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Science and engineering problems subject to uncertainty are frequently both computationally expensive and feature nonsmooth parameter dependence, making standard Monte Carlo too slow, and excluding efficient use of accelerated uncertainty…
We investigate optimal discrimination between two projective quantum measurements on a single qubit. We consider scenario where the measurement that should be identified can be performed twice and we show that adaptive discrimination…
We derive, and experimentally demonstrate, an interferometric scheme for unambiguous phase estimation with precision scaling at the Heisenberg limit that does not require adaptive measurements. That is, with no prior knowledge of the phase,…
Using a circuit QED device, we present a theoretical study of real-time quantum state estimation via quantum Bayesian approach. Suitable conditions under which the Bayesian approach can accurately update the density matrix of the qubit are…
We consider measurement-based quantum computation using the state of a spin-lattice system in equilibrium with a thermal bath and free to evolve under its own Hamiltonian. Any single qubit measurements disturb the system from equilibrium…
We present a comprehensive investigation into the learning capabilities of a simple d-level system (qudit). Our study is specialized for classification tasks using real-world databases, specifically the Iris, breast cancer, and MNIST…
Fidelity estimation is a critical yet resource-intensive step in testing quantum programs on noisy intermediate-scale quantum (NISQ) devices, where the required number of measurements is difficult to predefine due to hardware noise, device…
We present a quantum algorithm for efficiently sampling transformed Gaussian random fields on $d$-dimensional domains, based on an enhanced version of the classical moving average method. Pointwise transformations enforcing boundedness are…
Quantum metrology leverages quantum resources such as entanglement and squeezing to enhance parameter estimation precision beyond classical limits. While optimal quantum control strategies can assist to reach or even surpass the Heisenberg…
We propose a quantum device that can approximate any projective measurement on a qubit. The desired measurement basis is selected by the quantum state of a "program register". The device is optimized with respect to maximal average fidelity…
Generalized quantum measurements are an important extension of projective or von Neumann measurements, in that they can be used to describe any measurement that can be implemented on a quantum system. We describe how to realize two…
Given the state of a quantum system, one can calculate the expectation value of any observable of the system. However, the inverse problem of determining the state by performing different measurements is not a trivial task. In various…
Continuous-time measurements are instrumental for a multitude of tasks in quantum engineering and quantum control, including the estimation of dynamical parameters of open quantum systems monitored through the environment. However, such…
We consider the classic question of state tomography: given copies of an unknown quantum state $\rho\in\mathbb{C}^{d\times d}$, output $\widehat{\rho}$ which is close to $\rho$ in some sense, e.g. trace distance or fidelity. When one is…
Quantum state learning is a fundamental problem in physics and computer science. As near-term quantum devices are error-prone, it is important to design error-resistant algorithms. Apart from device errors, other unexpected factors could…
We present an adaptive smoother for linear state-space models with unknown process and measurement noise covariances. The proposed method utilizes the variational Bayes technique to perform approximate inference. The resulting smoother is…
In quantum mechanics, measuring the expectation value of a general observable has an inherent statistical uncertainty that is quantified by variance or mean squared error of measurement outcome. While the uncertainty can be reduced by…
Quantum-limited estimation of an optical phase using adaptive (i.e. real-time feedback) techniques is reviewed. One case is explored in detail, as it can be understood using only elementary concepts such as photonic shot-noise and error…
Quantum instruments describe both the classical outcome and the updated state associated with a quantum measurement. We ask whether these processes can be simulated using only a natural subset of resources, namely projective measurements on…
We present general principles for the design and analysis of unbiased Monte Carlo estimators in a wide range of settings. Our estimators posses finite work-normalized variance under mild regularity conditions. We apply our estimators to…