Optimal synthesis of general multi-qutrit quantum computation

2023/10/18 by Jiang, Gui-Long, Liu, Wen-Qiang, Wei, Hai-Rui · 2 citations
#FOS: Physical sciences #Quantum Physics (quant-ph)

paper · doi:10.48550/arxiv.2310.11996

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(3ⁿ) (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 (41)/(96)⋅3²ⁿ-4⋅3^n-1-((n²)/(2)+(n)/(4)-(29)/(32)) GGXs and CINCs is presented. Such asymptotically optimal structure is the best known result so far.

Cited by

• Physically motivated decompositions of single qutrit gates
• Non-Abelian dynamics on a cube: improving quantum compilation through qudit-based simulations

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