Related papers: Exact solutions of the isoholonomic problem and th…
A universal set of quantum gates is constructed for the recently developed jump-error correcting quantum codes. These quantum codes are capable of correcting errors arising from the spontaneous decay of distinguishable qubits into…
We consider the problem of selectively controlling couplings in a practical quantum processor with always-on interactions that are diagonal in the computational basis, using sequences of local NOT gates. This methodology is well-known in…
The CNOT gate is a two-qubit gate which is essential for universal quantum computation. A well-established approach to implement it within Majorana-based qubits relies on subsequent measurement of (joint) Majorana parities. We propose an…
We study the Hamiltonian-independent contribution to the complexity of quantum optimal control problems. The optimization of controls that steer quantum systems to desired objectives can itself be considered a classical dynamical system…
Optimal control theory is a powerful tool for solving control problems in quantum mechanics, ranging from the control of chemical reactions to the implementation of gates in a quantum computer. Gradient-based optimization methods are able…
We propose a method for exact circuit synthesis using a discrete gate set, as required for fault-tolerant quantum computing. Our approach translates the problem of synthesizing a gate specified by its unitary matrix into a boolean…
This paper is concerned with constructing an optimal controller in the coherent quantum Linear Quadratic Gaussian problem. A coherent quantum controller is itself a quantum system and is required to be physically realizable. The use of…
In this paper, we demonstrate that optimal control algorithms can be used to speed up the implementation of modules of quantum algorithms or quantum simulations in networks of coupled qubits. The gain is most prominent in realistic cases,…
We explore the implementation of hybridly protected quantum operations combining the merits of holonomy, dynamical decoupling approach and dephasing-free feature based on a simple and experimentally achievable spin model. The implementation…
We present a nonlocal construction of universal gates by means of holonomic (geometric) quantum teleportation. The effect of the errors from imperfect control of the classical parameters, the looping variation of which builds up holonomic…
An explicit algorithm for calculating the optimized Euler angles for both qubit state transfer and gate engineering given two arbitary fixed Hamiltonians is presented. It is shown how the algorithm enables us to efficiently implement single…
Among existing approaches to holonomic quantum computing, the adiabatic holonomic quantum gates (HQGs) suffer errors due to decoherence, while the non-adiabatic HQGs either require additional Hilbert spaces or are difficult to scale. Here,…
This thesis explores the concept of realizing quantum gates using physical systems like atoms and oscillators perturbed by electric and magnetic fields. The basic idea is that if a time-independent Hamiltonian $H_0$ is perturbed by a…
In this article we study a finite horizon optimal control problem with monotone controls. We consider the associated Hamilton-Jacobi-Bellman (HJB) equation which characterizes the value function. We consider the totally discretized problem…
We study a model of quantum computation based on the continuously-parameterized yet finite-dimensional Hilbert space of a spin system. We explore the computational powers of this model by analyzing a pilot problem we refer to as the close…
This paper is concerned with a boundary control problem for the Cahn--Hilliard equation coupled with dynamic boundary conditions. In order to handle the control problem, we restrict our analysis to the case of regular potentials defined on…
The purpose of this paper is to describe the numerical solution of the Hamilton-Jacobi-Bellman (HJB) for an optimal control problem for quantum spin systems. This HJB equation is a first order nonlinear partial differential equation defined…
This article considers some control problems for closed and open two-level quantum systems. The closed system's dynamics is governed by the Schr\"odinger equation with coherent control. The open system's dynamics is governed by the…
The performance of the Variational Quantum Eigensolver (VQE) is promising compared to other quantum algorithms, but also depends significantly on the appropriate design of the underlying quantum circuit. Recent research by Bowles, Ahmend \&…
In this paper, we consider the infinite horizon optimal control problem for nonlinear systems. Under the conditions of controllability of the linearized system around the origin, and nonlinear controllability of the system to a terminal set…