-3

What is the matrix for the CCTShift(1) gate? It has to be a $(27 \times 27)$ matrix.

Suppose we have two control qutrits and a single target qutrit. If one control qutrit is found in state $|2\rangle$ and the other control qutrit is found in state $|1\rangle$ then how would the target qutrit change, would it be TShifted at all? Thanks

Callum
  • 977
  • 1
  • 4
  • 20
Root Groves
  • 59
  • 5
  • 1
    What is your definition of CCTShift? From whence did you get that term? – Mark Spinelli Mar 12 '24 at 18:53
  • @Root Groves By $\text{TShift}(1)$ do you mean this ternary operation from a previous post? -> https://quantumcomputing.stackexchange.com/questions/35208/matrix-representation-of-the-qutrit-gate-analogous-to-pauli-x-gate/35210#35210? $$\text{TShift} = \begin{pmatrix} 0 & 0 & 1 \ 1 & 0 & 0 \ 0 & 1 & 0 \end{pmatrix}$$ – Callum Mar 12 '24 at 23:44
  • Also how are you defining the controls here? What state do the control qutrits need to be in for the ternary shift ($\text{TShift}$) to be applied to the target qutrit? – Callum Mar 12 '24 at 23:53
  • @Callum exactly.The CCTShift(1) gate for 3 qutrits is what is the CCNOT gate for a 3 qubits. – Root Groves Mar 13 '24 at 12:01
  • Seems the Toffoli gate isn't uniquely defined for qutrits. I think there are different conventions. See SECTION V of this paper -> https://arxiv.org/pdf/1105.5485.pdf – Callum Mar 13 '24 at 16:14

0 Answers0