Research
Now is a golden age for quantum information: the first quantum technologies already appeared on the industrial market a few years ago and initiatives seeking to build a full-fledged quantum computer are multiplying. Quantum information—that is, information encoded in quantum degrees of freedom of physical systems—promises advantages notably for computing, cryptography, simulation, sensing, and communication, over classical information. This very exciting perspective raises the following fundamental questions:
Whether in the context of computing, cryptography, simulation, sensing, or communication, what leads to a quantum advantage? And once we get a such an advantage, how do we check the correct functioning of the quantum device, especially when its computing performance exceeds that of any classical machine?
Answering the first question is of major importance for finding useful tasks that we can use quantum information for, while answering the second is a timely problem in the absence of fault-tolerant mechanisms, for benchmarking existing and upcoming quantum devices.
I have been approaching these questions notably in the context of continuous-variable quantum information, in which the information is encoded using continuous degrees of freedom of a physical system. In my quest for the origin of quantum advantage, a significant part of my work has been devoted to the understanding of non-Gaussian states as a resource for quantum advantages with continuous variables.
Below are a few selected works and a list of my papers can be accessed here.
Selected works
Holomorphic representation of quantum computations
Ulysse Chabaud and Saeed Mehraban
Quantum 6, 831 (2022)
We study bosonic quantum computations using the stellar representation of quantum states. This holomorphic representation not only gives a canonical description of bosonic quantum computing using basic elements of complex analysis but also provides a unifying picture which delineates the boundary between discrete- and continuous-variable quantum information theory. Using this representation, we show that the evolution of a single bosonic mode under a Gaussian Hamiltonian can be described as an integrable classical dynamical system. We then generalize the properties of the stellar representation to the multimode case, deriving a non-Gaussian hierarchy of quantum states and relating entanglement to factorization properties of holomorphic functions. Finally, we apply this formalism to discrete- and continuous-variable quantum measurements and obtain a classification of subuniversal quantum computational models that are generalizations of Boson Sampling and Gaussian quantum computing.
Contextuality and Wigner negativity are equivalent for continuous-variable quantum measurements
Robert I. Booth, Ulysse Chabaud, Pierre-Emmanuel Emeriau
Phys. Rev. Lett. 129, 230401 (2022)
Quantum computers promise considerable speedups with respect to their classical counterparts. However, the identification of the innately quantum features that enable these speedups is challenging. In the continuous-variable setting—a promising paradigm for the realization of universal, scalable, and fault-tolerant quantum computing—contextuality and Wigner negativity have been perceived as two such distinct resources. Here we show that they are in fact equivalent for the standard model of continuous-variable quantum computing. While our results provide a unifying picture of continuous-variable resources for quantum speedup, they also pave the way toward practical demonstrations of continuous-variable contextuality and shed light on the significance of negative probabilities in phase-space descriptions of quantum mechanics.
Efficient verification of Boson Sampling
Ulysse Chabaud, Frédéric Grosshans, Elham Kashefi, Damian Markham
Quantum 5, 578 (2021)
The demonstration of quantum speedup, also known as quantum computational supremacy, that is the ability of quantum computers to outperform dramatically their classical counterparts, is an important milestone in the field of quantum computing. While quantum speedup experiments are gradually escaping the regime of classical simulation, they still lack efficient verification protocols and rely on partial validation. In this work, we derive an efficient protocol for verifying with trusted measurements the output states of a large class of continuous variable quantum circuits demonstrating quantum speedup, including Boson Sampling experiments, thus enabling a convincing demonstration of quantum speedup with photonic computing. Beyond the quantum speedup milestone, our results also enable the efficient and reliable certification of a large class of intractable continuous variable multi-mode quantum states.
Stellar representation of non-Gaussian states
Ulysse Chabaud, Damian Markham, Frédéric Grosshans
Phys. Rev. Lett. 124, 063605 (2020)
The stellar formalism allows us to represent the non-Gaussian properties of single-mode quantum states by the distribution of the zeros of their Husimi Q function in phase space. We use this representation in order to derive an infinite hierarchy of single-mode states based on the number of zeros of the Husimi Q function: the stellar hierarchy. We give an operational characterization of the states in this hierarchy with the minimal number of single-photon additions needed to engineer them, and derive equivalence classes under Gaussian unitary operations. We study in detail the topological properties of this hierarchy with respect to the trace norm, and discuss implications for non-Gaussian state engineering, and continuous variable quantum computing.