KAKURO - A CONSTRAINT SATISFACTION PROBLEM
Özlem Salehi, Adam Glos
Coding Competition
GENERAL SOLUTION
Mark states that correspond to correct assignments
Each binary variable can be represented by a qubit
OUR SOLUTION
Also used in our new paper FUNC-QAOA
Inspiration
GM-QAOA
OUR SOLUTION
Some constraints are already handled when preparing the initial state
Custom initial state
OUR SOLUTION
x_0 \neq x_1\\
x_2+2 \neq x_3\\
x_3 \neq x_4 \\
x_1 \neq x_3\\
x_3 \neq x_5\\
x_5 \neq x_6\\
x_0 \neq x_2\\
x_1 \neq x_5\\
x_4 \neq x_6\\
x_3 = 2\\
x_2+x_4+x_3 = 3
x_0 \neq x_2\\
x_0 \neq x_1\\
x_1 \neq x_5\\
x_5 \neq x_6\\
x_4 \neq x_6\\
x_2+2 \neq x_3\\
x_3 \neq x_4 \\
x_1 \neq x_3\\
x_3 \neq x_5\\
x_3 = 2\\
x_2+x_4+x_3 = 3
= \left(\frac{1}{\sqrt 2}(|101010\rangle + |010101\rangle \right) \otimes \frac{1}{2}\left(|00\rangle + |01\rangle + |10\rangle + |11\rangle \right)
|x_2,x_0,x_1,x_5,x_6,x_4\rangle \otimes |x_3\rangle \\
Initial State
Oracle
- Each constraint is checked and information is stored
1: Constraint is satisfied
0: Constraint is not satisfied
- MCZ gate is applied on all qubits that hold information about whether the constraint is satisfied
- More costly initial state and diffusion operator
DISADVANTAGES
- Smaller number of Grover iterations
- Simpler oracle resulting in reduced CNOT count
ADVANTAGES
- MCZ is implemented with RCCX gates
- Some constraints are implemented in place
ADDITIONAL SAVINGS
RESULT
86 CNOT gates
Problem
- Two cells on the same row/column cannot have the same number.
- The sum of the cells on each row/column should equal the matching filled cell.
x_0 \neq x_1\\
x_2+2 \neq x_3\\
x_3 \neq x_4 \\
x_1 \neq x_3\\
x_3 \neq x_5\\
x_5 \neq x_6\\
x_0 \neq x_2\\
x_1 \neq x_5\\
x_4 \neq x_6\\
x_3 = 2\\
x_2+x_4+x_3 = 3
x_i\in \{0,1\}, x_{3} \in \{0,1,2,3\}
classiq
By Özlem
