Robust Quantum Gate Complexity: Foundations

TL;DR

This paper explores the foundational aspects of robust quantum gate complexity, emphasizing the importance of robustness in quantum control systems amidst noise and errors, and proposing a new approach inspired by geometric interpretations.

Contribution

It introduces a novel framework for analyzing robustness in quantum control, linking it to gate complexity and geometric control theory.

Findings

Defines robustness in quantum control context

Connects robustness to gate complexity implications

Proposes a geometric interpretation-based approach

Abstract

Optimal control of closed quantum systems is a well studied geometrically elegant set of computational theory and techniques that have proven pivotal in the implementation and understanding of quantum computers. The design of a circuit itself corresponds to an optimal control problem of choosing the appropriate set of gates (which appear as control operands) in order to steer a qubit from an initial, easily prepared state, to one that is informative to the user in some sense, for e.g., an oracle whose evaluation is part of the circuit. However, contemporary devices are known to be noisy, and it is not certain that a circuit will behave as intended. Yet, although the computational tools exist in broader optimal control theory, robustness of adequate operation of a quantum control system with respect to uncertainty and errors has not yet been broadly studied in the literature. In this paper, we propose a new approach inspired by the closed quantum optimal control and its connection to geometric interpretations. To this end, we present the appropriate problem definitions of robustness in the context of quantum control, focusing on its broader implications for gate complexity.