Efficient measurement of quantum dynamics via compressive sensing

The resources required to characterize the dynamics of engineered quantum systems--such as quantum computers and quantum sensors--grow exponentially with system size. Here we adapt techniques from compressive sensing to exponentially reduce the experimental configurations required for quantum process tomography. Our method is applicable to processes that are nearly sparse in a certain basis and can be implemented using only single-body preparations and measurements. We perform efficient, high-fidelity estimation of process matrices of a photonic two-qubit logic gate. The database is obtained under various decoherence strengths. Our technique is both accurate and noise robust, thus removing a key roadblock to the development and scaling of quantum technologies.     

Hamiltonian Reduction of Quantum Systems Controlled by Pulses

We explores Hamiltonian reduction in pulse-controlled finite-dimensional quantum systems with near-degenerate eigenstates. A quantum system with a non-degenerate ground state and several near-degenerate excited states is controlled by a short pulse, and the objective is to maximize the collective population on all excited states when we treat all of them as one level. Two cases of the systems are shown to be equivalent to effective two-level systems. When the pulse is weak, simple relations between the original systems and the reduced systems are obtained. When the pulse is strong, these relations are still available for pulseswith only one frequency under the first-order approximation.     

Rapid synthesis of an electron-deficient t-BuPHOX ligand: cross-coupling of aryl bromides with secondary phosphine oxides

Herein an efficient and direct copper-catalyzed coupling of oxazoline-containing aryl bromides with electron-deficient secondary phosphine oxides is reported. The resulting tertiary phosphine oxides can be reduced to prepare a range of PHOX ligands. The presented strategy is a useful alternative to known methods for constructing PHOX derivatives.     

High dimensional model representation constructed by support vector regression. I. Independent variables with known probability distributions

High dimensional model representation (HDMR) is a general set of quantitative model assessment and analysis tools for capturing high dimensional input-output system behavior. In practice, the HDMR component functions are each approximated by an appropriate basis function expansion. This procedure often requires many input-output samples which can restrict the treatment of high dimensional systems. In order to address this problem we introduce svr-based HDMR to efficiently and effectively construct the HDMR expansion by support vector regression (SVR) for a function \(f(\mathbf{x})\). In this paper the results for independent variables sampled over known probability distributions are reported. The theoretical foundation of the new approach relies on the kernel used in SVR itself being an HDMR expansion (referred to as the HDMR kernel ), i.e., an ANOVA kernel whose component kernels are mutually orthogonal and all non-constant component kernels have zero expectation. Several HDMR kernels are constructed as illustrations. While preserving the characteristic properties of HDMR, the svr-based HDMR method enables efficient construction of high dimensional models with satisfactory prediction accuracy from a modest number of samples, which also permits accurate computation of the sensitivity indices. A genetic algorithm is employed to optimally determine all the parameters of the component HDMR kernels and in SVR. The svr-based HDMR introduces a new route to advance HDMR algorithms. Two examples are used to illustrate the capability of the method.     

Global analytical potential energy surfaces for HO2(X2A") based on high-level ab initio calculations

Two global analytical potential energy surfaces for the HO2(X2A") system have been developed by fitting approximately 15,000 ab initio points at the icMRCI+Qaug-cc-pVQZ level of theory, using the reproducing kernel Hilbert space method. One analytical potential is designed to give a very accurate representation of the low energy range that determines the vibrational spectrum, while the other attempts to provide a fast and uniformly accurate potential function for reaction dynamics. The quality of the fitted potential functions is confirmed by good agreement of the (J=0) HO2 vibrational spectrum and (J=0) quantum reaction probability for the H+O2(ji=0,nui=0) reaction with those obtained using the spline fitted potential. Quasiclassical trajectory calculations carried out on the new potential energy surface provided the reaction probability with a zero impact parameter (b=0), which is in reasonably good agreement with the J=0 quantum results.     

Photonic reagent control of dynamically homologous quantum systems

The general objective of quantum control is the manipulation of atomic scale physical and chemical phenomena through the application of external control fields. These tailored fields, or photonic reagents, exhibit systematic properties analogous to those of ordinary laboratory reagents. This analogous behavior is explored further here by considering the controlled response of a family of homologous quantum systems to a single common photonic reagent. A level set of dynamically homologous quantum systems is defined as the family that produces the same value(s) for a target physical observable(s) when controlled by a common photonic reagent. This paper investigates the scope of homologous quantum system control using the level set exploration technique (L-SET). L-SET enables the identification of continuous families of dynamically homologous quantum systems. Each quantum system is specified by a point in a hypercube whose edges are labeled by Hamiltonian matrix elements. Numerical examples are presented with simple finite level systems to illustrate the L-SET concepts. Both connected and disconnected families of dynamically homologous systems are shown to exist.     

Observation-assisted optimal control of quantum dynamics

This paper explores the utility of instantaneous and continuous observations in the optimal control of quantum dynamics. Simulations of the processes are performed on several multilevel quantum systems with the goal of population transfer. Optimal control fields are shown to be capable of cooperating or fighting with observations to achieve a good yield, and the nature of the observations may be optimized to more effectively control the quantum dynamics. Quantum observations also can break dynamical symmetries to increase the controllability of a quantum system. The quantum Zeno and anti-Zeno effects induced by observations are the key operating principles in these processes. The results indicate that quantum observations can be effective tools in the control of quantum dynamics.     

Optimal coherent control of coherent anti-Stokes Raman scattering: signal enhancement and background elimination

The ability to enhance resonant signals and eliminate the non-resonant background is analyzed for coherent anti-Stokes Raman scattering (CARS). The analysis is done at a specific frequency as well as for broadband excitation using femtosecond pulse-shaping techniques. An appropriate objective functional is employed to balance resonant signal enhancement against non-resonant background suppression. Optimal enhancement of the signal and minimization of the background can be achieved by shaping the probe pulse alone while keeping the pump and Stokes pulses unshaped. In some cases analytical forms for the probe pulse can be found, and numerical simulations are carried out for other circumstances. It is found that a good approximate optimal solution for resonant signal enhancement in two-pulse CARS is a superposition of linear and arctangent-type phases for the pump. The well-known probe delay method is shown to be a quasi-optimal scheme for broadband background suppression. The results should provide a basis to improve the performance of CARS spectroscopy and microscopy.     

A scalable algorithm for molecular property estimation in high dimensional scaffold-based libraries

An algorithm is presented for the estimation of molecular properties over a library built around a scaffold, which has N sites for functionalization with M _i moieties at the ith scaffold site, corresponding to a library of ${\prod_{i=1}^N M_i}$ molecules. The algorithm relies on a series of operations involving (i) synthesis and property measurement of a minimal number of T randomly sampled members of the library, (ii) expression of the observed property in terms of a high-dimensional model representation (HDMR) of the moiety → property map, (iii) optimization of the ordered sequence of moieties on each site to regularize the HDMR map and (iv) interpolation using the map to estimate the properties of as yet unsynthesized compounds. The set of operations is performed iteratively aiming to reach convergence of the predictive HDMR map with as few synthesized samples as possible. Through simulation, the number T of required random molecular samples is shown to scale very favorably with ${T < < \prod^N_{i=1} M_i}$ for cases up to N = 20 and M _i = 20. For example, high estimation quality was attained for simulated libraries with T ~ 5,000 sampled compounds for a library of 20¹² members and T ~ 12,500 sampled compounds for a library of 20²⁰ members. The algorithm is based on the assumption that a systematic pattern exists in the moiety → property map provided that the moieties are optimally ordered on the scaffold sites within the context of HDMR. The overall procedure is referred to as the substituent reordering HDMR algorithm (SR-HDMR). The technique was also successfully tested with laboratory data for estimating C¹³-NMR shifts in a tri-substituted benzene library and for lac operon repression binding.     

Enhancing the efficiency of directed evolution in focused enzyme libraries by the adaptive substituent reordering algorithm

Directed evolution is a broadly successful strategy for protein engineering in the quest to enhance the stereoselectivity, activity, and thermostability of enzymes. To increase the efficiency of directed evolution based on iterative saturation mutagenesis, the adaptive substituent reordering algorithm (ASRA) is introduced here as an alternative to traditional quantitative structure-activity relationship (QSAR) methods for identifying potential protein mutants with desired properties from minimal sampling of focused libraries. The operation of ASRA depends on identifying the underlying regularity of the protein property landscape, allowing it to make predictions without explicit knowledge of the structure-property relationships. In a proof-of-principle study, ASRA identified all or most of the best enantioselective mutants among the synthesized epoxide hydrolase from Aspergillus niger, in the absence of peptide seeds with high E-values. ASRA even revealed a laboratory error from irregularities of the reordered E-value landscape alone.