Related papers: Quantum control without access to the controlling …
Using the fact that any linear representation of a group can be embedded into permutations, we propose a constructive description of quantum behavior that provides, in particular, a natural explanation of the appearance of complex numbers…
Descriptions of classical mechanics in Hilbert space go back to the work of Koopman and von Neumann in the 1930s. Decades later, van Hove derived a unitary representation of the group of contact transformations which recently has been used…
We study the extent to which the outcomes of a quantum measurement can be manipulated by changing the state of the measurement apparatus. The measurement process is modeled as decoherence induced by the experimenter, to gain knowledge about…
The present analysis deals with the regularity of solutions of bilinear control systems of the type $x'=(A+u(t)B)x$where the state $x$ belongs to some complex infinite dimensional Hilbert space, the (possibly unbounded) linear operators $A$…
We study controllable exchange coupling between two singlet-triplet qubits. We start from the original second quantized Hamiltonian of a quadruple quantum dot system and obtain the effective spin-spin interaction between the two qubits…
The basic notions of quantum mechanics are formulated in terms of separable infinite dimensional Hilbert space $\mathcal{H}$. In terms of the Hilbert lattice $\mathcal{L}$ of closed linear subspaces of $\mathcal{H}$ the notions of state and…
Simple, precise, and robust control is demanded for operating a large quantum information processor. However, existing routes to high-fidelity quantum control rely heavily on arbitrary waveform generators that are difficult to scale up.…
A unifying framework for the control of quantum systems with non-Abelian holonomy is presented. It is shown that, from a control theoretic point of view, holonomic quantum computation can be treated as a control system evolving on a…
We demonstrate that nonlinear magnetic solitary excitations (solitons) traveling through a Heisenberg spin chain may be used as a robust tool capable of coherent control of the qubit's state. The physical problem is described by a…
We investigate the evolution of a single qubit subject to a continuous unitary dynamics and an additional interrupting influence which occurs periodically. One may imagine a dynamically evolving closed quantum system which becomes open at…
We present a set of concrete and realistic ideas for the implementation of a small-scale quantum computer using electron spins in lateral GaAs/AlGaAs quantum dots. Initialization is based on leads in the quantum Hall regime with tunable…
The reachable set for a finite dimensional quantum system is shown to be the orbit of the group corresponding to the internal and control Hamiltonians, even if this group is not compact.
We demonstrate the possibility of controlling the border between the quantum and the classical world by performing nonselective measurements on quantum systems. We consider a quantum harmonic oscillator initially prepared in a Schroedinger…
Adaptive quantum circuits-where a quantum many-body state is controlled using measurements and conditional unitary operations-are a powerful paradigm for state preparation and quantum error correction tasks. They can support two types of…
Various notions from geometric control theory are used to characterize the behavior of the Markovian master equation for N-level quantum mechanical systems driven by unitary control and to describe the structure of the sets of reachable…
We provide a sufficient condition for the controllability of a bilinear closed quantum system steered by a static field and a time-varying field, based on the notion of weakly conically connected spectrum. More precisely, we show that if a…
Recent development in quantum information sciences and technologies, especially building programmable quantum computers, provide us new opportunities to study fundamental aspects of quantum mechanics. We propose qubit models to emulate the…
Structured decompositions of a desired unitary operator are employed to derive control schemes that achieve certain control objectives for finite-level quantum systems using only sequences of simple control pulses such as square waves with…
We propose the assumption of quantum mechanics on a discrete space and time, which implies the modification of mathematical expressions for some postulates of quantum mechanics. In particular we have a Hilbert space where the vectors are…
A pivotal task in quantum metrology, and quantum parameter estimation in general, is to de- sign schemes that achieve the highest precision with given resources. Standard models of quantum metrology usually assume the dynamics is fixed, the…