# Coherent quantum control of discrete and continuous variable systems

Lead Research Organisation:
Imperial College London

Department Name: Dept of Physics

### Abstract

In any protocol aimed at manipulating or transmitting information, symbols are encoded in states of some physical system. If this system is quantum mechanical rather than classical, as is bound to become common if the miniaturisation of processing units persists at the current rate, the laws of information processing are different than the ones governing ordinary classical computers. Quantum Information (QI) science investigates these laws, exploring the novel, potentially revolutionary, possibilities offered by quantum mechanical systems across the whole spectrum of information technologies, from the possibility to run unique and faster algorithms on a quantum computer to applications in high precision metrology, and in general providing a new insight into the foundation of quantum mechanics. In the last two decades we have witnessed the rise of QI science from the realm of theoretical conjecture to that of actual technological application, with the prominent example of operating quantum cryptographic systems. Yet, a major obstacle still stands in the way of the day to day realisation of QI protocols: preserving quantum coherence, as necessary for QI processing, in most scalable systems at room conditions is always a very difficult challenge, mainly due to the undesired interactions between the small quantum system and its large environment. The field of quantum control offers one of the most promising ways to cope with the problem of decoherence (the unwanted demise of coherent quantum properties). Quantum control consists in the application of a series of externally controlled actions and manipulations on the system where the information is being stored or processed, such that, typically, decoherence is delayed, or specific quantum states, useful as resources for QI, can be prepared. Although the area of quantum control is well-established and has shown considerable promise, its application to QI science is still in its first steps, and the impact control techniques could have on the path towards daily QI processing is arguably still underestimated. This research project intends to study, develop and apply novel quantum control and feedback techniques, and to optimise them for specific quantum information tasks and for specifically promising physical systems (in particular atomic ensembles, trapped ions and solid state devices). The project is divided in three main objectives: i) the analysis of local controllability for continuous-variable and hybrid many-body systems; ii) the analysis of the entanglement enhancement by means of the interspersing of ''fast'' local operations and classical communication; iii) the generalisation of entanglement optimisation feedback techniques to noisy systems. The results obtained pursuing these objectives will hopefully prompt experimental groups, working on promising quantum technologies for quantum information, to use the developed techniques for their purposes.

### Planned Impact

The proposed research project will surely contribute to strengthen the leadership of UK in two strategic areas of interest for EPSRC as quantum information science and research at nano/microscopic scale. Indeed, since the birth of quantum information, the possibility of coherently control quantum systems was recognised as the main challenge to possible implementations. Thus theoretical investigations on the controllability properties of emerging and promising quantum technologies will certainly enhance the UK community competitiveness in these promising contexts, contributing to make a step further towards the ''day to day realisation'' of quantum information protocols. At a long-term the proposed research is potentially of the highest impact for the society as a whole. In fact, the implementation of quantum computers and in general the processing of quantum information would permit to realise tasks that are inaccessible to the actual technologies. Furthermore, quantum information is also providing a new insight into the foundation of quantum mechanics and the history of science teaches that its impact on the society fully discloses only many years after the discoveries themselves and in usually unpredictable ways. Thus, it is reasonable to guess that we still do not know which will be the major applications of quantum information/computation in the everyday life and we will discover them only in the next years.

## People |
## ORCID iD |

Marco Giovanni Genoni (Principal Investigator) |

### Publications

Blandino R
(2012)

*Homodyne estimation of Gaussian quantum discord.*in Physical review letters
Campbell E
(2013)

*Continuous-variable entanglement distillation and noncommutative central limit theorems*in Physical Review A
Genoni M
(2013)

*Detecting quantum non-Gaussianity via the Wigner function*in Physical Review A
Genoni M
(2013)

*Optimal feedback control of linear quantum systems in the presence of thermal noise*in Physical Review A
Genoni M
(2013)

*Optimal estimation of joint parameters in phase space*in Physical Review A
Genoni M
(2015)

*Squeezing of mechanical motion via qubit-assisted control*in New Journal of Physics
Genoni M
(2012)

*Optimal quantum estimation of the coupling constant of Jaynes-Cummings interaction*in The European Physical Journal Special Topics
Genoni M
(2012)

*Optical interferometry in the presence of large phase diffusion*in Physical Review A
Genoni MG
(2012)

*Dynamical recurrence and the quantum control of coupled oscillators.*in Physical review letters
Lulli A
(2012)

*Robustness of tripartite entanglement transfer from bosonic modes to localized qubits*in The European Physical Journal Special TopicsDescription | The goal of quantum control is to prepare physical systems in quantum states which may be useful for quantum technologies applications. During this fellowship I studied different problems related to quantum control. First we have been able to translate a known mathematical criterion for the quantum controllability of a system described by a finite dimensional Hilbert space (e.g. a spin systems) to the case of infinite dimension. This is particularly relevant both from a fundamental and an applicative point of view as infinite-dimensional quantum systems are quite ubiquitous (e.g. the electromagnetic field, mechanical oscillators, bosonic atoms, etc.). We have also focused ourselves on the usefulness of continuous-measurement and feedback protocols to control and prepare quantum systems characterized by useful resources as squeezing and entanglement. We investigated in particular the role of thermal noise, which may be relevant if one wants to apply these protocols to nano-mechanical oscillators or in microwave quantum optics. A feedback-control protocol has been also proposed in a hybrid system, where a mechanical oscillator interacts with a qubit (which may correspond to an atom in a cavity, or the electronic spin of a nitrogen vacancy centre in diamond). We demonstrated how to prepare a squeezed state of the oscillator by measuring and controlling the qubit system. In parallel to these "quantum-control oriented" results, we have also studied different problems in quantum technology. In particular it is worth to mention: i) several works of quantum metrology and quantum estimation, in particular the optimal quantum estimation of a complex displacement and the estimation of quantum discord for continuos-variable systems via homodyne detection; ii) the characterisation of "quantum non-Gaussian" states, i.e. states that can be generated only via high non-linearities in quantum optics. |

Exploitation Route | The results on the quantum controllability for continuous-variable systems pave the way to the design of novel quantum control protocols able to engineer specific operations (such as single-mode and two-mode squeezing operations, beam-splitters, phase-rotations) on networks of quantum oscillators. This may turn very useful for opto-mechanics control, where different bosonic modes (representing the cavity electromagnetic modes, the mechanical oscillator, etc.) interact. In the same way the analysis of the usefulness of continuous-measurement and feedback control in bosonic systems subjected to a thermal noise, will be relevant for the control of mechanical oscillators and in microwave quantum optics. The feedback protocol proposed to generate squeezing of a mechanical oscillator interacting with a qubit system is in fact the first protocol of this kind proposed for hybrid systems. For this reason we expect that our findings will pave the way to a new generation of control protocols able to exploit the opportunities offered by these systems. The techniques and the results obtained on the quantum estimation of a complex displacement have already been used and will be used by researchers working in the context of multi-parameter quantum estimation. The criteria proposed to detect quantum non-Gaussian states represents a new tool offered to experimental groups which are interested in certifying that a non-classical state (e.g. a single photon Fock state) has been generated in their experiments. |

Sectors | Digital/Communication/Information Technologies (including Software) |

Description | The results about controllability of continuous-variable systems have been further generalised to the case of systems described by Hamiltonian operators with a discrete spectrum. The possibilities offered by continuous measurement and feedback on bosonic systems subjected to thermal noise have been further analysed, in particular discussing the results obtained through a general-dyne measurement. The criteria proposed to detect quantum non-Gaussian states have been further generalised and compared with the other existing criteria presented in literature, in view of possible experimental applications. The results obtained in multi-parameter quantum metrology, in particular the optimal estimation of joint parameters in phase space and the optimal estimation of quantum discord, are currently used and cited by different research groups working on this relevant research topic. |

First Year Of Impact | 2011 |

Sector | Digital/Communication/Information Technologies (including Software) |

Impact Types | Societal,Economic |