Research project A10 – SFB 1227 DQ-mat – Leibniz University Hannover

Introduction

Quantum error correction is the central tool to ameliorate the effects of decoherence during quantum computations. Recently QEC was considered as a candidate to enhance quantum metrology in a noisy environment and, motivated by rapid development of quantum sensors and the maturing status of quantum error correction, quantum codes were introduced by several groups independently; it has been shown that QEC can improve the sensitivity for probes sensing a signal under dephasing noise. A general condition known as “Hamiltonian-not-in-Lindblad-span” condition has been discovered to enable Heisenberg-limited metrology for Hamiltonian estimation under Markovian noise, generalised to the “Hamiltonian-not-in-Kraus-span” condition for general maps. Although conditions are known for metrological QECCs, the theory of such codes is far less mature in comparison with the state of the art of QEC in quantum computation. In particular, only a handful of constructions are known, which typically rely on numerical searches via semidefinite programs

Objectives

The central question of this project is to find a general theory of metrological QECCs, first in the stabiliser setting, and then to explore nonstabiliser generalizations by analogy with, e.g., constructions using low-energy subspaces of gapless models. The role of transversal local operations plays a key role in the discovery of QEC schemes. Thus quantum Reed-Muller codes as probe states will be assessed as a first prototype. Further, we will investigate the role of biased noise and the exploitation of error mitigation schemes and discover large QEC schemes for metrology in the presence of non- Markovian noise. Finally, the main question of this project is to study the metrological limits of noisy quantum systems and to develop QEC protocols to achieve these limits. These metrological schemes will then be adapted for implementation in spinor BEC and trapped-ion architectures to approach the limits of sensitivity.