Related papers: On Trajectory-Based Stability Analysis for $1$-bit…
Stable quantum computation requires noisy results to remain bounded even in the presence of noise fluctuations. Yet non-stationary noise processes lead to drift in the varying characteristics of a quantum device that can greatly influence…
Stabilizer states form an important class of states in quantum information, and are of central importance in quantum error correction. Here, we provide an algorithm for deciding whether one stabilizer (target) state can be obtained from…
In this paper, we consider finite difference approximations of the second order wave equation. We use finite difference operators satisfying the summation-by-parts property to discretize the equation in space. Boundary conditions and grid…
Characterizing noisy quantum processes is important to quantum computation and communication (QCC), since quantum systems are generally open. To date, all methods of characterization of quantum dynamics (CQD), typically implemented by…
A stability analysis is performed on high-order schemes formulated using the Flux Reconstruction (FR) approach. The one-dimensional advection model equation is used for the assessment of the stability region of these schemes when coupled…
Experimental progress in qubit manufacturing calls for the development of new theoretical tools to analyze quantum data. We show how an unsupervised machine-learning technique can be used to understand short-range entangled many-qubit…
We propose a procedure to design a state-quantizer with finitely many bins for a marginally stable stochastic linear system evolving in $\R^d$, and a bounded policy based on the resulting quantized state measurements to ensure bounded…
Quantum error-correction codes would protect an arbitrary state of a multi-qubit register against decoherence-induced errors, but their implementation is an outstanding challenge for the development of large-scale quantum computers. A first…
We consider fully discrete schemes based on the scalar auxiliary variable (SAV) approach and stabilized SAV approach in time and the Fourier-spectral method in space for the phase field crystal (PFC) equation. Unconditionally energy…
This note proposes a data-driven output-feedback stabilizing policy iteration for unknown linear discrete-time systems with unmeasurable states. Existing policy iteration methods for optimal control must start from a stabilizing control…
Quantum state tomography, which aims to find the best description of a quantum state -- the density matrix, is an essential building block in quantum computation and communication. Standard techniques for state tomography are incapable of…
We discuss the stability theory and numerical analysis of the Helmholtz equation with variable and possibly non-smooth or oscillatory coefficients. Using the unique continuation principle and the Fredholm alternative, we first give an…
Quantum trajectories are dynamical equations for quantum states conditioned on the results of a time-continuous measurement, such as a continuous-in-time current $\vec y_t$. Recently there has been renewed interest in dynamical maps for…
Runtime monitoring checks, during execution, whether a partial signal produced by a hybrid system satisfies its specification. Signal First-Order Logic (SFO) offers expressive real-time specifications over such signals, but currently comes…
The use of low-bit quantization has emerged as an indispensable technique for enabling the efficient training of large-scale models. Despite its widespread empirical success, a rigorous theoretical understanding of its impact on learning…
We propose a method for the stabilisation of quantum computations (including quantum state storage). The method is based on the operation of projection into $\cal SYM$, the symmetric subspace of the full state space of $R$ redundant copies…
We consider the linear equation including two fractional order difference operators, viz. $\Delta^{\alpha}$ and $\Delta^{\beta}$, $0<\beta<\alpha \leq 1$. The sequence representation will be provided to find the solution in an easier way.…
Quantum state purification is crucial in quantum communication and computation, aiming to recover a purified state from multiple copies of an unknown noisy state. This work introduces a general state purification framework designed to…
First order quantum phase transitions (1QPTs) are signaled, in the thermodynamic limit, by discontinuous changes in the ground state properties. These discontinuities affect expectation values of observables, including spatial correlations.…
The dynamics at the critical-point of a general first-order quantum phase transition in a finite system is examined, from an algebraic perspective. Suitable Hamiltonians are constructed whose spectra exhibit coexistence of states…