Publications

Hamiltonian encoding is a methodology for revealing the mechanism behind the dynamics governing controlled quantum systems. In this paper, following Mitra and Rabitz [Phys. Rev. A 67, 033407 (2003)], we define mechanism via pathways of eigenstates that describe the evolution of the system, where each pathway is associated with a complex-valued amplitude corresponding to a term in the Dyson series. The evolution of the system is determined by the constructive and destructive interference of these pathway amplitudes. Pathways with similar attributes can be grouped together into pathway classes. The amplitudes of pathway classes are computed by modulating the Hamiltonian matrix elements and decoding the subsequent evolution of the system rather than by direct computation of the individual terms in the Dyson series. The original implementation of Hamiltonian encoding was computationally intensive and became prohibitively expensive in large quantum systems. This paper presents two new encoding algorithms that calculate the amplitudes of pathway classes by using techniques from graph theory and algebraic topology to exploit patterns in the set of allowed transitions, greatly reducing the number of matrix elements that need to be modulated. These new algorithms provide an exponential decrease in both computation time and memory utilization with respect to the Hilbert space dimension of the system. To demonstrate the use of these techniques, they are applied to two illustrative state-to-state transition problems.

The photo-induced dissociative ionization of lanthanide complexes Ln(hfac)3 (Ln = Pr, Er, Yb) is studied using ultrafast shaped laser pulses in a time-of-flight (TOF) mass spectrometry setup. Various fluorine and Ln-containing mass fragments were observed, which can be interpreted by the photo-fragmentation mechanistic pathway involving C–C bond rotation processes proposed previously. A set of experiments used pulse shaping guided by closed-loop feedback control to identify pulses that optimize the ratio of LnF+/LnO+. In agreement with previous studies in which very little LnO+ was observed, broad pulses were found to maximize the LnF+/LnO+ ratio, which involves metal–ligand bond-breaking followed by bond rotation and bond rearrangement. In contrast, a transform limited (TL) pulse favored the formation of LnO+. Finally, the recently developed experimental control pulse slicing (CPS) technique was applied to elucidate the dynamics induced by fields that either maximize or minimize the LnF+/LnO+ ratio, which also indicates that longer laser pulses facilitate LnF+ formation during the C–C bond rotation dissociative-ionization process.

There is a great promise in utilizing shallow paramagnetic luminescent defects such as NVcenters in conjunction with spin-labeled receptor proteins in biological and chemical sensing. One of the major challenges is the accurate and efficient placement of the receptor protein in the close vicinity of the luminescent center deposited within the host material. We analyze the FRET-driven functionalization of the surface, where the emission of the luminescent center serves as a donor of the excitation, and the photolabile group on the surface as the acceptor. The efficiency of biological detection with a combination of spin-labeled protein receptor and a shallow NV- center is considered.

The effort required for quantum system control, particularly in terms of measurements during calibration, needs to be low enough to compensate for system parameter changes or fast enough to allow for periodic re-calibration. Complete system characterization can provide accurate numerical models for gate calibration. On the other hand, model-free learning control, although costly and laborious, represents a data-driven calibration technique. As quantum systems increase in size, these methods become more measurement-intensive. Here, we use a technique to extract the quantum processor dynamics and map them to a known Hamiltonian and a neural network capturing the unknown dynamics. This combined approach, known as residual modeling, allows for a comprehensive representation of the experimentally observed dynamics with minimal effort. This characterization technique enables low-effort calibration of the closed-system model. Subsequently, a reinforcement-learning gate-calibration agent is equipped with the acquired model and initiated using a numerically derived guess. Such a low-resource approach could enable scaling up quantum processors calibrated by reinforcement learning agents and sidestep the looming bottleneck of quantum control.

Practical quantum information processing depends on long coherence times and fast and accurate quantum control. Understanding the boundaries of quantum system control is crucial to improving quantum processor design. One common challenge of quantum system control is the undetected spontaneous decay of excited states through spontaneous emission. The framework of continuous spontaneous localization can model spontaneous emission. Continuous spontaneous localization is a modification of quantum mechanics that addresses the measurement problem. It suggests that all particles have a constant and random localization process, which leads to an exponential suppression of superposition states with an increasing number of particles. This theory proposes that localization occurs continuously rather than due to a measurement or environmental interaction. In this study, we investigate the compatibility and realizability of decoherence-free subspaces to protect against spontaneous emission modeled by continuous spontaneous localization. Decoherence-free subspaces are quantum subspaces resistant to certain types of noise and decoherence, resulting in non-unitary dynamics due to system-bath couplings. By encoding quantum information in a decoherence-free subspace, the information can be protected from environmental disturbances and remain coherent for extended periods of time.

Efficacious quantum information processing relies on extended coherence and precise control. Investigating the limitations surrounding quantum processors is vital for their advancement. In their operation, one challenge is inadvertent wave function collapse. Decoherence-free subspaces, theoretically capable of mitigating specific non unitary dynamics, present a promising avenue. However, our study unveils their inability to safeguard against spontaneous wave function collapse. Thus, the spontaneous-collapse rate becomes a critical limiting factor for quantum systems’ physical coherence, restricting the options for maintaining coherence to active error correction.

This short paper introduces a novel approach to global sensitivity analysis, grounded in the variance-covariance structure of random variables derived from random measures. The proposed methodology facilitates the application of information-theoretic rules for uncertainty quantification, offering several advantages. Specifically, the approach provides valuable insights into the decomposition of variance within discrete subspaces, similar to the standard ANOVA analysis. To illustrate this point, the method is applied to datasets obtained from the analysis of randomized controlled trials on evaluating the efficacy of the COVID-19 vaccine and assessing clinical endpoints in a lung cancer study.

Simple, precise, and robust control is demanded for qubit operations on large quantum information processors. However, existing routes to high-fidelity quantum control heavily rely on arbitrary waveform generators that are difficult to scale up. Here, we show that the arbitrary control of a quantum system can be achieved by simply turning the control fields on and off in a proper sequence. The switching instances can be designed using conventional quantum optimal control algorithms, while the required computational resources for matrix exponentials can be substantially reduced. We demonstrate the flexibility and robustness of the resulting control protocol, and illustrate it in the context of superconducting quantum circuits. We expect this proposal to be achievable with current semiconductor and superconductor technologies, which offers a significant step towards scalable quantum computing.

The exact single-magnon entanglement evolution in Heisenberg chains is obtained using the Quantum Correlation Transfer Function (QCTF) formulation. The individual spins’ entanglement is given by a hypergeometric function, and its transient behavior is described via a Bessel function of the first kind. The presented characterization through the lens of QCTF allowed for calculating the ballistic single-magnon entanglement edge velocity in Heisenberg chains, which has not been achieved before. Our results can be extended to the multi-magnon regime, therefore opening up the means to explain equilibration dynamics and thermodynamics in Heisenberg chains.

The goal of quantum tracking control is to identify shaped fields to steer observable expectation values along designated time-dependent tracks. The fields are determined via an iteration-free procedure, which is based on inverting the underlying dynamical equations governing the controlled observables. In this paper, we generalize the ideas in [Phys. Rev. A 98, 043429 (2018)] to the task of orienting symmetric top molecules in three dimensions. To this end, we derive equations for the control fields capable of directly tracking the expected value of the three-dimensional dipole orientation vector along a desired path in time. We show this framework can be utilized for tracking the orientation of linear molecules as well, and present numerical illustrations of these principles for symmetric-top tracking control problems.

We provide a brief review of a recently proposed approach to robust quantum control which rests on three theoretical foundations: the classic method of averaging, set-membership uncertainty modeling, and the known topological properties of the quantum control landscape. Application of the method of averaging directly results in a multi-criterion optimization problem consisting of the uncertainty-free fidelity competing with a generic robustness measure, the latter being a norm of a time-domain product of a function of the uncertainty-free system and the character of the uncertainty set. If this term is sufficiently small, then at most, only fourth order error effects can accrue. Lastly, the topological features promote a two-stage algorithm: in stage-1 the uncertainty-free fidelity is set to a high threshold, then in stage-2 the robustness measure is minimized while maintaing the threshold. Each stage-2 control update is found by solving a convex optimization problem.

A new framework is formulated to study entanglement dynamics in many-body quantum systems along with an associated geometric description. In this formulation, called the Quantum Correlation Transfer Function (QCTF), the system’s wave function or density matrix is transformed into a new space of complex functions with isolated singularities. Accordingly, entanglement dynamics is encoded in specific residues of the QCTF, and importantly, the explicit evaluation of the system’s time dependence is avoided. Notably, the QCTF formulation allows for various algebraic simplifications and approximations to address the normally encountered complications due to the exponential growth of the many-body Hilbert space with the number of bodies. These simplifications are facilitated through considering the patterns, in lieu of the elements, lying within the system’s state. Consequently, a main finding of this paper is the exterior (Grassmannian) algebraic expression of many-body entanglement as the collective areas of regions in the Hilbert space spanned by pairs of projections of the wave function onto an arbitrary basis. This latter geometric measure is shown to be equivalent to the second-order Renyi entropy. Additionally, the geometric description of the QCTF shows that characterizing features of the reduced density matrix can be related to experimentally observable quantities. The QCTF-based geometric description offers the prospect of theoretically revealing aspects of many-body entanglement, by drawing on the vast scope of methods from geometry.

Results from global sensitivity analysis (GSA) often guide the understanding of complicated input–output systems. Kernel-based GSA methods have recently been proposed for their capability of treating a broad scope of complex systems. In this paper, we develop a new set of kernel GSA tools when only a single set of input–output data is available. Three key advances are made: (1) A new numerical estimator is proposed that demonstrates an empirical improvement over previous procedures. (2) A computational method for generating inner statistical functions from a single data set is presented. (3) A theoretical extension is made to define conditional sensitivity indices, which reveal the degree that the inputs carry shared information about the output when inherent input–input correlations are present. Utilizing these conditional sensitivity indices, a decomposition is derived for the output uncertainty based on what is called the optimal learning sequence of the input variables, which remains consistent when correlations exist between the input variables. While these advances cover a range of GSA subjects, a common single data set numerical solution is provided by a technique known as the conditional mean embedding of distributions. The new methodology is implemented on benchmark systems to demonstrate the provided insights.

Photoexcitation and photodissociation dynamics of the water molecule have been extensively studied both experimentally and theoretically, strongly motivated by atmospheric and biological importance of this system. While most of these studies focused on the dynamics induced by a single vacuum-ultraviolet photon, the same range of excited states can be populated by two-photon absorption. Since the latter process can be efficiently driven by wavelength-tunable femtosecond ultraviolet (UV) sources, it significantly facilitates time-domain measurements. In this work, we explore the dynamics induced by two-photon excitation of water in a femtosecond UV pump / near-infrared (NIR) probe experiment. Here, the NIR probe pulse ionizes the UV-excited neutral molecule, and the time evolution of the system is mapped by measuring the yields and kinetic energy distributions of the resulting ionic fragments as a function of UV-NIR delay. We analyze the wavelength dependence of two-photon excitations in 240-250 nm range and compare the results for H₂O and D₂O molecules.

Physicists revolutionized the scientific world when they invented the laser in 1960. During the next two decades, fruitful interplay occurred between theoreticians and experimentalists seeking progress in laser-selective chemistry. In the Early Era, defined as 1960∼1985, scientists gradually realized the immense complexity of the problem of performing tailored manipulations at the molecular scale. However, their efforts opened the doors to a new, broader scientific field of research called quantum control which developed in the Modern Era, defined as 1985 to the present time. This Perspective aims to show that the roots of quantum control may be linked to endeavors to manipulate chemical reactions with lasers and thus reaches as far back as the invention of the laser in 1960. We will emphasize the role of advancing technology, the prescience in the questions raised by researchers, and the role of interdisciplinary research. The Perspective concludes with an assessment of what was achieved in the Early Era.

Quantum state tomography (QST) is the process of reconstructing the state of a quantum system (mathematically described as a density matrix) through a series of different measurements, which can be solved by learning a parameterized function to translate experimentally measured statistics into physical density matrices. However, the specific structure of quantum measurements for characterizing a quantum state has been neglected in previous work. In this paper, we explore the similarity between highly structured sentences in natural language and intrinsically structured measurements in QST. To fully leverage the intrinsic quantum characteristics involved in QST, we design a quantum-aware transformer (QAT) model to capture the complex relationship between measured frequencies and density matrices. In particular, we query quantum operators in the architecture to facilitate informative representations of quantum data and integrate the Bures distance into the loss function to evaluate quantum state fidelity, thereby enabling the reconstruction of quantum states from measured data with high fidelity. Extensive simulations and experiments (on IBM quantum computers) demonstrate the superiority of the QAT in reconstructing quantum states with favorable robustness against experimental noise.

This Perspective addresses the often observed surprising ease of achieving optimal control of nonlinear phenomena in quantum and classical complex systems. The circumstances involved are wide-ranging, with scenarios including manipulation of atomic scale processes, maximization of chemical and material properties or synthesis yields, Nature’s optimization of species’ populations by natural selection, and directed evolution. Natural evolution will mainly be discussed in terms of laboratory experiments with microorganisms, and the field is also distinct from the other domains where a scientist specifies the goal(s) and oversees the control process. We use the word “control” in reference to all of the available variables, regardless of the circumstance. The empirical observations on the ease of achieving at least good, if not excellent, control in diverse domains of science raise the question of why this occurs despite the generally inherent complexity of the systems in each scenario. The key to addressing the question lies in examining the associated control landscape, which is defined as the optimization objective as a function of the control variables that can be as diverse as the phenomena under consideration. Controls may range from laser pulses, chemical reagents, chemical processing conditions, out to nucleic acids in the genome and more. This Perspective presents a conjecture, based on present findings, that the systematics of readily finding good outcomes from controlled phenomena may be unified through consideration of control landscapes with the same common set of three underlying assumptions─the existence of an optimal solution, the ability for local movement on the landscape, and the availability of sufficient control resources─whose validity needs assessment in each scenario. In practice, many cases permit using myopic gradient-like algorithms while other circumstances utilize algorithms having some elements of stochasticity or introduced noise, depending on whether the landscape is locally smooth or rough. The overarching observation is that only relatively short searches are required despite the common high dimensionality of the available controls in typical scenarios.

We present a simple optical capability for generating spatially resolved chemical concentration maps of mixing fluids using a chemically sensitive dye, 1-hydroxy-3,6,8-pyrenetrisulfonic acid, detected by planar laser induced fluorescence. To demonstrate an application of this capability, we investigate the collision and mixing of a pair of microdroplets in air. The two microdroplets are composed of different fluids, methanol and water, with the dye initially in the methanol droplet. When the droplets collide and mixing process develops, the fluorescence of the dye shifts from blue to green as the solvent environment changes. A series of spectral-temporal images of the collision and subsequent mixing are recorded, from which we extract the distribution of the two intermixing droplet species reflected in the spatially resolved dye spectra. Images reveal material transfer between droplets in both coalescing and non-coalescing droplet collisions.

This textbook chapter (pp 65-92) presents results on enhancing robustness of quantum systems with uncertainties using the sampling-based learning control (SLC) method. In Sect. 4.2, the SLC method is applied to state control of superconducting qubits, robust control of photoassociation of O+H and synchronizing a laser with molecules for charge transfer. Robust control based on SLC and b-GRAPE is presented for generating quantum gates in Sect. 4.3 and SLC of open quantum systems is investigated in Sect. 4.4.

To achieve the dream of useful quantum computation, there are two main thrusts to make improvements: quantum system design and control. Now at the junction of realizing effective quantum error correction, the boundaries of quantum system control become an essential piece of information. Establishing the limits of efficient, scalable, and accurate quantum control can inform the efficacy and choice of different kinds of error correction. The effort of quantum system control, specifically in terms of measurements during calibration, must be sufficiently low to compensate for system parameter drift or fast enough to enable periodic re-calibration. The effectiveness of different control routines can be evaluated using theoretical and numerical studies. While theoretical models help inform on general structures of quantum control landscapes, the controllability, or the complexity of the computational effort, they are often insufficient to represent the real quantum system. Complete system characterization can lead to accurate numerical models representing the entire quantum system but are incredibly cumbersome. Model-free learning control, a laboratory-costly approach, represents the other extreme. These methods tend to be highly laborious and measurement-intensive as systems scale in size. Here, we discuss our insights and perspective on the limits and capabilities of quantum control, the role of theoretical studies, and the methods available for experimental quantum control from a measurement point of view. Finally, we explore the design of quantum control schemes that are as robust as possible to system uncertainties while remaining resource-efficient.

Useful quantum information processors require their control to be robust to the inherent noise and system uncertainties. We propose an approach to design robust quantum operations via a two-stage algorithm. We first improve the control fidelities close to optimality before optimizing for robustness in system uncertainties. The two-stage approach leverages the control landscape topology to enable a computationally efficient method. The algorithm aims to maintain high control fidelities while increasing the robustness. To verify the utility and efficacy of the theoretically and numerically developed approach, we test it on a multi-quit NMR system. We experimentally extract the maximally possible fidelity of single- and multi-qubit gates designed by the algorithm. The algorithm designs the control instances using incomplete knowledge of the quantum system and upper bounds of the system uncertainties, such as the coupling to environmental two-level systems. The algorithm successfully compensates for unknown system couplings and outperforms standard optimal control algorithms. The numerically and experimentally implemented algorithm enables the design of quantum logic gates under realistic circumstances in which only limited knowledge of the accurate and complete system Hamiltonian is available. The proposed robustness approach eases the experimental effort to characterize the quantum system meticulously and enables efficient and high-fidelity quantum logic gate design under these uncertainties.

Robust control over the dynamics of a quantum system is indispensable for realizing useful quantum information processors. Here, we utilize the classical method of averaging to realize an approach for robustness analysis and synthesis of controls for quantum logic gates. By separating the system Hamiltonian into a nominal (uncertainty-free) and interaction (error) Hamiltonian, the robustness measure is defined as the size of the average of the interaction Hamiltonian. The result is a multi-criterion optimization competing uncertainty-free fidelity with the robustness measure. Exploiting the topology of the control landscape at high fidelity (as determined by the null space of the nominal fidelity Hessian), we arrive at a two-stage optimization algorithm: first, improve the nominal fidelity until sufficiently high, and then reduce the robustness measure while maintaining high nominal fidelity. An optimal solution is obtained by approximating the nominal fidelity and robustness measure as quadratics in the control increments. The approximation enables the control increments at each iteration to be solved by a convex optimization. For each iteration, the goal is to keep the nominal fidelity high while reducing the robustness measure. This approach reduces the experimental quantum-system-characterization effort, enabling robust and high-fidelity quantum logic gate design.

In the context of the Born approximation, i.e., neglecting system-environment correlations in the composite system state and assuming a time-independent environment state, we develop the dynamics of controlled, time-dependent quantum systems in the presence of irreversible environment-induced decoherence. We show that in the interaction picture, these dynamics separate the time evolution of the system into a sequence of unitary and nonunitary operations exactly. For state-dependent objectives, quantum optimal control is applied to the corresponding dynamical equations, and using a composite system model of interacting spins as an illustrative example, we find that simple and versatile controls are able to discover and use decoherence-free subspaces (when they exist) to optimize the state objectives. Results from several numerical control simulations will be presented and discussed. SNL is managed and operated by NTESS under DOE NNSA contract DE-NA0003525. SAND2022-14340 A.