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A method for encoding a multiqubit system into the quantized motional states of ion string in an anharmonic linear trap is proposed. Control over this system is achieved by applying oscillatory electric fields (rf) shaped optimally for desired state-to-state transitions. Anharmonicity of the vibrational spectrum of the system plays a key role in this approach to the control and quantum computation, since it allows resolving different state-to-state transitions and addressing them selectively. The anharmonic trap architecture proposed earlier [ Phys. Rev. A 83 022305 (2011) ] is explored here and the optimal control theory is used to derive pulses for a set of universal quantum gates. An accurate choice of pulse parameters allows deriving gates that are both accurate and simple. A practical realization of this approach seems to be within the reach of today's technology. [ABSTRACT FROM AUTHOR]

Anharmonicity of the quantized motional states of ions in a Paul trap can be utilized to address the state-to-state transitions selectively and control the motional modes of trapped ions coherently and adiabatically [ Zhao and Babikov Phys. Rev. A 77 012338 (2008) ]. In this paper we study two sources of the vibrational anharmonicity in the ion traps: the intrinsic Coulomb anharmonicity due to ion-ion interactions and the external anharmonicity of the trapping potential. An accurate numerical approach is used to compute energies and wave functions of vibrational eigenstates. The magnitude of the Coulomb anharmonicity is determined and shown to be insufficient for successful control. In contrast, anharmonicity of the trapping potential allows one to control the motion of ions very efficiently using the time-varying electric fields. Optimal control theory is used to derive the control pulses. One ion in a slightly anharmonic trap can be easily controlled. In the two- and three-ion systems the symmetric stretching mode is dark and cannot be controlled at all. The other two normal modes of the three-ion system can be controlled and used, for example, to encode a two-qubit system into the motional states of ions. A trap architecture that allows the necessary amount of vibrational anharmonicity to be achieved is proposed. [ABSTRACT FROM AUTHOR]

A program named MQCT is developed for calculations of rotationally and vibrationally inelastic scattering of molecules using the mixed quantum/classical theory approach. Calculations of collisions between two general asymmetric top rotors are now possible, which is a feature unavailable in other existing codes. Vibrational states of diatomic molecules can also be included in the basis set expansion, to carry out calculations of ro-vibrational excitation and quenching. Minimal input for the code assumes several defaults and is very simple, easy to set-up and run by non-experts. Multiple options, available for expert calculations, are listed in the Supplemental Information. The code is parallel and takes advantage of intrinsic massive parallelism of the mixed quantum/classical approach. A Monte-Carlo sampling procedure, implemented as option in the code, enables calculations for complicated systems with many internal states and large number of partial scattering waves. The coupled-states approximation is also implemented as an option. Integral and differential cross sections can be computed for the elastic channel. Rotational symmetry of each molecule, as well as permutation symmetry of two collision partners, are implemented. Potential energy surfaces for H 2 O + He, H 2 O + H 2 , and H 2 O + H 2 O are included in the code. Example input files are also provided for these systems. Program title: MQCT Program files doi: http://dx.doi.org/10.17632/sg36r35njz.1 Licensing provisions: GNU GPL v3.0 Programming language: FORTRAN Supplementary material: MQCT user guide Nature of problem: Calculations of rotationally and vibrationally inelastic scattering of two molecules, with possible applications in astrophysics and atmospheric chemistry. Solution method: Mixed quantum/classical theory (MQCT) approach Additional comments: This code can be used to simulate a collision of two asymmetric top rotors, such as H 2 O + H 2 O. [ABSTRACT FROM AUTHOR]

This is a revised and updated version of the package MQCT. The package includes routines for the calculations of ro-vibrational state-to-state transition cross sections for molecule + molecule collisions, using the mixed quantum/classical theory approach. One important addition to the package is an efficient and accurate adiabatic-trajectory approximation method (AT-MQCT), which enables calculations for larger and more complex molecules. An efficient parallel IO is implemented for state-to-state transition matrix, which now permits to handle very large matrixes, but also helps to truncate these matrixes by neglecting insignificant matrix elements and to balance the load on different CPUs during the matrix calculations and during the trajectory propagation. A stable recursive approach is added for computation of Wigner 3 j -symbols, which expands the range of rotational states of molecules up to j ∼ 100. Examples of input files are provided for all ten system types covered by the package, along with updated user manual. Program title: MQCT 2024 CPC Library link to program files: https://doi.org/10.17632/sg36r35njz.2 Developer's repository link: https://github.com/MarquetteQuantum/MQCT Code Ocean capsule: https://codeocean.com/capsule/1260072/tree/v1 Licensing provisions: GNU GPL v3.0 Programming language: FORTRAN Journal reference of previous version: Comput. Phys. Commun. 252 (2020) 107155 Does the new version supersede the previous version?: Yes Reasons for the new version: 1) Recently, we developed and tested the adiabatic-trajectory method [1–3] within MQCT framework, which appears to be both efficient and accurate, and is likely to become a "workhorse" for inelastic scattering calculations in molecule + molecule systems. In the new version of the package this method is made available as an option, AT-MQCT. 2) Since MQCT trajectory calculations became more affordable with AT-MQCT, we started doing calculations with larger and larger rotational basis sets and quickly encountered several new problems. The major one was an extremely slow serial IO of the state-to-state transition matrix to a single file, which is now replaced by a parallel IO to multiple files written to a separate directory. Very large matrixes (up to 1010 non-zero matrix elements) are now handled efficiently. 3) Another problem was an incorrect calculation of Wigner 3 j -symbols for the rotational states around j ∼ 40 and above. In the revised version a new stable subroutine is employed that uses a recursive method and works properly at least up to j = 100. 4) Several "bugs" were caught and fixed, with one major in the Monte-Carlo sampling of MQCT trajectories. Now users can add a batch of new trajectories to the previously sampled batch. In addition, users can monitor the convergence of Monte-Carlo sampling in detail. These options work for all levels of theory, including AT-MQCT. Several errors were found in the equations for calculations of state-to-state transition matrix using the expansion of potential energy surface, and in symmetrization of matrix elements for the case of identical collision partners. All these have been corrected. Summary of revisions: Several technical revisions concern the treatment of diatomic molecules in the code: A bug was found and fixed in the PES interface that converts the units of vibrational coordinate (the diatomic bond distance). Now the PES can be expressed in either Angstrom or Bohr, as specified in the input file. Integration of matrix elements over the vibrational coordinate is modified to use an equidistant grid by default (Gauss-Legendre method is still available as option). And the same for integration over Euler angles α and γ (for all system types). Integration over β uses Gauss-Legendre quadrature only. The format of ro-vibrational wavefunctions pre-computed externally and supplied as input is made more intuitive, as described in the manual. Finally, a new method for the sampling of orbital quantum number ℓ is implemented, which skips some values of ℓ and obtains results by interpolation of the data at the retained values of ℓ (for all system types, as described in the manual). Last version of the code is always available at https://github.com/MarquetteQuantum/MQCT. Supplementary material: Updated and expanded MQCT user guide Nature of problem: Calculations of rotationally and vibrationally inelastic scattering of two molecules, with possible applications in astrophysics and atmospheric chemistry Solution method: Mixed quantum/classical theory (MQCT) approach [1] B. Mandal, A. Semenov and D. Babikov, J. Phys. Chem. A 124 (2020) 9877-9888 [2] B. Mandal, C. Joy, A. Semenov and D. Babikov, ACS Earth Space Chem. 6 (2022) 521-529 [3] B. Mandal, C. Joy, D. Bostan, A. Eng and D. Babikov, J. Phys. Chem. Lett. 14 (2023) 817–824. [ABSTRACT FROM AUTHOR]

We present SpectrumSDT – a program for calculations of energies and lifetimes of bound rotational-vibrational states below and scattering resonances above the dissociation threshold on a global potential energy surface of a triatomic system, which may include stable molecules, weekly-bound van-der-Waals complexes, and unbound atom + diatom scattering systems. Large-amplitude vibrational motion is treated explicitly using hyper-spherical coordinates. Three options for the rotational-vibrational interaction are supported: uncoupled (symmetric top rotor), partially coupled (to include interaction between several nearest states only) and full-coupled (vibrating asymmetric-top rotor). In addition to energies and lifetimes, SpectrumSDT is able to integrate ro-vibrational wave functions over the user-defined regions of potential energy surface, which helps to classify these states. In this release of the code, SpectrumSDT is limited to ABA-type molecules with wave functions that do not extend into the regions near Eckart singularities. Program title: SpectrumSDT CPC Library link to program files: https://doi.org/10.17632/9gftxjs4yk.1 Developer's repository link: https://github.com/IgorGayday/SpectrumSDT Licensing provisions: GNU General Public License 3 (GPL) Programming language: Fortran Nature of problem: Calculations of energies and lifetimes of bound rotational-vibrational states below and scattering resonances above the dissociation threshold on a global potential energy surface of a triatomic system, which may include stable molecules, weekly-bound van-der-Waals complexes, and unbound atom + diatom scattering systems. Solution method: A Hamiltonian matrix is built in APH coordinates using an optimal 2D basis set, adjusted for a given problem. A complex absorbing potential (CAP) is added to define a boundary condition for calculation of scattering resonances above the dissociation threshold. The eigenstates of the Hamiltonain matrix are found using a state-of-the-art iterative eigensolver. Restrictions: The present version is restricted to ABA-molecules and wave functions that do not extend into linear and equilateral triangle configurations. Additional comments including restriction and unusual features: Probabilities and lifetimes of the wave functions can be calculated in user-defined regions on the PES, which allows to analyze their localization properties (i.e. automatic isotopomer assignment) and obtain channel-specific lifetimes for scattering resonances. [ABSTRACT FROM AUTHOR]