Related papers: Implementation of logical gates on infinite dimens…
Quantum control for error correction is critical for the practical use of quantum computers. We address quantum optimal control for single-shot multi-qubit gates by framing as a feasibility problem for the Hamiltonian model and then solving…
In this paper, we study the problem of controllability of Schr\"odinger equation. We prove that the system is exactly controllable in infinite time to any position. The proof is based on an inverse mapping theorem for multivalued functions.…
Path integrals are usually formulated in discrete Euclidean time using the Trotter formula. We propose a new method to study discrete quantum systems, in which we work directly in the Euclidean time continuum. The method is of general…
We consider the problem of finding (in some sense) the best approximation control for an infeasible double integrator. The control function is constrained by upper and lower bounds that are too tight and thus cause infeasibility. The…
We present sufficient conditions for the exact controllability in projection of the linear Schr{\"o}dinger equations in the case where the spectrum of the free Hamiltonian is pure point. We consider the general case in which the Hamiltonian…
Optimal control of bilinear systems has been a well-studied subject in the area of mathematical control. However, techniques for solving emerging optimal control problems involving an ensemble of structurally identical bilinear systems are…
We propose a new analytical method to solve for nonexactly soluble Schrodinger equation via expansions through some existing quantum numbers. Successfully, it is applied to the rational non-polynomial oscillator potential. Moreover, a…
For linear infinite systems the approximate controllability problem by control constraints is considered. Controllability conditions represented via system parameters are obtained. Partial differential control systems and control systems…
The controllability condition for finite dimensional quantum systems, the Lie Algebra Rank Condition, has been stated assuming that the right invariant differential system under consideration is bilinear. We remark that this assumption is…
Quantum confinement is studied by numerically solving time-dependent Schr\"odinger equation. An imaginary-time evolution technique is employed in conjunction with the minimization of an expectation value, to reach the global minimum.…
Existing approaches to analogue quantum simulations of time-dependent quantum systems rely on perturbative corrections to quantum simulations of time-independent quantum systems. We overcome this restriction to perturbative treatments with…
The ability to perform gates in multiqubit systems that are robust to noise is of crucial importance for the advancement of quantum information technologies. However, finding control pulses that cancel noise while performing a gate is made…
We have developed a simple method to solve anharmonic oscillators equations. The idea of our method is mainly based on the partitioning of the potential curve into (n+1) small intervals, solving the Schr\"odinger equation in each…
We consider the optimal control problem of determining electromagnetic pulses for implementing logical gates in a closed quantum system, where the Hamiltonian models the dynamics of coupled superconducting qudits. The quantum state is…
Hybrid quantum-classical algorithms hold great promise for solving quantum control problems on near-term quantum computers. In this work, we employ the hybrid framework that integrates digital quantum simulation with classical optimization…
In modern computers, computation is performed by assembling together sets of logic gates. Popular gates like AND, OR, XOR, processing two logic inputs and yielding one logic output, are often addressed as irreversible logic gates where the…
We consider a quantum system consisting of a one-dimensional chain of M identical harmonic oscillators with natural frequency $\omega$, coupled by means of springs. Such systems have been studied before, and appear in various models. In…
Scalable quantum computation in realistic devices requires that precise control can be implemented efficiently in the presence of decoherence and operational errors. We propose a general constructive procedure for designing robust unitary…
We present a mathematically rigorous quantum-mechanical treatment of a two-dimensional nonrelativistic quantum dual theories (with oscillator and Coulomb like potentials) on a plane and compare their spectra and the sets of eigenfunctions.…
We derive and analyze a hybridizable discontinuous Galerkin (HDG) method for approximating weak solutions to the equations of time-harmonic linear elasticity on a bounded Lipschitz domain in three dimensions. The real symmetry of the stress…