相关论文: Small Denominators, Frequency Operators, and Lie T…
Classical mechanics is formulated in complex Hilbert space with the introduction of a commutative product of operators, an antisymmetric bracket, and a quasidensity operator. These are analogues of the star product, the Moyal bracket, and…
We suggest a numerical integration procedure for solving the equations of motion of certain classical spin systems which preserves the underlying symplectic structure of the phase space. Such symplectic integrators have been successfully…
Local operators are the basic observables in quantum field theory which encode the physics observed by a local experimentalist. However, when gravity is dynamical, diffeomorphism symmetries are gauged which apparently obstructs a sensible…
Frequency entrainment of continuous-variable oscillators has to date been restrained to the weakly nonlinear regime. Here we overcome this bottleneck and extend frequency entrainment of quantum continuous-variable oscillators to arbitrary…
We discuss how to simulate simple quantum logic operations with a large number of qubits. These simulations are needed for experimental testing of scalable solid-state quantum computers. Quantum logic for remote qubits is simulated in a…
We extend the method for constructing symmetry operators of higher order for two-dimensional quantum Hamiltonians by Kalnins, Kress and Miller (2010). This expansion method expresses the integral in a finite power series in terms of lower…
Although spin is a core property in fermionic systems, its symmetry can be easily violated in a variational simulation, especially when strong correlation plays a vital role therein. In this study, we will demonstrate that the broken…
Synchronization in quantum systems has been recently studied through persistent oscillations of local observables, which stem from undamped modes of the dissipative dynamics. However, the existence of such modes requires fine-tuning the…
The behavior of coupled harmonic oscillators in systems with specified boundary conditions is typically characterized by resonances whose frequency spectra represent harmonics according to properties of the individual oscillators, the…
Control over electron-spin states, such as coherent manipulation, filtering and measurement promises access to new technologies in conventional as well as in quantum computation and quantum communication. We review our proposal of using…
We present a method of a quantum simulation of a quantum harmonic oscillator in a special case of the deformed commutation relation, which corresponds to the so-called q-deformed oscillator on an IBM quantum computer. Using the method of…
A formalism for quantum error correction based on operator algebras was introduced in [1] via consideration of the Heisenberg picture for quantum dynamics. The resulting theory allows for the correction of hybrid quantum-classical…
One of the open challenges in quantum computing simulations of problems of chemical interest is the proper enforcement of spin symmetry. Efficient quantum circuits implementing unitaries generated by spin-adapted operators remain elusive,…
Electron spins in semiconductor quantum dots are good candidates of quantum bits for quantum information processing. Basic operations of the qubit have been realized in recent years: initialization, manipulation of single spins, two qubit…
Unitary operators are essential to quantum mechanics, however for discrete systems larger than a qubit, it is difficult to express them in a self-contained way. This report presents just such a description, providing a compact, useful…
We present a systematic treatment of scattering processes for quantum systems whose time evolution is discrete. We define and show some general properties of the scattering operator, in particular the conservation of quasi-energy which is…
Coupled micro- and nanomechanical oscillators are of fundamental and technical interest for emerging quantum technologies. Upon interfacing with long-lived solid-state spins, the coherent manipulation of the quantum hybrid system becomes…
Quantum metrology promises high-precision measurements of classical parameters with far reaching implications for science and technology. So far, research has concentrated almost exclusively on quantum-enhancements in integrable systems,…
We discuss the role of commuting operators for quantum superintegrable systems, showing how they are used to build eigenfunctions. These ideas are illustrated in the context of resonant harmonic oscillators, the Krall-Sheffer operators,…
We show that quantum computation can be performed in a system at thermal equilibrium if a spontaneous symmetry breaking occurs. The computing process is associated to the time evolution of the statistical average of the qubit coherence…