Optimizing performance of quantum operations with non-Markovian decoherence: the tortoise or the hare?

TL;DR

This paper introduces an efficient method to optimize quantum control in non-Markovian environments, revealing a trade-off between process speed and fidelity, with slower processes leveraging environmental memory for better performance.

Contribution

It develops a process tensor-based gradient method for optimal quantum control in non-Markovian settings, demonstrating how environmental memory can enhance fidelity.

Findings

Slower processes achieve higher fidelity by exploiting non-Markovian effects.

A trade-off exists between process speed and fidelity in quantum control.

The method accurately characterizes the maximum achievable fidelity over time.

Abstract

The interaction between a quantum system and its environment limits our ability to control it and perform quantum operations on it. We present an efficient method to find optimal controls for quantum systems coupled to non-Markovian environments, by using the process tensor to compute the gradient of an objective function. We consider state transfer for a driven two-level system coupled to a bosonic environment, and characterize performance in terms of speed and fidelity. We thus determine the best achievable fidelity as a function of process duration. We show there is a trade-off between speed and fidelity, and that slower processes can have higher fidelity by exploiting non-Markovian effects.