Related papers: Quantum Trajectories for a Class of Continuous Mat…
An ordering between the quantum states emerging from a single mode gauge-covariant bosonic Gaussian channel is proven. Specifically, we show that within the set of input density matrices with the same given spectrum, the element passive…
We consider the evolution of a quantum simple harmonic oscillator in a general Gaussian state under simultaneous time-continuous weak position and momentum measurements. We deduce the stochastic evolution equations for position and momentum…
We provide a unified picture for the master equation approach and the quantum trajectory approach to a measurement problem of a two-state quantum system (a qubit), an electron coherently tunneling between two coupled quantum dots (CQD's)…
The permanent is pivotal to both complexity theory and combinatorics. In quantum computing, the permanent appears in the expression of output amplitudes of linear optical computations, such as in the Boson Sampling model. Taking advantage…
Finance, especially option pricing, is a promising industrial field that might benefit from quantum computing. While quantum algorithms for option pricing have been proposed, it is desired to devise more efficient implementations of costly…
The dynamics of many open quantum systems are described by stochastic master equations. In the discrete-time case, we recall the structure of the derived quantum filter governing the evolution of the density operator conditioned to the…
In this thesis we consider primarily the dynamics of quantum systems subjected to continuous observation. In the Schr\"{o}dinger picture the evolution of a continuously monitored quantum system, referred to as a `quantum trajectory', may be…
We examine most-likely paths between initial and final states for diffusive quantum trajectories in continuously monitored pure-state qubits, obtained as extrema of a stochastic path integral. We demonstrate the possibility of "multipaths"…
Quantum computation in the one-way model requires the preparation of certain resource states known as cluster states. We describe how the construction of continuous-variable cluster states for optical quantum computing relate to the…
State preparation is a necessary component of many quantum algorithms. In this work, we combine a method for efficiently representing smooth differentiable probability distributions using matrix product states with recently discovered…
Optomechanics is currently believed to provide a promising route towards the achievement of genuine quantum effects at the large, massive-system scale. By using a recently proposed figure of merit that is well suited to address…
By modeling the interaction of an open quantum system with its environment through a natural generalization of the classical concept of continuous time random walk, we derive and characterize a class of non-Markovian master equations whose…
The simulation of quantum systems is a task for which quantum computers are believed to give an exponential speedup as compared to classical ones. While ground states of one-dimensional systems can be efficiently approximated using Matrix…
We construct a quantum-inspired classical algorithm for computing the permanent of Hermitian positive semidefinite matrices, by exploiting a connection between these mathematical structures and the boson sampling model. Specifically, the…
One of the most striking features of quantum mechanics is the appearance of phases of matter with topological origins. These phases result in remarkably robust macroscopic phenomena such as the edge modes in integer quantum Hall systems,…
The fidelity between the state of a continuously observed quantum system and the state of its associated quantum filter, is shown to be always a submartingale. The observed system is assumed to be governed by a continuous-time Stochastic…
Common wisdom says that the entanglement of fermionic systems can be low in the second quantization formalism but is extremely large in the first quantization. Hence Matrix Product State (MPS) methods based on moderate entanglement have…
We present a matrix-product-state-based numerical approach for simulating systems composed of several qubits and a common one-dimensional waveguide. In the presented approach, the one-dimensional waveguide is modeled in real space. Thus,…
Analyses of serially-sampled data often begin with the assumption that the observations represent discrete samples from a latent continuous-time stochastic process. The continuous-time Markov chain (CTMC) is one such generative model whose…
We consider the deterministic generation of entangled multi-qubit states by the sequential coupling of an ancillary system to initially uncorrelated qubits. We characterize all achievable states in terms of classes of matrix product states…