Alex et al. - Error-Reduced Quantum Battleship Radar

Error-Reduced Quantum Battleship Radar

Team Members: ● Annaliese ● Ian ● Sebastian ● Oscar ● Alex

Description

We chose prompt 4 to tackle during this Qiskit Fall Fest. Our aim was to extend the Elitzur-Vaidman bomb tester to “solve” a game of battleship without needing to fire a single shot (Nobel Peace Prize???). The code takes in a secret grid corresponding to where the opponent’s ships are found akin to a game of battleship, essentially acting as a “black box” that will spit out the maximum likelihood grid as an output without ever having interacted with them. It will then generate 2N quantum circuits in the case for an NxN grid, this is to leverage the fact that we can entangle entire rows/columns and check for the presence of a ship on a per row/column basis. The intersections are then used to pinpoint a ship. Finally, as an output, our opponent will be very surprised to find that their secret grid is right there in front of them!

Optimizations

Several modifications have been made to our approach in order to increase performance. First, as mentioned above, by entangling entire rows or columns together, we reduced search complexity from O(𝑁 ) to O(N). In addition to that, 2 we modified the quantum circuits to minimize the event of our photon being detected. The Hadamard gates (beam splitters) were replaced with a cascade of smaller rotations in order to keep most of the wavefunction on the non-interacting path. By carefully choosing the rotation value of the gates and the number of gates in the cascade, we can make the error rate arbitrarily small [1]. This greatly reduces the amount of repetitions needed to validate a result (i.e. found a ship without interacting). [1] 2111.02896

(McGill Quantum Group note - you can find the code and the original document(s) in the attached google drive)