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The importance of quantum error correction in paving the way to build a practical quantum computer is no longer in doubt. This dissertation makes a threefold contribution to the mathematical theory of quantum error-correcting codes.…
Bosonic error correcting codes utilize the infinite dimensional Hilbert space of a harmonic oscillator to encode a qubit. Bosonic rotation codes are characterized by a discrete rotation symmetry in their Wigner functions and include codes…
The center of mass motion of trapped ions and neutral atoms is suitable for approximation by a time-dependent driven quantum harmonic oscillator whose frequency and driving strength may be controlled with high precision. We show the time…
We present a method for the steady state optimization of nonlinear delay differential equations. The method ensures stability and robustness, where a system is called robust if it remains stable despite uncertain parameters. Essentially, we…
These are the lecture notes from the 2019 Les Houches Summer School on "Quantum Information Machines". After a brief introduction to quantum error correction and bosonic codes, we focus on the case of cat qubits stabilized by a nonlinear…
In this paper, we propose a driven-dissipative scheme for generating non-Gaussian mechanical entangled states and remotely preparing mechanical Schr\"{o}dinger cat states via the entanglement. The system under study consists of a cavity…
Coherent errors are a dominant noise process in many quantum computing architectures. Unlike stochastic errors, these errors can combine constructively and grow into highly detrimental overrotations. To combat this, we introduce a simple…
The paradigm of reservoir computing exploits the nonlinear dynamics of a physical reservoir to perform complex time-series processing tasks such as speech recognition and forecasting. Unlike other machine-learning approaches, reservoir…
In this work, we propose a nonlinear stabilization technique for scalar conservation laws with implicit time stepping. The method relies on an artificial diffusion method, based on a graph-Laplacian operator. It is nonlinear, since it…
Stabilization is a key dependability property for dealing with unanticipated transient faults, as it guarantees that even in the presence of such faults, the system will recover to states where it satisfies its specification. One of the…
We report the computational discovery of complex, topologically charged, and spectrally stable states in three-dimensional multi-component nonlinear wave systems of nonlinear Schr{\"o}dinger type. While our computations relate to…
Recent advances illustrate the power of reservoir engineering in applications to many-body systems, such as quantum simulators based on superconducting circuits. We present a framework based on kinetic equations and noise spectra that can…
The approach to equilibrium of a nondegenerate quantum system involves the damping of microscopic population oscillations, and, additionally, the bringing about of detailed balance, i.e. the achievement of the correct Boltzmann factors…
A new class of error-correcting quantum codes is introduced capable of stabilizing qubits against spontaneous decay arising from couplings to statistically independent reservoirs. These quantum codes are based on the idea of using an…
Harmonic stator-rotor coupling offers a promising approach for the interconnection of rotating subsystems in the simulation of electric machines. This paper studies the stability of discretization schemes based on harmonic coupling in the…
We propose a method to create "spin cat states", i.e. macroscopic superpositions of coherent spin states, in Bose-Einstein condensates using the Kerr nonlinearity due to atomic collisions. Based on a detailed study of atom loss, we conclude…
Quantum machine learning is a rapidly advancing discipline that leverages the features of quantum mechanics to enhance the performance of computational tasks. Quantum reservoir processing, which allows efficient optimization of a single…
In the paper, we develop a bosonic quantum error correction code based on squeezed Fock states. We compare our proposed code with one based on squeezed Schrodinger's cat states using the Knill-Laflamme cost function and the Petz map…
An open question in mechanics is whether mechanical resonators can be made nonlinear with vibrations approaching the quantum ground state. This requires engineering a mechanical nonlinearity far beyond what has been realized thus far. Here…
In this paper we present a method to derive an exact master equation for a bosonic system coupled to a set of other bosonic systems, which plays the role of the reservoir, under the strong coupling regime, i.e., without resorting to either…