Related papers: Wiener Filtering for Passive Linear Quantum System…
A new method is described for constructing a generalized solution for stochastic differential equations. The method is based on the Cameron-Martin version of the Wiener Chaos expansion and provides a unified framework for the study of…
Quantum interferometry methods exploit quantum resources, such as photonic entanglement, to enhance phase estimation beyond classical limits. Nonlinear optics has served as a workhorse for the generation of entangled photon pairs, ensuring…
In this paper we study von Neumann un-biasing normalisation for ideal and real quantum random number generators, operating on finite strings or infinite bit sequences. In the ideal cases one can obtain the desired un-biasing. This relies…
Several quantities of interest in quantum information, including entanglement and purity, are nonlinear functions of the density matrix and cannot, even in principle, correspond to proper quantum observables. Any method aimed to determine…
We show that nonlinear problems including nonlinear partial differential equations can be efficiently solved by variational quantum computing. We achieve this by utilizing multiple copies of variational quantum states to treat…
In this paper we will develop linear and nonlinear filtering methods for a large class of nonlinear wave equations that arise in applications such as quantum dynamics and laser generation and propagation in a unified framework. We consider…
Computer Vision (CV) labelling algorithms play a pivotal role in the domain of low-level vision. For decades, it has been known that these problems can be elegantly formulated as discrete energy minimization problems derived from…
Quantum annealing (QA) is an efficient method for finding the ground-state energy of the problem Hamiltonian. However, in practical implementation, the system suffers from decoherence. On the other hand, recently, ``Localized virtual…
Machine learning techniques have led to broad adoption of a statistical model of computing. The statistical distributions natively available on quantum processors are a superset of those available classically. Harnessing this attribute has…
We present a classical algorithm to find approximate solutions to instances of quadratic unconstrained binary optimisation. The algorithm can be seen as an analogue of quantum annealing under the restriction of a product state space, where…
The Koopman-von Neumann (KvN) formalism recasts classical mechanics in a Hilbert space framework using complex wavefunctions and linear operators, akin to quantum mechanics. Instead of evolving probability densities in phase space (as in…
Both in classical and quantum stochastic control theory a major role is played by the filtering equation, which recursively updates the information state of the system under observation. Unfortunately, the theory is plagued by…
We investigate the effects of noise on parameterised quantum circuits using spectral analysis and classical signal processing tools. For different noise models, we quantify the additional, higher frequency modes in the output signal caused…
Evaluating the expectation of a quantum circuit is a classically difficult problem known as the quantum mean value problem (QMV). It is used to optimize the quantum approximate optimization algorithm and other variational quantum…
Quantum annealing was originally proposed as an approach for solving combinatorial optimisation problems using quantum effects. D-Wave Systems has released a production model of quantum annealing hardware. However, the inherent noise and…
With rapid advances in quantum hardware, a central question is whether quantum devices with or without full error correction can outperform classical computers on practically relevant problems. Variational Quantum Algorithms (VQAs) have…
We present a quantum solver for partial differential equations based on a flexible matrix product operator representation. Utilizing mid-circuit measurements and a state-dependent norm correction, this scheme overcomes the restriction of…
The theory of Gaussian quantum fluctuations around classical steady states in nonlinear quantum-optical systems (also known as standard linearization) is a cornerstone for the analysis of such systems. Its simplicity, together with its…
We study quantum filters that are driven by basic quantum noises and construct classical versions. Our approach is based on exploiting the quantum markovian component of the observation and measurement processes of the filters. This…
Quantum computing has attracted significant interest in the optimization community because it potentially can solve classes of optimization problems faster than conventional supercomputers. Several researchers proposed quantum computing…