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Understanding the computational complexity of quantum states is a central challenge in quantum many-body physics. In qubit systems, fermionic Gaussian states can be efficiently simulated on classical computers and hence can be employed as a…
Fermionic non-Gaussianity quantifies a quantum state's deviation from a classically tractable free-fermionic description, constituting a necessary resource for computational quantum advantage. Here we use fermionic antiflatness (FAF) to…
We define fermionic convolution and demonstrate its utility in characterizing fermionic non-Gaussian components, which are essential to the computational advantage of fermionic systems. Using fermionic convolution, we propose an efficient…
The experimental interest and developments in quantum spin-1/2-chains has increased uninterruptedly over the last decade. In many instances, the target quantum simulation belongs to the broader class of non-interacting fermionic models,…
Leveraging the unique quantum properties of non-Gaussian states is crucial for advancing continuous variable quantum technologies. Recent experimental advancements in generating non-Gaussian states, coupled with theoretical findings of…
Gaussian quantum states and channels are pivotal across many branches of quantum science and their applications, including the processing and storage of quantum information, the investigation of thermodynamics in the quantum regime, and…
Fermionic Gaussian states are a fundamental tool in many-body physics, faithfully representing non-interacting quantum systems and allowing for efficient numerical simulations. Given a many-body wave function, it is therefore interesting to…
The experimental realization of increasingly complex quantum states underscores the pressing need for new methods of state learning and verification. In one such framework, quantum state tomography, the aim is to learn the full quantum…
Classically hard to simulate quantum states, or "magic states", are prerequisites to quantum advantage, highlighting an apparent separation between classically and quantumly tractable problems. Classically simulable states such as Clifford…
Modern quantum devices are highly susceptible to errors, making the verification of their correct operation a critical problem. Usual tomographic methods rapidly become intractable as these devices are scaled up. In this paper, we introduce…
Direct measurement of quantum non-Gaussianity requires some variant of a discrete photon-resolving detection, which is feasible only for low mean photon numbers. For a large mean photon number, intensity detection by linear photodiodes…
This paper introduces an innovative approach for representing Gaussian fermionic states, pivotal in quantum spin systems and fermionic models, within a range of alternative quantum bases. We focus on transitioning these states from the…
Generation of high fidelity photonic non-Gaussian states is a crucial ingredient for universal quantum computation using continous-variable platforms, yet it remains a challenge to do so efficiently. We present a general framework for a…
We study the fermionic non-Gaussianity in typical quantum states, focusing on Haar random states of qubits with or without a global $U(1)$ symmetry. Using the Weingarten calculus, we derive analytical predictions for the non-Gaussianity,…
We propose efficient algorithms for classically simulating fermionic linear optics operations applied to non-Gaussian initial states. By gadget constructions, this provides algorithms for fermionic linear optics with non-Gaussian…
A major roadblock for large-scale photonic quantum technologies is the lack of practical reliable certification tools. We introduce an experimentally friendly - yet mathematically rigorous - certification test for experimental preparations…
We derive a theoretical framework for the experimental certification of non-Gaussian features of quantum states using double homodyne detection. We rank experimental non-Gaussian states according to the recently defined stellar hierarchy…
Gaussian states and measurements collectively are not powerful-enough resources for quantum computing, as any Gaussian dynamics can be simulated efficiently, classically. However, it is known that any one non-Gaussian resource -- either a…
Full reconstruction of quantum states from measurement samples is often a prohibitively complex task, both in terms of the experimental setup and the scaling of the sample size with the system. This motivates the relatively easier task of…
Gaussian states have played on important role in the physics of continuous-variable quantum systems. They are appealing for the experimental ease with which they can be produced, and for their compact and elegant mathematical description.…