A reduced complexity numerical method for optimal gate synthesis

TL;DR

This paper introduces a numerical method that reduces complexity in optimal quantum gate synthesis, enabling efficient approximation of unitary gates like those in SU(4), which are otherwise computationally intractable.

Contribution

It applies max-plus curse of dimensionality free techniques to quantum control, significantly lowering computational complexity compared to traditional grid-based methods.

Findings

Successfully synthesized an SU(4) quantum gate

Reduced computational complexity in optimal control calculations

Demonstrated effectiveness of the method on complex quantum systems

Abstract

Although quantum computers have the potential to efficiently solve certain problems considered difficult by known classical approaches, the design of a quantum circuit remains computationally difficult. It is known that the optimal gate design problem is equivalent to the solution of an associated optimal control problem, the solution to which is also computationally intensive. Hence, in this article, we introduce the application of a class of numerical methods (termed the max-plus curse of dimensionality free techniques) that determine the optimal control thereby synthesizing the desired unitary gate. The application of this technique to quantum systems has a growth in complexity that depends on the cardinality of the control set approximation rather than the much larger growth with respect to spatial dimensions in approaches based on gridding of the space, used in previous literature. This technique is demonstrated by obtaining an approximate solution for the gate synthesis on $SU(4)$- a problem that is computationally intractable by grid based approaches.