Optimal synthesis of general multi-qutrit quantum computation

• URL: http://arxiv.org/abs/2310.11996v1
• Date: Wed, 18 Oct 2023 14:28:31 GMT
• Title: Optimal synthesis of general multi-qutrit quantum computation
• Authors: Gui-Long Jiang, Wen-Qiang Liu and Hai-Rui Wei
• Abstract summary: Quantum circuits of a general quantum gate acting on multiple $d$-level quantum systems play a prominent role in quantum computation. We propose a new Cartan decomposition of semi-simple unitary Lie group $U(n)$ (arbitrary $n$-qutrit gate) We design an explicit quantum circuit for implementing arbitrary two-qutrit gates, and the cost of our construction is 21 generalized controlled X (GCX) and controlled increment (CINC) gates less than the earlier best result of 26 GGXs.
• Score: 1.556591713973462
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Quantum circuits of a general quantum gate acting on multiple $d$-level quantum systems play a prominent role in multi-valued quantum computation. We first propose a new recursive Cartan decomposition of semi-simple unitary Lie group $U(3^n)$ (arbitrary $n$-qutrit gate). Note that the decomposition completely decomposes an n-qutrit gate into local and non-local operations. We design an explicit quantum circuit for implementing arbitrary two-qutrit gates, and the cost of our construction is 21 generalized controlled X (GCX) and controlled increment (CINC) gates less than the earlier best result of 26 GGXs. Moreover, we extend the program to the $n$-qutrit system, and the quantum circuit of generic $n$-qutrit gates contained $\frac{41}{96}\cdot3^{2n}-4\cdot3^{n-1}-(\frac{n^2}{2}+\frac{n}{4}-\frac{29}{32})$ GGXs and CINCs is presented. Such asymptotically optimal structure is the best known result so far.

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