A quantum network is an open system consisting of several component Markovian input-output subsystems interconnected by boson field channels carrying quantum stochastic signals. Generalizing the work of Chebotarev and Gregoratti, we formulate the model description by prescribing a candidate Hamiltonian for the network including details the component systems, the field channels, their interconnections, interactions and any time delays arising from the geometry of the network. (We show that the candidate is a symmetric operator and proceed modulo the proof of self-adjointness.) The model is non-Markovian for finite time delays, but in the limit where these delays vanish we recover a Markov model and thereby deduce the rules for introducing feedback into arbitrary quantum networks. The type of feedback considered includes that mediated by the use of beam splitters. We are therefore able to give a system-theoretic approach to introducing connections between quantum mechanical state-based input-output systems, and give a unifying treatment using non-commutative fractional linear, or Mobius, transformations.
We consider separating the problem of designing Hamiltonian quantum feedback control algorithms into a measurement (estimation) strategy and a feedback (control) strategy, and consider optimizing desirable properties of each under the minimal constraint that the available strength of both is limited. This motivates concepts of information extraction and disturbance which are distinct from those usually considered in quantum information theory. Using these concepts we identify an information trade-off in quantum feedback control.
Enviroment - caused dissipation disrupts the hamiltonian evolution of all quantum systems not fully isolated from any bath. We propose and examine a feedback-control scheme to eliminate such dissipation, by tracking the free hamiltonian evolution. We determine a driving-field that maximizes the projection of the actual molecular system onto the freely propagated one. The evolution of a model two level system in a dephasing bath is followed, and the driving field that overcomes the decoherence is calculated. An implementation of the scheme in the laboratory using feedback control is suggested.
Feedback control is expected to considerably protect quantum states against decoherence caused by interaction between the system and environment. Especially, Markovian feedback scheme developed by Wiseman can modify the properties of decoherence and eventually recover the purity of the steadystate of the corresponding master equation. This paper provides a condition for which the modified master equation has a pure steady state. By applying this condition to a two-qubit system, we obtain a complete parametrization of the feedback Hamiltonian such that the steady state becomes a maximally entan…
We show that it is possible to construct closed quantum systems governed by a bilinear Hamiltonian depending on an arbitrary input signal. This is achieved by coupling the system to a quantum input field and performing a feedback of the output field back into the system to cancel out the stochastic effects, with the signal being added to the field between these events and later subtracted. Here we assume the zero time delay limit between the various connections and operations.
For the symmetric harmonic oscillator and the symmetric bouncer defined in 2-D, two different Hamiltonian are given describing the same classical dynamics; however, their quantum dynamics behavior are different.
Time is a valuable resource and it seems intuitive that longer time should lead to better precision in Hamiltonian parameter estimation. However recent studies have put this intuition into question, showing longer time may even lead to worse estimation in certain cases. Here we show that the intuition can be restored if coherent feedback controls are included. By deriving asymptotically optimal feedback controls we present a quantification of the maximal improvement feedback controls can provide in Hamiltonian parameter estimation and show a universal time scaling for the precision limit of Ha…
Measurement and estimation of parameters are essential for science and engineering, where the main quest is to find out the highest achievable precision with given resources and design schemes to attain it. Two schemes, the sequential feedback scheme and the parallel scheme, are usually studied in quantum parameter estimation. While the sequential feedback scheme represents the most general scheme, it remains unknown whether it can outperform the parallel scheme for any quantum estimation tasks. In this Letter we show that the sequential feedback scheme has a 3-fold improvement over the parall…
Since quantum feedback is based on classically accessible measurement results, it can provide fundamental insights into the dynamics of quantum systems by making available classical information on the evolution of system properties and on the conditional forces acting on the system. In this paper, the feedback-induced interaction dynamics between a pair of quantum systems is analyzed. It is pointed out that any interaction Hamiltonian can be simulated by local feedback if the levels of decoherence are sufficiently high. The boundary between genuine entanglement generating quantum interactions …
Recently, the coherent Ising machine (CIM) as a degenerate optical parametric oscillator (DOPO) network has been researched to solve Ising combinatorial optimization problems. We formulate a theoretical model for the CIM with discrete-time measurement feedback processes, and perform numerical simulations for the simplest network, composed of two degenerate optical parametric oscillator pulses with the anti-ferromagnetic mutual coupling. We evaluate the extent to which quantum coherence exists during the optimization process.
We present a quantum description of photon creation via dynamical Casimir effect based on the standard Hamiltonian formulation. The particle representation is constructed in the expansion of field operators fixed with the initial modes. The Hamiltonian is presented in terms of the creation and annihilation operators with the time-varying couplings which originate from the external properties such as an oscillating boundary or a plasma mirror of a semiconductor slab. Some consideration is also made for the experimental realization with a semiconductor plasma mirror.
We characterize the set of generalized quantum measurements that can be decomposed into a continuous measurement process using a stream of probe qubits and a tunable interaction Hamilto- nian. Each probe in the stream interacts weakly with the target quantum system, then is measured projectively in a standard basis. This measurement result is used in a closed feedback loop to tune the interaction Hamiltonian for the next probe. The resulting evolution is a stochastic process with the structure of a one-dimensional random walk. To maintain this structure, and require that at long times the meas…
We utilize quantum Fisher information to investigate the damping parameter precision of a dissipative qubit. PT symmetric non-Hermitian Hamiltonian is used to enhance the parameter precision in two models: one is direct PT symmetric quantum feedback; the other is that the damping rate is encoded into a effective PT symmetric non-Hermitian Hamiltonian conditioned on the absence of decay events. We find that compared with the case without feedback and with Hermitian quantum feedback, direct PT symmetric non-Hermitan quantum feedback can obtain better precision of damping rate. And in the second …
In the pilot-wave theory of quantum mechanics particles have definite positions and velocities and the system evolves deterministically. The velocity of a particle is determined by the wave function of the system (the guidance equation) and the wave function evolves according to Schrodinger's equation. In this paper I first construct a Hamiltonian that gives Schrodinger's equation and the guidance equation for the particle. I then find the Hamiltonian for a relativistic particle in Dirac's theory and for a quantum scalar field.
The traditional approach to feedback control is to apply forces to a system by modifying the Hamiltonian. Here we show that quantum systems can be controlled without any Hamiltonian feedback, purely by exploiting the random quantum back-action of a continuous weak measurement. We demonstrate that, quite remarkably, the quantum back-action of such an adaptive measurement is just as effective at controlling quantum systems as traditional feedback.
A number of recent works employ bilinear Hamiltonian interactions between Linear Quantum Stochastic Systems (LQSSs). Contrary to naturally occurring Hamiltonian interactions between physical systems, such interactions must be engineered. In this work, we propose a simple model for the implementation of an arbitrary bilinear interaction between two given LQSSs via a feedback interconnection.
For a free falling particle moving in a media which has quadratic velocity force effect on the particle, two equivalent constants of motion, with units of energy, two Lagrangians, and two Hamiltonians are deduced. These quantities describe the dynamics of the same classical system. However, their quantization and the associated statistical mechanics (for an ensemble of particles) describe two completely different quantum and statistical systems. This is shown at first order in the dissipative parameter.
We study feedback control of classical Hamiltonian systems with the controlling parameter varying slowly in time. The control aims to change system's energy. We show that the control problems can be solved with help of an adiabatic invariant that generalizes the conservation of the phase-space volume to control situations. New mechanisms of control for achieving heating, cooling, entropy reduction and particle trapping are found. The feedback control of a many-body system via one of its coordinates is discussed. The results are illustrated by two basic models of non-linear physics.
We express the rules for forming quantum feedback networks using the Stratonovich form of quantum stochastic calculus rather than the Ito, or SLH form. Remarkably the feedback reduction rule implies that we obtain the Schur complement of the matrix of Stratonovich coupling operators where we short out the internal input/output coefficients.
These short notes present to the reader (students, in particular) a concise approach to the derivation of the propagator of Hamiltonians with position-dependent kinetic energy. The formalism is applied to the von Roos Hamiltonian with arbitrary ordering ambiguity parameters, and a simple scheme to convert the problem to a constant-mass motion is presented. The motion in curved spaces is treated along the same lines, where a phase space formulation is used to derive the propagator for arbitrary discretization choices.
We demonstrate that the effective Hamiltonians obtained with the downfolding procedure based on double unitary coupled cluster (DUCC) ansatz can be used in the context of Greens function coupled cluster (GFCC) formalism to calculate spectral functions of molecular systems. This combined approach (DUCC-GFCC) provides a significant reduction of numerical effort and good agreement with the corresponding all-orbital GFCC methods in energy windows that are consistent with the choice of active space. These features are demonstrated on the example of two benchmark systems: H2O and N2, where DUCC-GFCC…
A scheme making use of an isolated feedback loop was recently proposed in \cite{GP_} for creating an arbitrary bilinear Hamiltonian interaction between two multi-mode Linear Quantum Stochastic Systems (LQSSs). In this work we examine the presence of an isolated feedback loop in a general SLH network, and derive the modified Hamiltonian of the network due to the presence of the loop. In the case of a bipartite network with an isolated loop running through both parts, this results in modified Hamiltonians for each subnetwork, as well as a Hamiltonian interaction between them. As in the LQSS case…
We review and compare different variational formulations for the Schrödinger field. Some of them rely on the addition of a conveniently chosen total time derivative to the hermitic Lagrangian. Alternatively, the Dirac-Bergmann algorithm yields the Schrödinger equation first as a consistency condition in the full phase space, second as canonical equation in the reduced phase space. The two methods lead to the same (reduced) Hamiltonian. As a third possibility, the Faddeev-Jackiw method is shown to be a shortcut of the Dirac method. By implementing the quantization scheme for systems with second…
We offer a new Hamiltonian formulation of the classical Pais-Uhlenbeck Oscillator and consider its canonical quantization. We show that for the non-degenerate case where the frequencies differ, the quantum Hamiltonian operator is a Hermitian operator with a positive spectrum, i.e., the quantum system is both stable and unitary. A consistent description of the degenerate case based on a Hamiltonian that is quadratic in momenta requires its analytic continuation into a complex Hamiltonian system possessing a generalized PT-symmetry (an involutive antilinear symmetry). We devise a real descriptio…
Hamiltonian Lattice Formulation of Compact Maxwell-Chern-Simons Theory
Massachusetts Institute of Technology（麻省理工学院）；University of Perugia（佩鲁贾大学）；University of Bonn（波恩大学）；The Cyprus Institute（塞浦路斯研究所）；Deutsches Elektronen-Synchrotron DESY（德国电子同步辐射中心）；Harvard University（哈佛大学）
The De Donder-Weyl (DW) covariant Hamiltonian formulation of Palatini first-order Lagrangian of vielbein (tetrad) gravity and its precanonical quantization are presented. No splitting into the space and time is required in this formulation. Our recent generalization of Dirac brackets is used to treat the second class primary constraints appearing in the DW Hamiltonian formulation and to find the fundamental brackets. Quantization of the latter yields the representation of vielbeins as differential operators with respect to the spin connection coefficients, and the Dirac-like precanonical Schrö…
