Limit of 4-way detect with 4 duplicates

[837951602]

However, I only used 3 of inputs, the last one is burnt

What's the actual limit? Any reference about?

[evenbly]

It is not obvious to me what the ideal strategy would look like or if one could apply known results (e.g. "Optimal Quantum Cloning Machines" of Buzek and Hillery), given the particular set-up of the level (i.e. only a discrete set of inputs states is given, and the outputs are only judged as correct if they match exactly).

My own solution (which used all four input copies) averages 927 correct, although I suspect that it would be possible to do much better. Maybe we should start a leaderboard?

[837951602]

I assumed it reasonable to read the question as "output two bits indicating its rotation" so the set-ups fits more

p.s. The 75% solution (issue/1) treat input as pairs, read on 45 and 135 degrees then decide

[837951602]

It is not obvious to me what the ideal strategy would look like or if one could apply known results (e.g. "Optimal Quantum Cloning Machines" of Buzek and Hillery), given the particular set-up of the level (i.e. only a discrete set of inputs states is given, and the outputs are only judged as correct if they match exactly).

My own solution (which used all four input copies) averages 927 correct, although I suspect that it would be possible to do much better. Maybe we should start a leaderboard?

I improved mine, now 927 still using only 3 copies

[837951602]

It is not obvious to me what the ideal strategy would look like or if one could apply known results (e.g. "Optimal Quantum Cloning Machines" of Buzek and Hillery), given the particular set-up of the level (i.e. only a discrete set of inputs states is given, and the outputs are only judged as correct if they match exactly).
My own solution (which used all four input copies) averages 927 correct, although I suspect that it would be possible to do much better. Maybe we should start a leaderboard?

I improved mine, now 927 still using only 3 copies

I can only fix 1/4 of the rest, by measuring again in the outputting direction(1/2 1/2) and rotate 90 degree if incorrect(can't get exact direction, no qubit remain)

{"name":"Clone-a-saurus","tag":"extraA","version":"v1.1.7","tiles":[4,2,76,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,74,2,5,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,54,40,84,40,56,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,1,3,89,65,2,65,2,68,2,2,5,24,44,48,85,2,2,62,2,78,-1,-1,15,84,3,70,72,60,84,1,23,51,21,-1,-1,24,42,84,-1,-1,-1,3,67,2,68,2,32,5,1,24,47,21,-1,-1,23,40,25,-1,-1,-1,84,42,56,-1,-1,21,69,71,23,51,23,85,2,2,62,32,79,-1,-1,-1,-1,-1,-1,-1,21,1,3,62,60,84,-1,24,44,22,26,1,-1,-1,-1,-1,-1,-1,-1,43,61,22,42,22,48,44,48,26,-1,-1,1,-1,-1,-1,-1,-1,-1,-1,84,84,-1,-1,-1,23,26,-1,-1,-1,-1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,74,2,6],"gates":[[18,5,"qCompare","free",0,-1.570796326795,0,2,-1],[18,8,"qCompare","free",1,-1.570796326795,0,4,-1],[16,0,"qCreate","free",0,0,0,2,492],[16,13,"qCreate","free",0,0,0,2,492],[2,0,"qCreate","free",2,0,0,1,492],[1,4,"cCreate","free",0,1,0,0,-1],[2,4,"switch","free",0,1,0,1,-1],[3,4,"trash","free",0,0.785398163397,0,0,-1],[4,4,"switch","free",0,1,0,1,-1],[5,4,"cCreate","free",2,1,0,0,-1],[2,5,"qCombine","free",0,0,0,0,-1],[2,5,"qCombine","free",1,0,1,0,-1],[4,5,"qCombine","free",0,0,0,0,-1],[4,5,"qCombine","free",1,0,1,0,-1],[4,8,"cCreate","free",2,1,0,0,-1],[3,8,"switch","free",2,1,0,1,-1],[2,8,"trash","free",0,0.785398163397,0,0,-1],[3,7,"qCombine","free",0,0,0,0,-1],[3,7,"qCombine","free",3,0,1,0,-1],[3,6,"trash","free",0,0.785398163397,0,0,-1],[6,5,"qFlip","free",0,0,0,0,-1],[6,5,"qFlip","free",0,1.570796326795,1,0,-1],[5,6,"qControl","free",0,0,0,0,-1],[6,6,"qControl","free",2,1.570796326795,0,0,-1],[7,6,"measure","free",0,5.497787143782,0,0,-1],[8,6,"trash","free",0,0.785398163397,0,0,-1],[5,7,"qFlip","free",0,1.570796326795,0,0,-1],[5,7,"qFlip","free",0,1.570796326795,1,0,-1],[8,8,"qFlip","free",1,0,0,0,-1],[9,8,"qControl","free",1,1.570796326795,0,0,-1],[8,8,"qFlip","free",1,0,1,0,-1],[8,10,"measure","free",1,0,0,0,-1],[7,10,"switch","free",3,0,0,1,-1],[8,10,"measure","free",1,4.712388980385,1,0,-1],[7,11,"trash","free",0,0.785398163397,0,0,-1],[8,11,"trash","free",0,0.785398163397,0,0,-1],[10,9,"rotate","free",0,0,0,0,-1],[10,10,"switch","free",2,1,0,1,-1],[10,9,"rotate","free",0,4.712388980385,1,0,-1],[11,9,"measure","free",0,0,0,0,-1],[12,9,"trash","free",0,0.785398163397,0,0,-1],[11,7,"cCombine","free",3,0,0,0,-1],[11,8,"cSplit","free",3,0,0,0,-1],[11,6,"cSplit","free",3,0,0,0,-1],[13,5,"upgrade","free",0,0,0,0,-1],[13,8,"upgrade","free",0,0,0,0,-1],[11,5,"cCombine","free",0,0,0,0,-1],[12,5,"cSplit","free",0,0,0,0,-1],[16,5,"rotate","free",0,0,0,0,-1],[16,8,"rotate","free",0,0,0,0,-1],[16,7,"switch","free",0,1,0,1,-1],[16,8,"rotate","free",0,1.570796326795,1,0,-1],[16,6,"switch","free",2,1,0,1,-1],[16,5,"rotate","free",0,1.570796326795,1,0,-1],[12,10,"cSplit","free",0,0,0,0,-1],[14,10,"cSplit","free",0,0,0,0,-1],[13,10,"cCombine","free",0,0,0,0,-1],[1,5,"delay","free",0,0,0,7,-1],[17,6,"trash","free",0,0.785398163397,0,0,-1],[15,9,"cCombine","free",0,0,0,0,-1]]}