Wolfram Language Paclet Repository
Community-contributed installable additions to the Wolfram Language
Addition of Numbers
Here, we introduce a quantum circuit implementation of addition.
Make sure that Q3 is loaded.
In[32]:=
Needs["QuantumMob`Q3`"]
The two numbers to add are initially stored in quantum registers A and B, respectively. Temporary register T is to store the carrier bits.
In[33]:=
Let[Qubit,A,B,T]
Suppose that we added two numbers each represented by n binary digits. Note that we need one more bit in the temporary register T.
In[34]:=
$n=3;kk=Range[$n];AA=A[kk,$];BB=B[kk,$];TT=T[Range[$n+1],$];
The result is stored in the register B. Note, however, that the last carrier bit is still stored in T only.
In[39]:=
elm=Flatten@Table[{CNOT[{A[k],B[k]},T[k+1]],CNOT[A[k],B[k]],CNOT[{B[k],T[k]},T[k+1]],CNOT[T[k],B[k]]},{k,$n}];
In[40]:=
qc=QuantumCircuit[Sequence@@elm,"Invisible"{A[$n+1/2],B[$n+1/2]}]
Out[40]=
In[41]:=
bs=Basis[AA,BB];
In[42]:=
EchoTiming[out=qc**bs;]
⌚
2.34428
In[43]:=
ab={FromDigits[Reverse[#@AA],2],FromDigits[Reverse[#@BB],2]}&/@bs;cc=FromDigits[Reverse@Join[#@BB,#@T@{$n+1}],2]&/@out;Thread[abcc]//TableForm
Out[45]//TableForm=
{0,0}0 |
{0,4}4 |
{0,2}2 |
{0,6}6 |
{0,1}1 |
{0,5}5 |
{0,3}3 |
{0,7}7 |
{4,0}4 |
{4,4}8 |
{4,2}6 |
{4,6}10 |
{4,1}5 |
{4,5}9 |
{4,3}7 |
{4,7}11 |
{2,0}2 |
{2,4}6 |
{2,2}4 |
{2,6}8 |
{2,1}3 |
{2,5}7 |
{2,3}5 |
{2,7}9 |
{6,0}6 |
{6,4}10 |
{6,2}8 |
{6,6}12 |
{6,1}7 |
{6,5}11 |
{6,3}9 |
{6,7}13 |
{1,0}1 |
{1,4}5 |
{1,2}3 |
{1,6}7 |
{1,1}2 |
{1,5}6 |
{1,3}4 |
{1,7}8 |
{5,0}5 |
{5,4}9 |
{5,2}7 |
{5,6}11 |
{5,1}6 |
{5,5}10 |
{5,3}8 |
{5,7}12 |
{3,0}3 |
{3,4}7 |
{3,2}5 |
{3,6}9 |
{3,1}4 |
{3,5}8 |
{3,3}6 |
{3,7}10 |
{7,0}7 |
{7,4}11 |
{7,2}9 |
{7,6}13 |
{7,1}8 |
{7,5}12 |
{7,3}10 |
{7,7}14 |
In fact, one can store the result spread over registers B and T. Then, one can remove some quantum circuit elements.
In[46]:=
elm=Flatten@Table[{CNOT[{A[k],B[k]},T[k+1]],CNOT[A[k],B[k]],CNOT[{B[k],T[k]},T[k+1]]},{k,$n}];
In[47]:=
qc=QuantumCircuit[Sequence@@elm,"Invisible"{A[$n+1/2],B[$n+1/2]}]
Out[47]=
To extract the sum, you need to consider both registers B and T.