Related papers: Algebraic structure of path-independent quantum co…
Ancilla systems are often indispensable to universal control of a nearly isolated quantum system. However, ancilla systems are typically more vulnerable to environmental noise, which limits the performance of such ancilla-assisted quantum…
A quantum theory in a finite-dimensional Hilbert space can be geometrically formulated as a proper Hamiltonian theory as explained in [2, 3, 7, 8]. From this point of view a quantum system can be described in a classical-like framework…
Quantum information is very fragile to environmentally and operationally induced imperfections. Therefore, the construction of practical quantum computers requires quantum error-correction techniques to protect quantum information. In…
We propose a molecular setup for the physical implementation of a barrier global quantum computation scheme based on the electron-doped pi-conjugated copolymer architecture of nine blocks PPP-PDA-PPP-PA-(CCH-acene)-PA-PPP-PDA-PPP (where…
The Path integral Quantum Control (PiQC) algorithm was recently introduced by Villanueva et al. (2025) as a new approach for computing optimal controls in open and closed quantum systems. Originally proposed for pulse-based quantum control,…
The quantum geometric tensor (QGT) characterizes the Hilbert space geometry of the eigenstates of a parameter-dependent Hamiltonian. In recent years, the QGT and related quantities have found extensive theoretical and experimental utility,…
We study a family of integrable systems of nonlinearly coupled harmonic oscillators on the classical and quantum levels. We show that the integrability of these systems follows from their symmetry characterized by algebras called here…
Executing a control sequence requires computation. While this is a simple observation, developing a framework that relates a controller's required computation to its ability to successfully control a system (e.g. lower control cost) is…
Quantum control is an important logical primitive of quantum computing programs, and an important concept for equational reasoning in quantum graphical calculi. We show that controlled diagrams in the ZXW-calculus admit rich algebraic…
Non commutative quantum mechanics can be viewed as a quantum system represented in the space of Hilbert-Schmidt operators acting on non commutative configuration space. Taking this as departure point, we formulate a coherent state approach…
In our model a fixed Hamiltonian acts on the joint Hilbert space of a quantum system and its controller. We show under which conditions measurements, state preparations, and unitary implementations on the system can be performed by quantum…
In this article, the two-parameter quantum Heisenberg enveloping algebra, which serves as a model for certain quantum generalized Heisenberg algebras, have been studied at roots of unity. In this context, the quantum Heisenberg enveloping…
In the general setting of quantum controls, it is unrealistic to control all of the degrees of freedom of a quantum system. We consider a scenario where our direct access is restricted to a small subsystem $S$ that is constantly interacting…
This article investigates the two-parameter quantum matrix algebra at roots of unity. In the roots of unity setting, this algebra becomes a Polynomial Identity (PI) algebra and it is known that simple modules over such algebra are…
This paper deals with the problem of control of partially known nonlinear systems, which have an open-loop stable equilibrium, but we would like to add a PI controller to regulate its behavior around another operating point. Our main…
Quantum computing offers advantages over classical computation, yet the precise features that set the two apart remain unclear. In the standard quantum circuit model, adding a 1-qubit basis-changing gate -- commonly chosen to be the…
The possibility of extending the canonical formulation of quantum mechanics (QM) to a space-time symmetric form has recently attracted wide interest. In this context, a recent proposal has shown that a spacetime symmetric many-body…
Quantum control in large dimensional Hilbert spaces is essential for realizing the power of quantum information processing. For closed quantum systems the relevant input/output maps are unitary transformations, and the fundamental challenge…
We study Heisenberg's matrix mechanics within an algebraic pre-Hilbert framework of arbitrary finite dimension. The commutator of the position and momentum matrices naturally generates a third Hermitian operator whose unbounded character…
A major challenge to the control of infinite dimensional quantum systems is the irreversibility which is often present in the system dynamics. Here we consider systems with discrete-spectrum Hamiltonians operating over a Schwartz space…