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Magnetic resonance imaging (MRI) has become a crucial tool in the diagnosis and staging of prostate cancer, owing to its superior tissue contrast. However, it also creates large volumes of data that must be assessed by trained experts, a time-consuming and laborious task. This has prompted the development of machine learning tools for the automation of Prostate cancer (PCa) risk classification based on multiple MRI modalities (T2W, ADC, and high-b-value DWI). Understanding and interpreting the predictions made by the models, however, remains a challenge. We analyze Random Forests (RF) and Support Vector Machines (SVM), for two complementary datasets, the public Prostate-X dataset, and an in-house, mostly early-stage PCa dataset to elucidate the contributions made by first-order statistical features, Haralick texture features, and local binary patterns to the classification. Using correlation analysis and Shapley impact scores, we find that many of the features typically used are strongly correlated, and that the majority of features have negligible impact on the classification. We identify a small set of features that determine the classification outcome, which may aid the development of explainable AI approaches.

Dynamic control via optimized, piecewise-constant pulses is a common paradigm for open-loop control to implement quantum gates. While numerous methods exist for the synthesis of such controls, there are many open questions regarding the robustness of the resulting control schemes in the presence of model uncertainty; unlike in classical control, there are generally no analytical guarantees on the control performance with respect to inexact modeling of the system. In this paper a new robustness measure based on the differential sensitivity of the gate fidelity error to parametric (structured) uncertainties is introduced, and bounds on the differential sensitivity to parametric uncertainties are used to establish performance guarantees for optimal controllers for a variety of quantum gate types, system sizes, and control implementations. Specifically, it is shown how a maximum allowable perturbation over a set of Hamiltonian uncertainties that guarantees a given fidelity error, can be reliably computed. This measure of robustness is inversely proportional to the upper bound on the differential sensitivity of the fidelity error evaluated under nominal operating conditions. Finally, the results show that the nominal fidelity error and differential sensitivity upper bound are positively correlated across a wide range of problems and control implementations, suggesting that in the high-fidelity control regime, rather than there being a trade-off between fidelity and robustness, higher nominal gate fidelities are positively correlated with increased robustness of the controls in the presence of parametric uncertainties., Comment: Previous version was missing a paragraph (highlighted in blue)

Robust control of quantum systems is an increasingly relevant field of study amidst the second quantum revolution, but there remains a gap between taming quantum physics and robust control in its modern analytical form that culminated in fundamental performance bounds. With certain exceptions such as quantum optical systems that can be modeled as linear stochastic differential equations, quantum systems are not amenable to linear, time-invariant, measurement-based robust control techniques, and thus novel gap-bridging techniques must be developed. This survey is written for control theorists to provide a review of the current state of quantum control and outline the challenges faced in trying to apply modern robust control to quantum systems. We present issues that arise when applying classical robust control theory to quantum systems, typical methods used by quantum physicists to explore such systems and their robustness, as well as a discussion of open problems to be addressed in the field. We focus on general, practical applications and recent work to enable control researchers to contribute to advancing this burgeoning field., Comment: Minor revisions to earlier version

Recent achievements in quantum control have resulted in advanced techniques for designing controllers for applications in quantum communication, computing, and sensing. However, the susceptibility of such systems to noise and uncertainties necessitates robust controllers that perform effectively under these conditions to realize the full potential of quantum devices. The time-domain log-sensitivity and a recently introduced robustness infidelity measure (RIM) are two means to quantify controller robustness in quantum systems. The former can be found analytically, while the latter requires Monte-Carlo sampling. In this work, the correlation between the log-sensitivity and the RIM for evaluating the robustness of single excitation transfer fidelity in spin chains and rings in the presence of dephasing is investigated. We show that the expected differential sensitivity of the error agrees with the differential sensitivity of the RIM, where the expectation is over the error probability distribution. Statistical analysis also demonstrates that the log-sensitivity and the RIM are linked via the differential sensitivity, and that the differential sensitivity and RIM are highly concordant. This unification of two means (one analytic and one via sampling) to assess controller robustness in a variety of realistic scenarios provides a first step in unifying various tools to model and assess robustness of quantum controllers., Comment: 6 pages, 4 figures, 2 tables, comments welcome

A strictly time-domain formulation of the log-sensitivity of the error signal to structured plant uncertainty is presented and analyzed through simple but representative classical and quantum systems. Results demonstrate that across a wide range of physical systems, maximization of performance (minimization of the error signal) asymptotically or at a specific time comes at the cost of increased log-sensitivity, implying a time-domain constraint analogous to the frequency-domain identity $\mathbf{S(s) + T(s) = I}$. While of limited value in classical problems based on asymptotic stabilization or tracking, such a time-domain formulation is valuable in assessing the reduced robustness cost concomitant with high-fidelity quantum control schemes predicated on time-based performance measures., Comment: 12 pages, 10 figures, 1 table. in IEEE Transactions on Automatic Control. Scheduled for publication Feb 2024

Development of robust quantum control has been challenging and there are numerous obstacles to applying classical robust control to quantum system including bilinearity, marginal stability, state preparation errors, nonlinear figures of merit. The requirement of marginal stability, while not satisfied for closed quantum systems, can be satisfied for open quantum systems where Lindbladian behavior leads to non-unitary evolution, and allows for nonzero classical stability margins, but it remains difficult to extract physical insight when classical robust control tools are applied to these systems. We consider a straightforward example of the entanglement between two qubits dissipatively coupled to a lossy cavity and analyze it using the classical stability margin and structured perturbations. We attempt, where possible, to extract physical insight from these analyses. Our aim is to highlight where classical robust control can assist in the analysis of quantum systems and identify areas where more work needs to be done to develop specific methods for quantum robust control., Comment: Accepted to IEEE CDC 2022

We study the problem of robust performance of quantum systems under structured uncertainties. A specific feature of closed (Hamiltonian) quantum systems is that their poles lie on the imaginary axis and that neither a coherent controller nor physically relevant structured uncertainties can alter this situation. This changes for open systems where decoherence ensures asymptotic stability and creates a unique landscape of pure performance robustness, with the distinctive feature that closed-loop stability is secured by the underlying physics and needs not be enforced. This stability, however, is often detrimental to quantum-enhanced performance, and additive perturbations of the Hamiltonian give rise to dynamic generators that are nonlinear in the perturbed parameters, invalidating classical paradigms to assess robustness to structured perturbations such as singular value analysis. This problem is addressed using a fixed-point iteration approach to determine a maximum perturbation strength $\delta_{\max}$ that ensures that the transfer function remains bounded, $||T_\delta||<\delta^{-1}$ for $\delta<\delta_{\max}$., Comment: Accepted for IEEE CDC 2021

Spin-based metal-oxide-semiconductor field-effect transistors (MOSFET) with a high-mobility III-V channel are studied using self-consistent quantum corrected ensemble Monte Carlo device simulations of charge and spin transport. The simulations including spin-orbit coupling mechanisms (Dresselhaus and Rashba coupling) examine the electron spin transport in the 25 nm gate length In$_{0.7}$Ga$_{0.3}$As MOSFET. The transistor lateral dimensions (the gate length, the source-to-gate, and the gate-to-drain spacers) are increased to investigate the spin-dependent drain current modulation induced by the gate from room temperature of 300 K down to 77 K. This modulation increases with increasing temperature due to increased Rashba coupling. Finally, an increase of up to 20 nm in the gate length, source-to-gate, or the gate-to-drain spacers increases the spin polarization and enhances the spin-dependent drain current modulation at the drain due to polarization-refocusing effects.

We explore the use of policy gradient methods in reinforcement learning for quantum control via energy landscape shaping of XX-Heisenberg spin chains in a model agnostic fashion. Their performance is compared to finding controllers using gradient-based L-BFGS optimisation with restarts, with full access to an analytical model. Hamiltonian noise and coarse-graining of fidelity measurements are considered. Reinforcement learning is able to tackle challenging, noisy quantum control problems where L-BFGS optimization algorithms struggle to perform well. Robustness analysis under different levels of Hamiltonian noise indicates that controllers found by reinforcement learning appear to be less affected by noise than those found with L-BFGS., Comment: 7 pages, 7 figures

Quantum spin networks form a generic system to describe a range of quantum devices for quantum information processing and sensing applications. Understanding how to control them is essential to achieve devices with practical functionalities. Energy landscape shaping is a novel control paradigm to achieve selective transfer of excitations in a spin network with surprisingly strong robustness towards uncertainties in the Hamiltonians. Here we study the effect of decoherence, specifically generic pure dephasing, on the robustness of these controllers. Results indicate that while the effectiveness of the controllers is reduced by decoherence, certain controllers remain sufficiently effective, indicating potential to find highly effective controllers without exact knowledge of the decoherence processes., Comment: 6 pages, 6 figures

Spin-based logic devices could operate at very high speed with very low energy consumption and hold significant promise for quantum information processing and metrology. Here, an in-house developed, experimentally verified, ensemble self-consistent Monte Carlo device simulator with a Bloch equation model using a spin-orbit interaction Hamiltonian accounting for Dresselhaus and Rashba couplings is developed and applied to a spin field effect transistor (spinFET) operating under externally applied voltages on a gate and a drain. In particular, we simulate electron spin transport in a \SI{25}{nm} gate length \chem{In_{0.7}Ga_{0.3}As} metal-oxide-semiconductor field-effect transistor (MOSFET) with a CMOS compatible architecture. We observe non-uniform decay of the net magnetization between the source and gate and a magnetization recovery effect due to spin refocusing induced by a high electric field between the gate and drain. We demonstrate coherent control of the polarization vector of the drain current via the source-drain and gate voltages, and show that the magnetization of the drain current is strain-sensitive and can be increased twofold by strain induced into the channel., Comment: 16 pages, 18 figures

The purpose of this paper is to exhibit a quantum network phenomenon - the anti-core---that goes against the classical network concept of congestion core. Classical networks idealized as infinite, Gromov hyperbolic spaces with least-cost path routing (and subject to a technical condition on the Gromov boundary) have a congestion core, defined as a subnetwork that routing paths have a high probability of visiting. Here, we consider quantum networks, more specifically spin chains, define the so-called maximum excitation transfer probability $p_{\max}(i,j)$ between spin $i$ and spin $j$, and show that the central spin has among all other spins the lowest probability of being excited or transmitting its excitation. The anti-core is singled out by analytical formulas for $p_{\mathrm{max}}(i,j)$, revealing the number theoretic properties of quantum chains. By engineering the chain, we further show that this probability can be made vanishingly small., Comment: to appear in QIP

This paper explores the role of a priori knowledge in the optimization of quantum information processing by investigating optimum unambiguous discrimination problems for both the qubit and qutrit states. In general, a priori knowledge in optimum unambiguous discrimination problems can be classed into two types: a priori knowledge of discriminated states themselves and a priori probabilities of preparing the states. It is clarified that whether a priori probabilities of preparing discriminated states are available or not, what type of discriminators one should design just depends on what kind of the classical knowledge of discriminated states. This is in contrast to the observation that choosing the parameters of discriminators not only relies on the a priori knowledge of discriminated states, but also depends on a priori probabilities of preparing the states. Two types of a priori knowledge can be utilized to improve optimum performance but play the different roles in the optimization from the view point of decision theory.

We report some improvements to the gradient ascent pulse engineering (GRAPE) algorithm for optimal control of quantum systems. These include more accurate gradients, convergence acceleration using the BFGS quasi-Newton algorithm as well as faster control derivative calculation algorithms. In all test systems, the wall clock time and the convergence rates show a considerable improvement over the approximate gradient ascent., Comment: Submitted for publication

A measure for the maximum quantum information transfer capacity (ITC) between nodes of a spin network is defined, and shown to induce a metric on a space of equivalence classes of nodes for homogeneous chains with XX and Heisenberg couplings. The geometry and curvature of spin chains with respect of this metric are studied and compared to the physical network geometry. For general networks hierarchical clustering is used to elucidate the proximity of nodes with regard to the maximum ITC. Finally, it is shown how minimal control can be used to overcome intrinsic limitations and speed up information transfer., Comment: 6 pages, several figures and tables, IEEE tex

The problem of identifiability of model parameters for open quantum systems is considered by investigating two-level dephasing systems. We discuss under which conditions full information about the Hamiltonian and dephasing parameters can be obtained. Using simulated experiments several different strategies for extracting model parameters from limited and noisy data are compared.

For paving the way to novel applications in quantum simulation, computation, and technology, increasingly large quantum systems have to be steered with high precision. It is a typical task amenable to numerical optimal control to turn the time course of pulses, i.e. piecewise constant control amplitudes, iteratively into an optimised shape. Here, we present the first comparative study of optimal control algorithms for a wide range of finite-dimensional applications. We focus on the most commonly used algorithms: GRAPE methods which update all controls concurrently, and KROTOV-type methods which do so sequentially. Guidelines for their use are given and open research questions are pointed out. --- Moreover we introduce a novel unifying algorithmic framework, DYNAMO (dynamic optimisation platform) designed to provide the quantum-technology community with a convenient MATLAB-based toolset for optimal control. In addition, it gives researchers in optimal-control techniques a framework for benchmarking and comparing new proposed algorithms to the state-of-the-art. It allows for a mix-and-match approach with various types of gradients, update and step-size methods as well as subspace choices. Open-source code including examples is made available at http://qlib.info., Comment: update incl. 3 new figures, comments welcome

Based on a parametrization of pure quantum states we explicitly construct a sequence of (at most) $4N-5$ local time-continuous waveform controls to achieve a specified state transition for $N$-level quantum systems when sufficient controls of the Hamiltonian are available. The control magnitudes are further optimized in terms of a time-energy performance, which is a generalization of the time performance index. Trajectory-constrained optimal local time-continuous waveform controls, including both local sine-waveforms and $n^{\rm th}$-order-polynomial waveform controls are obtained in terms of time-energy performance. It is demonstrated that constrained optimal local $n^{\rm th}$-order-polynomial waveform controls approach constrained optimal bang-bang controls when $n\rightarrow\infty$., Comment: 4 pages, 1 figures

For many quantum information protocols such as state transfer, entanglement transfer and entanglement generation, standard notions of controllability for quantum systems are too strong. We introduce the weaker notion of accessible pairs, and prove an upper bound on the achievable fidelity of a transformation between a pair of states based on the symmetries of the system. A large class of spin networks is presented for which this bound can be saturated. In this context, we show how the inaccessible dark states for a given excitation-preserving evolution can be calculated, and illustrate how some of these can be accessed using extra catalytic excitations. This emphasises that it is not sufficient for analyses of state transfer in spin networks to restrict to the single excitation subspace. One class of symmetries in these spin networks is exactly characterised in terms of the underlying graph properties., Comment: 14 pages, 3 figures v3: rewritten for increased clarity

Identifying the Hamiltonian of a quantum system from experimental data is considered. General limits on the identifiability of model parameters with limited experimental resources are investigated, and a specific Bayesian estimation procedure is proposed and evaluated for a model system where a-priori information about the Hamiltonian's structure is available., Comment: 4 pages, submitted to ISCCSP09

We consider how to characterize the dynamics of a quantum system from a restricted set of initial states and measurements using Bayesian analysis. Previous work has shown that Hamiltonian systems can be well estimated from analysis of noisy data. Here we show how to generalize this approach to systems with moderate dephasing in the eigenbasis of the Hamiltonian. We illustrate the process for a range of three-level quantum systems. The results suggest that the Bayesian estimation of the frequencies and dephasing rates is generally highly accurate and the main source of errors are errors in the reconstructed Hamiltonian basis., Comment: 6 pages, 3 figures

We study open quantum systems whose evolution is governed by a master equation of Kossakowski-Gorini-Sudarshan-Lindblad type and give a characterization of the convex set of steady states of such systems based on the generalized Bloch representation. It is shown that an isolated steady state of the Bloch equation cannot be a center, i.e., that the existence of a unique steady state implies attractivity and global asymptotic stability. Necessary and sufficient conditions for the existence of a unique steady state are derived and applied to different physical models including two- and four-level atoms, (truncated) harmonic oscillators, composite and decomposable systems. It is shown how these criteria could be exploited in principle for quantum reservoir engineeing via coherent control and direct feedback to stabilize the system to a desired steady state. We also discuss the question of limit points of the dynamics. Despite the non-existence of isolated centers, open quantum systems can have nontrivial invariant sets. These invariant sets are center manifolds that arise when the Bloch superoperator has purely imaginary eigenvalues and are closely related to decoherence-free subspaces., Comment: 16 pages, 4 figures, marginally revised version, mainly fixed some notational inconsistencies that had crept in when we change the notation in some figures without changing the captions and text

Spin chains have been proposed as quantum wires for information transfer in solid state quantum architectures. We show that huge gains in both transfer speed and fidelity are possible using a minimalist control approach that relies only a single, local, on-off switch actuator. Effective switching time sequences can be determined using optimization techniques for both ideal and disordered chains. Simulations suggest that effective optimization is possible even in the absence of accurate models., Comment: revtex4, 4 pages, 5 figures

The implementation of fault-tolerant quantum gates on encoded logic qubits is considered. It is shown that transversal implementation of logic gates based on simple geometric control ideas is problematic for realistic physical systems suffering from imperfections such as qubit inhomogeneity or uncontrollable interactions between qubits. However, this problem can be overcome by formulating the task as an optimal control problem and designing efficient algorithms to solve it. In particular, we can find solutions that implement all of the elementary logic gates in a fixed amount of time with limited control resources for the five-qubit stabilizer code. Most importantly, logic gates that are extremely difficult to implement using conventional techniques even for ideal systems, such as the T-gate for the five-qubit stabilizer code, do not appear to pose a problem for optimal control., Comment: 18 pages, ioptex, many figures

We show how to apply Lyapunov control design to the problem of entanglement creation between two atoms in distant cavities connected by optical fibers. The Lyapunov control design is optimal in the sense that the distance from the target state decreases monotonically and exponentially, and the concurrence increases accordingly. This method is far more robust than simple geometric schemes., Comment: 6 pages, 5 figures

We present an empirical strategy to determine the Hamiltonian dynamics of a two-qubit system using only initialization and measurement in a single fixed basis. Signal parameters are estimated from measurement data using Bayesian methods from which the underlying Hamiltonian is reconstructed, up to three unobservable phase factors. We extend the method to achieve full control Hamiltonian tomography for controllable systems via a multi-step approach. The technique is demonstrated and evaluated by analyzing data from simulated experiments including projection noise., Comment: 15 pages

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 qubit gates even if the control is severely restricted and the experimentally accessible Hamiltonians are far from orthogonal. It is further shown that using the optimized Euler angles can significantly improve the fidelity of quantum operations even for systems where the experimentally accessible Hamiltonians are nearly orthogonal. Unlike schemes such as composite pulses, the proposed scheme does not significantly increase the number of local operations or gate operation times., Comment: approx. 11 pages, 3 figures, 1 table

We describe a mechanism for realizing a controlled phase gate for solid-state charge qubits. By augmenting the positionally defined qubit with an auxiliary state, and changing the charge distribution in the three-dot system, we are able to effectively switch the Coulombic interaction, effecting an entangling gate. We consider two architectures, and numerically investigate their robustness to gate noise., Comment: 14 pages, 11 figures, 2 tables, RevTeX4

Physical constraints such as positivity endow the set of quantum states with a rich geometry if the system dimension is greater than two. To shed some light on the complicated structure of the set of quantum states, we consider a stratification with strata given by unitary orbit manifolds, which can be identified with flag manifolds. The results are applied to study the geometry of the coherence vector for n-level quantum systems. It is shown that the unitary orbits can be naturally identified with spheres in R^{n^2-1} only for n=2. In higher dimensions the coherence vector only defines a non-surjective embedding into a closed ball. A detailed analysis of the three-level case is presented. Finally, a refined stratification in terms of symplectic orbits is considered., Comment: 15 pages LaTeX, 3 figures, reformatted, slightly modified version, corrected eq.(3), to appear in J. Physics A

We consider a mechanism to generate controllable qudit-qudit interactions in a charge-position paradigm for a quantum computer, through the use of auxiliary states. By controlling the tunneling rates onto these auxiliaries from the qudits proper, we can controllably switch the entangling operations. We consider a practical architecture in which to realize such a computer and examine the associated Hilbert space dimension., Comment: 4 pages, RevTeX4, 4 figures (eps/pdf)

We consider a quantum system with a finite number of distinguishable quantum states, which may be partitioned freely by a number of quantum particles, assumed to be maximally entangled. We show that if we partition the system into a number of qudits, then the Hilbert space dimension is maximized when each quantum particle is allowed to represent a qudit of order $e$. We demonstrate that the dimensionality of an entangled system, constrained by the total number quantum states, partitioned so as to maximize the number of qutrits will always exceed the dimensionality of other qudit partitioning. We then show that if we relax the requirement of partitioning the system into qudits, but instead let the particles exist in any given state, that the Hilbert space dimension is greatly increased., Comment: 4 pages, 3 figures, submitted for publication

An overview and synthesis of results and criteria for open-loop controllability of Hamiltonian quantum systems obtained using Lie group and Lie algebra techniques is presented. Negative results for open-loop controllability of dissipative systems are discussed, and the superiority of closed-loop (feedback) control for quantum systems is established., Comment: 6 pages, to appear in Proceedings of Conference on Lagrangian and Hamiltonian Methods in Non-Linear Control (Seville, Spain, 2003)

We demonstrate how structured decompositions of unitary operators can be employed to derive control schemes for finite-level quantum systems that require only sequences of simple control pulses such as square wave pulses with finite rise and decay times or Gaussian wavepackets. To illustrate the technique it is applied to find control schemes to achieve population transfers for pure-state systems, complete inversions of the ensemble populations for mixed-state systems, create arbitrary superposition states and optimize the ensemble average of dynamic observables., Comment: 28 pages, IoP LaTeX, principal author has moved to Cambridge University (sgs29@cam.ac.uk)

The problem of identifying the dynamical Lie algebras of finite-level quantum systems subject to external control is considered, with special emphasis on systems that are not completely controllable. In particular, it is shown that the dynamical Lie algebra for an N-level system with equally spaced energy levels and uniform transition dipole moments, is a subalgebra for $so(N)$ if $N=2\ell+1$, and a subalgebra of $sp(\ell)$ if $N=2\ell$. General conditions for obtaining either $so(2\ell+1)$ or $sp(\ell)$ are established., Comment: IoP LaTeX, ca. 14 pages

We address the question of which quantum states can be inter-converted under the action of a time-dependent Hamiltonian. In particular, we consider the problem applied to mixed states, and investigate the difference between pure and mixed-state controllability introduced in previous work. We provide a complete characterization of the eigenvalue spectrum for which the state is controllable under the action of the symplectic group. We also address the problem of which states can be prepared if the dynamical Lie group is not sufficiently large to allow the system to be controllable., Comment: 14 pages, IoP LaTeX, first author has moved to Cambridge university (sgs29@cam.ac.uk)

In this note we give an introduction to the topic of quantum control, explaining what its objectives are, and describing some of its limitations., Comment: 6 pages

Precise definitions for different degrees of controllability for quantum systems are given, and necessary and sufficient conditions are discussed. The results are applied to determine the degree of controllability for various atomic systems with degenerate energy levels and transition frequencies., Comment: 20 pages, IoP LaTeX, revised and expanded version

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 finite rise and decay times or Gaussian wavepackets. The technique is applied to find control schemes that achieve population transfers for pure-state systems, complete inversions of the ensemble populations for mixed-state systems, create arbitrary superposition states and optimize the ensemble average of observables., Comment: ca. 16 pages, 7 figures

The detrimental effect of spontaneous emission on the performance of control schemes designed to achieve population inversion between the ground state and a highly excited atomic state are studied using computer simulations., Comment: 2 pages latex, 5 figures

A general scheme for building a quantum memory by transferring quantum information to an essentially decoherence-free memory transition using quantum control is presented and illustrated by computer simulations., Comment: 2 pages latex, 2 figures

Complete controllability is a fundamental issue in the field of control of quantum systems, not least because of its implications for dynamical realizability of the kinematical bounds on the optimization of observables. In this paper we investigate the question of complete controllability for finite-level quantum systems subject to a single control field, for which the interaction is of dipole form. Sufficient criteria for complete controllability of a wide range of finite-level quantum systems are established and the question of limits of complete controllability is addressed. Finally, the results are applied to give a classification of complete controllability for four-level systems., Comment: 14 pages, IoP-LaTeX

In this paper we investigate the limits of control for mixed-state quantum systems. The constraint of unitary evolution for non-dissipative quantum systems imposes kinematical bounds on the optimization of arbitrary observables. We summarize our previous results on kinematical bounds and show that these bounds are dynamically realizable for completely controllable systems. Moreover, we establish improved bounds for certain partially controllable systems. Finally, the question of dynamical realizability of the bounds for arbitary partially controllable systems is shown to depend on the accessible sets of the associated control system on the unitary group U(N) and the results of a few control computations are discussed briefly., Comment: 5 pages, orginal June 30, 2000, revised September 28, 2000

Sufficient conditions for complete controllability of $N$-level quantum systems subject to a single control pulse that addresses multiple allowed transitions concurrently are established. The results are applied in particular to Morse and harmonic-oscillator systems, as well as some systems with degenerate energy levels. Morse and harmonic oscillators serve as models for molecular bonds, and the standard control approach of using a sequence of frequency-selective pulses to address a single transition at a time is either not applicable or only of limited utility for such systems., Comment: 8 pages, expanded and revised version

In [1] Zhu and Rabitz presented a rapidly convergent iterative algorithm for optimal control of the expectation value of a positive definite observable in a pure-state quantum system. In this paper we generalize this algorithm to a quantum statistical mechanics setting and show that it is both efficient in the mixed-state case and effective in achieving the control objective of maximizing the ensemble average of arbitrary observables in the cases studied., Comment: 8 pages, revised edition, improved content and figures