Approaching the theoretical limit in quantum gate decomposition
Péter Rakyta, Zoltán Zimborás
Abstract
In this work we propose a novel numerical approach to decompose general quantum programs in terms of single- and two-qubit quantum gates with a<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>C</mml:mi><mml:mi>N</mml:mi><mml:mi>O</mml:mi><mml:mi>T</mml:mi></mml:math>gate count very close to the current theoretical lower bounds. In particular, it turns out that<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mn>15</mml:mn></mml:math>and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mn>63</mml:mn></mml:math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>C</mml:mi><mml:mi>N</mml:mi><mml:mi>O</mml:mi><mml:mi>T</mml:mi></mml:math>gates are sufficient to decompose a general<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mn>3</mml:mn></mml:math>- and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mn>4</mml:mn></mml:math>-qubit unitary, respectively, with high numerical accuracy. Our approach is based on a sequential optimization of parameters related to the single-qubit rotation gates involved in a pre-designed quantum circuit used for the decomposition. In addition, the algorithm can be adopted to sparse inter-qubit connectivity architectures provided by current mid-scale quantum computers, needing only a few additional<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>C</mml:mi><mml:mi>N</mml:mi><mml:mi>O</mml:mi><mml:mi>T</mml:mi></mml:math>gates to be implemented in the resulting quantum circuits.