Quantum Time-Space Tradeoff for Finding Multiple Collision Pairs. (arXiv:2002.08944v5 [quant-ph] UPDATED)

We study the problem of finding $K$ collision pairs in a random function $f :
[N] \rightarrow [N]$ by using a quantum computer. We prove that the number of
queries to the function in the quantum random oracle model must increase
significantly when the size of the available memory is limited. Namely, we
demonstrate that any algorithm using $S$ qubits of memory must perform a number
$T$ of queries that satisfies the tradeoff $T^3 S \geq \Omega(K^3 N)$.
Classically, the …

algorithm collision computer function memory oracle problem prove quantum quantum computer qubits random size space study