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Preparing the thermal density matrix $\rho_{\beta} \propto e^{-\beta H}$ corresponding to a given Hamiltonian $H$ is a task of central interest across quantum many-body physics, and is particularly salient when attempting to study it with…
The Lindblad quantum master equation is one of the central approaches to the physics of open quantum systems. In particular, boundary driving enables the study of transport, where a steady state emerges in the long-time limit, which…
Local Hamiltonians of fermionic systems on a lattice can be mapped onto local qubit Hamiltonians. Maintaining the locality of the operators comes at the expense of increasing the Hilbert space with auxiliary degrees of freedom. In order to…
Floquet engineering of isolated systems is often based on the concept of the effective time-independent Floquet Hamiltonian, which describes the stroboscopic evolution of a periodically driven quantum system in steps of the driving period…
It is shown how to construct *-homomorphic quantum stochastic Feller cocycles for certain unbounded generators, and so obtain dilations of strongly continuous quantum dynamical semigroups on C* algebras; this generalises the construction of…
We extend the concept of Anderson localization, the confinement of quantum information in a spatially irregular potential, to quantum circuits. Considering matchgate circuits, generated by time-dependent spin-1/2 XY Hamiltonians, we give an…
We obtain the solutions of the generic bilinear master equation for a quantum oscillator with constant coefficients in the Gaussian form. The well-behavedness and positive semidefiniteness of the stationary states could be characterized by…
In the study of closed many-body quantum systems one is often interested in the evolution of a subset of degrees of freedom. On many occasions it is possible to approach the problem by performing an appropriate decomposition into a bath and…
What can one infer about the dynamical evolution of quantum systems just by symmetry considerations? For Markovian dynamics in finite dimensions, we present a simple construction that assigns to each symmetry of the generator a family of…
Given a quantum Hamiltonian and its evolution time, the corresponding unitary evolution operator can be constructed in many different ways, corresponding to different trajectories between the desired end-points and different series…
Building upon recent progress in Lindblad engineering for quantum Gibbs state preparation algorithms, we propose a simplified protocol that is shown to be efficient under the eigenstate thermalization hypothesis (ETH). The ETH reduces…
The Lindblad (GKLS) master equation, which represents the mathematical form for the general evolution of a density matrix, is a versatile and widely-used tool in open quantum systems. In contrast with the typical approach of imposing…
We have shown that quantum systems on finite-dimensional Hilbert spaces are equivalent under local transformations. Using these transformations give rise to a gauge group that connects the hamiltonian operators associated with each quantum…
We present an algebraic framework for approximate model reduction of Markovian open quantum dynamics that guarantees complete positivity and trace preservation by construction. First, we show that projecting a Lindblad generator on its…
We formulate a novel ground state quantum computation approach that requires no unitary evolution of qubits in time: the qubits are fixed in stationary states of the Hamiltonian. This formulation supplies a completely time-independent…
We derive a semiclassical approximation for the evolution generated by the Lindblad equation as a generalization of complex WKB theory. Linear coupling to the environment is assumed, but the Hamiltonian can be a general function of…
Within a unified framework, we reveal that the seemingly disparate control approaches for classical and quantum continuous-variable systems are interconnected via differential manifolds of the ancillary representations. For classical…
In this article, we present a comprehensive framework for constructing smooth, localized solutions in systems of semi-linear partial differential equations, with a particular emphasis to the Gray-Scott model. Specifically, we construct a…
We develop connections between generalised notions of entanglement and quantum computational devices where the measurements available are restricted, either because they are noisy and/or because by design they are only along Pauli…
A characterisation of quantum stochastic positive definite (PD) exponent is given in terms of the conditional positive definiteness (CPD) of their form-generator. The pseudo-Hilbert dilation of the stochastic form-generator and the…