# Tensor product approach to quantum control

## TL;DR

This paper demonstrates that tensor product algorithms can efficiently control large quantum systems, enabling the simulation and optimization of quantum states with reduced computational resources, which is crucial for advancing quantum computing.

## Contribution

It introduces a tensor product approach combined with the tAMEn algorithm for optimal quantum control, overcoming dimensionality challenges in large quantum systems.

## Key findings

- Successfully controlled a 41-spin quantum system on a single workstation.
- Achieved significant savings in computational time and memory.
- Enabled potential development of quantum computers with 50-100 qubits.

## Abstract

In this proof-of-concept paper we show that tensor product approach is efficient for control of large quantum systems, such as Heisenberg spin wires, which are essential for emerging quantum computing technologies. We compute optimal control sequences using GRAPE method, applying the recently developed tAMEn algorithm to calculate evolution of quantum states represented in the tensor train format to reduce storage. Using tensor product algorithms we can overcome the curse of dimensionality and compute the optimal control pulse for a 41 spin system on a single workstation with fully controlled accuracy and huge savings of computational time and memory. The use of tensor product algorithms opens new approaches for development of quantum computers with 50 to 100 qubits.