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Developments over the last two decades have opened the path towards quantum technologies in many quantum systems, such as cold atoms, trapped ions, cavity-quantum electrodynamics (QED), and circuit-QED. However the fragility of quantum…
Quantum mechanical systems exhibit an inherently probabilistic nature upon measurement which excludes in principle the singular direct observability continual case. Quantum theory of time continuous measurements and quantum prediction…
An analytical solution for the posterior estimate in Bayesian tomography of the unknown quantum state of an arbitrary quantum system (with a finite-dimensional Hilbert space) is found. First, we derive the Bayesian estimate for a pure…
Quantum computation offers a promising new kind of information processing, where the non-classical features of quantum mechanics can be harnessed and exploited. A number of models of quantum computation exist, including the now well-studied…
We present adaptive measurement techniques tailored for variational quantum algorithms on near-term small and noisy devices. In particular, we generalise earlier "learning to measure" strategies in two ways. First, by considering a class of…
A feedback scheme for preparation of photon number states in a microwave cavity is proposed. Quantum Non Demolition (QND) measurement of the cavity field provides information on its actual state. The control consists in injecting into the…
Constructing an integrated large-scale qubit system of realistic size requires addressing the challenge of physical crowding among qubits. This constraint poses an issue of coarse-grained (CG) measurement, wherein information from the…
The standard quantum formalism introduced at the undergraduate level treats measurement as an instantaneous collapse. In reality however, no physical process can occur over a truly infinitesimal time interval. A more subtle investigation of…
We derive the form of the Belavkin-Kushner-Stratonovich equation describing the filtering of a continuous observed quantum system via non-demolition measurements when the statistics of the input field used for the indirect measurement are…
Quantum state tomography is a fundamental tool in quantum information processing. It allows us to estimate the state of a quantum system by measuring different observables on many identically prepared copies of the system. This is, in…
The Gaussian state description of continuous variables is adapted to describe the quantum interaction between macroscopic atomic samples and continuous-wave light beams. The formalism is very efficient: a non-linear differential equation…
In variational quantum algorithms (VQAs), the most common objective is to find the minimum energy eigenstate of a given energy Hamiltonian. In this paper, we consider the general problem of finding a sufficient control Hamiltonian structure…
The engineering and control of devices at the quantum-mechanical level--such as those consisting of small numbers of atoms and photons--is a delicate business. The fundamental uncertainty that is inherently present at this scale manifests…
Continuous weak measurement allows localizing open quantum systems in state space, and tracing out their quantum trajectory as they evolve in time. Efficient quantum measurement schemes have previously enabled recording quantum trajectories…
In this work we introduce a general scheme for measurement based quantum computation in continuous variables. Our approach does not necessarily rely on the use of ancillary cluster states to achieve its aim, but rather on the detection of a…
Counting statistics of charge transfers in a point contact interacting with an arbitrary quantum system is studied. The theory for the charge specific density matrix is developed, allowing the evaluation of the probability of the outcome of…
We consider the problem of quantum-state tomography under the assumption that the state is pure, and more generally that its rank is bounded by a given value. In this scenario, new notions of informationally complete POVMs emerge, which…
We present a formulation of feedback in quantum systems in which the best estimates of the dynamical variables are obtained continuously from the measurement record, and fed back to control the system. We apply this method to the problem of…
Uncertainty quantification (UQ) is essential for deploying machine learning models in safety-critical physical systems, yet classical Bayesian approaches incur substantial computational overhead. We establish a formal connection between…
Considering ultracold atoms traversing a high-Q Fabry-Perot cavity, we theoretically demonstrate a quantum nondemolition measurement of the photon number. This fully quantum mechanical approach may be understood utilizing concepts as…