\rm in}

, and

c_{\rm out}

holds the carry-out

ab\oplus bc_{\rm in}\oplus ac_{\rm in}

, with no garbage anywhere. ((a)) Give a four-gate circuit (two Toffolis and two CNOTs) meeting this specification, stating the control(s) and target of each gate. ((b)) Verify it on the input

(a,b,c_{\rm in}) = (1,0,1)

, tracking all four wires through each gate. ((c)) State the total gate count and the number of garbage bits.

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